MathDial: A Dialogue Tutoring Dataset with Rich Pedagogical Properties Grounded in Math Reasoning Problems
Authors: Jakub Macina
Nico Daheim
Sankalan Pal Chowdhury
Tanmay Sinha
Manu Kapur
Iryna Gurevych
Mrinmaya Sachan
Venue: EMNLP 2023 Findings (2023)
Keywords: dialogue
dataset
collection
response generation
natural language generation
math
reasoning
tutoring

Abstract: While automatic dialogue tutors hold great potential in making education personalized and more accessible, research on such systems has been hampered by a lack of sufficiently large and high-quality datasets. Collecting such datasets remains challenging, as recording tutoring sessions raises privacy concerns and crowdsourcing leads to insufficient data quality. To address this, we propose a framework to generate such dialogues by pairing human teachers with a Large Language Model (LLM) prompted to represent common student errors.
We describe how we use this framework to collect MathDial, a dataset of 3k one-to-one teacher-student tutoring dialogues grounded in multi-step math reasoning problems. While models like GPT-3 are good problem solvers, they fail at tutoring because they generate factually incorrect feedback or are prone to revealing solutions to students too early. To overcome this, we let teachers provide learning opportunities to students by guiding them using various scaffolding questions according to a taxonomy of teacher moves. We demonstrate MathDial and its extensive annotations can be used to finetune models to be more effective tutors (and not just solvers). We confirm this by automatic and human evaluation, notably in an interactive setting that measures the trade-off between student solving success and telling solutions. The dataset is released publicly.

MATHDIAL: A Dialogue Tutoring Dataset with Rich Pedagogical Properties Grounded in Math Reasoning Problems
Jakub Macina
Nico Daheim Manu Kapur
Sankalan Pal Chowdhury'
Tanmay Sinha
Iryna Gurevych
Mrinmaya Sachan
ETH AI Center Department of Computer Science, ETH Zurich
Ubiquitous Knowledge Processing Lab (UKP Lab), Department of Computer Science and Hessian Center for Al (hessian.Al),, TU Darmstadt
National Institute of Education, Nanyang Technological University
Professorship for Learning Sciences and Higher Education, ETH Zurich Dakub.macinaa ethz.ch ch
Abstract
Problem Statemant:
Jamess whiles S-page letter to dffireent friands twios waek, How many pages doas while a year?
While automatic dialogue tutors hold great po- tential in making education personalized and more accessible, research on such systems has been hampered by a lack of sufficiently large and high-quality datasets. Collecting such datasets remains challenging, as recording tutoring sessions raises privacy concerns and crowdsourcing leads to insufficient data qual- ity. To address this, propose framework to generate such dialogues by pairing human teachers with Large Language Model (L.LM) prompted to represent common student errors. We describe how we use this framework to col- lect | MATUDIAL, dataset of 3k one-to-one leacher-student tutoring dialogues grounded in multi-step math reasoning problems. While models like GPT-3 good problem solvers, they fail at tutoring because they generate factu- ally incorrect feedback or are prone to revealing solutions students too early. To overcome this, we let teachers provide learning opportuni- ties students by guiding them using various scaffolding questions according to a taxonomy of teacher moves. We demonstrate MATH- DIAL and its extensive annotations can be used to finetune models to be more effective tutors (and not just solvers). We confirm this by au- tomatic and human evaluation, notably in an interactive setting that measures the trade-off between student solving success and telling so- lutions. The dataset is released publicly.
3-2-5 pager
Correct Answer:
pages every
That
12'5 pages year.
2 2 = 621
Student Solution Confusion:
Calculate the number of letters writen week: 2 letters - Caitubele the number latters with = 312 pagess par
pages per waek 52 woekor
2x 52 312
Teacker: Hi Winn could you plearee work me throughh your solution? Shadest
Sunel fiss tall itulltedd the rumber of interns withien in work whicc is pageo 2 letters 6 pages per week. Then imutiplled that number by 52 woeks to gel the number pages writee a year, wh is 312 pages per year.
Teoshor:
That sounds correct. Breat work!
Factually incerreet
loseher
You calculatad the number of pages wittian per weak correctly Howwver weet. pages per year Looking sulitins
james
calculation is: pages
CharoPT
Tooeber
There la ono important inportantsaywerrd thare: tiice. What does it to7
Figure I: Current models achieve high accuracy in solv- ing MWPs but struggle with teaching since they often give incorrect feedback reveal directly the solution too early. E MATHDIAL mitigates this using scaffold- ing questions and grounding annotations.
et al., 2023). However, the progress of scaling them is considerably hindered by a lack of high- quality datasets, which actually provide students with space for exploration by scaffolding their learning (Tack and Piech, 2022; Macina et al., 2023). The current datasets are frequently marred with issues like low pedagogical quality, are too small, or focus on noisy classroom settings. While recording tutoring sessions might be a scalable al- ternative, it bears strong privacy concerns (Dem- szky and Hill, 2023). On the other hand, crowd- sourcing dialogues is costly, requires synchronizing annotators, and can lead insufficient quality due to poor annotator training (Stasaski et al., 2020).
/ttps: http://hhhhhb...mmmtttt//l////aa
1 Introduction
At the same time, recent advancements in Large Language Models (LLMs) have enabled signifi- cant improvements in generative dialogue systems (Budzianowski and Vulić, 2019; Thoppilan et al., 2022; Xu et al., 2023) and simultaneously shown
Dialogue tutoring systems have demonstrated sig- nificant potential in augmenting learning outcomes across various domains (Woliny et al., 2021; Ji
"Equal contribution.

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Dutaset
Domain
Dialogues
Dialogic
Settings
Grounding Information
Teacher Moves
Bigram Entropy
Upiake
Aug. words
Pairs
per utterance
MATHDIAL (ours)
Math
2661
14 197
1:1 semi-syylheiie
confusion, unswers
4
3,51
0.83
17.3
CIMA (Slasaski al., 2020)
Language
391
315
1:1 role-playing
image, answer
5
3.12
0.83
13.0
TSCC (Caines al.,, 2020)
Language
102
2013
1:1 rutering
5
3.55
0.66
12.3
Moles (Suresh er al., 2022)
Science
567
9 280
classmoo
X
10
2,93
0.67
9.6
(Demszky
2023)
Math
classroom
3,57
Table I:
Comparison of dialogue tutoring datasets. larger while keeping high diversity and utterance lengths.
MATHDIAL grounding annotations, and is significantly
great success in reasoning over educational do- mains, such as math problems (Cobbe et al., 2021; Wei et al., 2022; Wang et al., 2023b; OpenAI, 2023). However, this has not yet translated to improve- ments in dialogue tutoring systems, showcased by the lack of pedagogical understanding and factu- ally incorrect behaviour of GPT-3 (Tack and Picch, 2022) and open-source LLMs (Macina et al., 2023). Figure shows examples of generations that reveal information to students too early and misunder- stand their solutions. This is also confirmed in our human evaluation: when asked ChatGPT to tutor a student teacher, it directly reveals the solution 66% % of times and provides incorrect feedback 59 % of times (cf. Section 6.3).
faithful to the teaching material than prompting larger LLMs (Section 6.3). Moreover, we propose an interactive, end-to-end tutoring simulation be- tween a teacher and student model where we mea- trade-off between student solving success and teachers directly revealing answers in (Sec- tion 6.4). Open-source LLMs that are finetuned on our dataset achieve similar student-solving success as ChatGPT while telling solutions less often. Finally, we highlight open challenges on this dataset, such as generalization to new problems.
2 Background & Related Work
2.1 Dialogue Datasets & Collection Methodologies
To address these issues, we collect and present a dialogue tutoring dataset called MATHDIAL. The dataset has rich tutoring quality which we mea- sure by equitable tutoring (Tamner, 2013): provid- ing opportunities for the student to learn, think and explore potential solutions. For this, we take inspi- ration from human tutoring strategies (Nye et al., 2014) and active learning approaches in classrooms (Freeman et al., 2014) 4) that show a positive impact on student learning gains.
Research on task-oriented dialogue systems has mainly focused on eustomer service, for instance, restaurant reservations (Henderson et al., 2014; Gašic et al., 2014). Notably, Wen et al. (2017) col- lect such dialogues with the Wizard-of-Oz (WoZ) paradigm (Kelley, 1984), where crowdworkers are connected to roleplay interlocutors. One plays the user who interacts with the system, and the other roleplays the system and is often exclusively given access domain knowledge. WoZ has been used to collect many popular datasets, such as Multi- WoZ (Budzianowski et al., 2018) and extensions (Kim et al., 2020; Zhu et al., 2020), Taskmaster (Byrne et al., 2019), and open-domain datascts like Wikipedia (Dinan et al.. 2019). Other collection methods include crowdworkers filling dialogue outlines (Shah et al., 2018; 8;; Rastogi al., 2020: Majewska et al., 2023), or scraping from the web (Li et al., 2017; Dziri et al., 2019).
We collect our dataset using a novel data collec- tion approach. This approach pairs human teach- ers with an LLM that simulates students and their errors, which the same teachers rate as represen- tative of real students in our study. +i MATH- DIAL grounded in math word problems and stu- dent confusions and therefore provides a challeng- ing testbed for creating faithful and equitable dia- logue tutoring models that can reason over complex data. Figure shows one dialogue from MATH- DIAL., where a teacher scaffolds student learning by asking an interactive scaffolding question in- stead of leaking the solution.
Multiple works have shown shortcomings in using non-expert crowdworkers. For instance, document--roundde corpora often contain hallu- cinations in ground-truth data (Dziri al., 2022), and task-oriented corpora tend suffer from anno- tation errors and low lexical diversity (Casanueva et al., 2022). More closely related to this work, cur- rent tutoring corpora lack sufficient tutoring quality
We benchmark various models on the task of gen- erating tutor responses for TI MATHDIAL, using both finetuning and prompting. We find that fine- tuning smaller open-source LLMs on our dataset can make them significantly more equitable and

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1. Student confusion selection using self-consistency sampling from GSM8k Solve step-by-step:
2. Teacher scaffolds student problem-solving
Jamen writes a 3-page letter to 2 different friends twice a week How many pogez does he write year?...
Human Teacher
LLM Student
Your solution: James writes 3x2
He writes cach friend 3*2-6 pages week. So he writes 6*2=12 pages every week. That means he writes 12*52-624 pages year. A:
Persona: Winnie thinks her answer correct
n=
Hi Winnic, could you please walk me through your solution?
(generic)
624
Sure! first calculated the number of letters written in week, which 3 pages
James writes x pages week. In year, there are 52 weeks, James writes 6xx
1ー1
pages per week.
=2 312 pages 312
There is also one important keyword there: twice. What does it refer to?
(focus)
He writes x x 12 pages a year.
n=7
1:
Correctly solved by student?
Correct
Incorrect
incorrect reasoning paths are selected
Overview of the data collection pipeline: First, student confusions are oversampled from an L.M and sorted by frequency. Then, human teacher synchronously interacts with a student simulated by an LLM that is instructed with student profile and incorrect solution.
Figure 2:
(Tack and Piech, 2022; Macina et al., 2023).
corpora are publicly available to our knowledge: CIMA (Stasaski et al., 2020), TSCC (Caines et al., 2020), TalkMoves (Suresh et al., 2022), and NCTE (Demszky and Hill, 2023). All of them suffer from several limitations, such as missing grounding in- formation (TSCC, TalkMoves, NCTE), low tutor- ing quality (CIMA), small dataset sizes (all), focus noisy classroom scenarios (see Table 1).
MATHDIAL mitigates these issues by adapt- ing the WoZ paradigm to using human teachers as experts in collaboration with an LLM.
2.2 Dialogue Tutoring Corpora & Teacher Moves
Thcoretical and empirical studies have shown the importance of questioning in human learning (Roscoe and Chi, 2008; Shahriar and Matsuda, 2021; Shridhar et al., 2022). Therefore, prior re- search has explored which types of questions in tu- toring conversations improve student learning. Nye al. (2014), for instance, show the effectiveness of deep reasoning questions, and (Howe et al., 2019) find that elaboration and challenging previous contributions can benefit student learning. This has led to series of human-authored dialogue tu- toring systems, like AutoTutor (Nye et al., 2014), which guide students in problem-solving using nat- ural language explanations. Assisting students to succeed in complex tasks commonly referred as scaffolding (Reiser, 2004; Anghileri, 2006). More recently, several rule-based dialogue systems with predefined goals have been proposed (Ruan et al., 2019; Winkler et al.. 2020; Cai et al., (021). but scaling them requires extensive human authoring and quickly becomes complex. As consequence, building effective automatic tutors at scale remains open problem.
2.3 Synthetic Dialogue Data Creation
LLMs have recently found their way synthetic di- alogue dataset generators due to their increasingly human-like behaviour. Both methods using fine- tuning (Dai et al., 2022) and prompting (Kim et al., 2022: Chen et al., 2023) haven been proposed. The human-like behaviour also manifests in them show- ing similar biases in logical reasoning as humans (Dasgupta et al., 2022; Binz and Schulz, 2023), and can be comparable to gold- hold-human annotations for generation tasks (Ziems et al., 2023). Consequently, they have been used simulate students for teacher training (Markel et al., 2023), suggesting that one might also rely upon them to create meaningful tutors. However, Tack and Piech (2022); Macina et al. (2023) show that they can not yet perform well as teachers out-of-the to--the-ooxo, because they of- ten incorrectly assess student solutions and reveal answers quickly.
3 MATHDIAL Collection Pipeline
While data-driven approaches seem like promising direction (Macina et al., 2023; Wang et al., 2023a), only a limited number of tutoring
This section introduces framework for collecting high-quality tutoring conversations, highlighted Figure 2. The core idea behind it is to connect

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Calegory
Intent
Example
Scek Strategy
So what should you do next?
Focus
Guiding Student Focus
Can you calculate...
Recall Relevant Information
Can you reread the question and tell me what is.
Asking for Explanation
Why do you think need to add these numbers?
Seeking Self Correction
Are you sure you need add here?
Probing
Perturbing the Question
How would things change they had ... items instead?
Seeking World Knowledge
How do you calculate the perimeter of square?
Revealing Strategy
You need to add
get your
Telling
Revealing Answer
No, had ... items.
Hi .i... how are you doing with the word problem?
Greeting/Fairvell
Good Job! Is there anything else I can help with?
Generie
General inquiry
Can you go walk me through your solution?
Table 2: Teacher moves with examples of utterances and their intents from the MATHDIAL dataset.
an expert annotator, who roleplays a teacher, with an LLM that simulates the student." | We use this methodology to collect dialogues based on GSM8k (Cobbe et al., 2021), a diverse collection of grade school multi-step math word problems (MWPs).
step-by-step solution, the exact step that led stu- dent confusion, and annotations indicating if it was resolved over the course the dialogue. Step- by-step and student solutions are also provided as equations.
First, we estimate student confusion for given MWP by using temperature sampling to obtain di- verse solutions from an LLM. We then select the most frequent incorrect solution. Therefore, each tutoring dialogue deals with the solution of exactly one MWP and one confusion. As a next step, we pair a human teacher with the LLM to create a dia- logue that should resolve the confusion. We ground the LLM in one of six student profiles. These stu- dent profiles consist of common misconceptions of students learning algebra, such struggling to recognize the problem type, and are taken from Booth et (2017). detailed description of these profiles is found in Section C.
3.1 Teacher Selection
We recruit professionals with teaching experience through Prolific?. We only select teachers who have completed at least 500 submissions and achieved a 100% completion rate. Annotators read guidelines for the task in an initial training phase (cf. Section D.3) and then complete test example con- versation to assess their understanding of the task. We only select annotators with 100% test scores for further rounds of data collection, similar to Zhang et al. (2023). We employ 91 expert annotators, which 71 identify as female and 18 as male. The majority of annotators are nationals of the UK, fol- lowed by the USA, Canada, Australia, India, and Germany, with median age of 39 years.
The teacher has access to the MWP and its cor- rect step-by-step solution, as well as the initial stu- dent confusion (cf. Figure 7). Then, the teacher is tasked guide the student to solve the problem by employing sequence of scaffolding moves, which we refer to as a teaching strategy. The teachers themselves can use their expertise determine the strategy but are required to select the current move before writing a response, as we have found this to lead to more diverse pedagogical patterns. We describe these moves in Section 3.4. The dialogue ends when the teacher marks the problem as solved certain time limit is reached.
3.2 Problem & Confusion Selection
We employ an LLM to generate plausible stu- dent confusions and base the dialogues on them. We pick the most frequent incorrect solution sam- pled from ChatGPT (gpt-3.5-turbo) (Ouyang et al., 2022) using chain-of-thought prompting. To be precise, we first temperature sampling ob- tain N 50 reasoning paths for every MWP in GSM8k, with T 0.7 and no top-k truncation Wang et al. (2023b). Then, we group incorrect so- lutions according to their final numeric answer and pick one from the set with the largest cardinality. More details can be found in Appendix B. As we will show in Section 4.1. teachers think that the
In addition to the collected dialogues, we obtain metadata that future work can explore for build- ing more effective tutor models. In particular, for each dialogue MATHDIAL contiiin the MWP,
II contrast, in WoZ. two users are connected, with one simulating a system.
chttps://wwwr http://wwwwwwlliiccco

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majority of sampled confusions are plausible and could also have been made by real student.
is similar to NCTE and TSCC which consist of transcripts of classroom and one-to-one tutoring sessions, respectively. This supports the obser- vation that expert annotators tend to create more diverse utterances than untrained crowdworkers (Casanueva et al., 2022), and also that LLMs can be used to generate diverse tutoring dialogues. Finally, measure the Uptake (Demszky al., 2021) of annotated teacher utterances. Uptake indicates how coherent the teacher's utterance is with respect the previous student's turn. We find that MATH- DIAL and CIMA have similar uptake. Both surpass the other datasets in our comparison.
3.3 Student Turn Generation
We use InstructGPT ((ext-davinci-003) (Ouyang et al., 2022) to generate student turns. We prompt the model with the previous dialogue history and additional information that grounds the next turn. The prompt contains the MWP, the initial student confusion, as well as the student profile which ex- plains the type of confusion and persona of the student.
3.4 Taxonomy of Teacher Moves
4.1 How well can LLMs simulate students?
This section defines the taxonomy of all teacher moves that are used in A MATHDIAL. We base the first two on the work of Reiser (2004), who sug- gest that scaffolding strategies can be split into two main categories: structure and problematize. These form the basis for the Focus and Probing moves employed in our study. Focus is used to constrain the student to make direct progress towards solving the problem. Probing is used to generalize certain aspects of the problem which allows the student to explore its underlying concepts. More concretely, a teacher might construct a new, related problem that targets only one specific concept that is needed to solve the original MWP. However, scaffolding might also fail, for example when a student gets stuck. Then, teachers may need to reveal parts of the answer. This is called Telling. Finally, turns that just serve conversational elements and have limited pedagogical value are classed as Generic. Table 2 lists finer-grained intents for each of these four categories along with a set of accompanying examples.
Our collection methodology relies on LLMs for simulating students. Therefore, it is crucial to en- sure that the turns simulated by the LLM also match what teacher would expect of real student, who in case is a sixth grader. In this section, we evaluate this quantitatively.
Figure shows that annotators rate the majority of generations by the model positively along two dimensions. The first one says that the confusion of the student is typical confusion of a sixth grader, The second one says that the interaction with the student whole is as expected of sixth grader. We release these annotations with our final datuset which allows users of MATHDIAL to filter out utterances that are of a lower quality.
Moreover, LLMS can be prone to incorrect arith- metic calculations. Therefore, we asked annota- tors to distinguish conceptual errors from such sim- ple calculation mistakes. Arithmetic errors may be easily resolved through calculators but concep- tual errors are likely to require tutors to resolve them, for example by scaffolding. Annotators iden- tified around 80% of the confusions as conceptual, leaving around a fifth containing arithmetic errors. Again, we include these annotations to allow for data filtering.
4
MATHDIAL Analyis
We quantitatively evaluate the collected tutoring dialogues to assess their quality. For this, we out- line descriptive statistics in Table First of all, we can see that our dataset is significantly larger in terms of the number of dialogues and utterances than all related datasets that are listed. By open- sourcing such a large dataset, we fill a crucial gap of sufficiently-sized open-source tutoring corpora which has so far hindered research in the area (Macina et al., 2023).
4.2 Which teaching strategies do annotators choose?
In this Section, we evaluate when teachers use which teacher moves in the conversations. Figure 4 shows that teachers most frequently use Focus ques- tions which are found in 37% of utterances. Focus is followed by Generic and Probing. Telling is the rarest move. To validate these annotations, we sampled 17 conversations consisting of 102 teacher utterances and asked two independent annotators to
Furthermore, MATHDIAL exhibits a higher diversity, measured in bigram entropy (Zhang et al., 2018), than CIMA and TalkMoves. The diversity

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Confusian was typical 6th grade student
Behaviour was typical for 6th grade student
Teacher Acts Dialogue Stages
200
50%
Rocus Geaame
Number of Dialogues
8000
70%9
6008
35%
Potcenkage of
40%0
200
2000
1
Likert Rating (1- very uniikely. 5 very likely)
055
109:
305
1055
4055
507
000
700
8000
500
10065
Consmattio
Figure 3: Teacher judgments on the ability of Instruct- GPT to simulate students. Teachers rate the simulated behaviour largely plausible. Lighter regions account for questions where the confusion was not re- solved.
Figure 4: Overall distribution of teacher moves (left) and their distribution each dialogue step (right). Teachers tend to start with Focus and Probing and then increas- ingly use Telling as the conversation progresses.
4.3 How often can student confusion be resolved?
annotate their moves. We obtain agreement of 0.60 between the two annotators and 0.49 and バ 0.34, respectively, between either of the annotators and the teacher. We note that Probing and Focus appear to be particularly challenging to distinguish and acknowledge that the boundary be- tween them may be subjective. Merging these two categories into one larger 'scaffolding' category improves agreements to 0.67, λ 0.75 and K 0.55. Our observations are in line with related works that have shown low inter-annotator agree- ment between experts for detailed teacher moves in classroom settings (Kelly et al., 2020).
The goal of ~ MATH is to enable building tutors that can help students resolve their confu- sion. Therefore, we would like to know how often teachers can do so in our collected data. This is an- notated by the teachers themselves, who assessed that they were successful in almost 89% of the con- versations. In ca. 75% of the conversations by using mainly scaffolding questions, and only in around 14% by revealing the majority the an- swer. The conversations in which confusions could not be resolved can still be useful, as they, for in- stance, can be used to train classifiers to determine when human intervention in such tutoring sessions is required.
The sequence of moves employed by the teach- ers constitutes their teaching strategy which we analyze in the following. Figure 4 shows the distri- bution of teacher moves for different stages of the conversations. We find that the initial utterance by the teacher is usually generic and serves con- versation opener, oftentimes by asking the student to repeat the question or solution attempt. During the conversation, teachers mainly use scaffolding to either probe the student or focus the conversa- tion on specific part of the problem. The more the conversations progress the more likely teachers are to resort to Telling because students often get stuck specific subproblem and unable to resolve it themselves. As consequence, less Prob- ing used. This has been shown to keep students engaged in the conversation who otherwise become frustrated by being stuck (VanLehn, 2011)
Modeling Tutors with + MATHDIAL
We focus our initial studies MATHDIAL on the task of tutor response generation. Tutor sponse generation aims model the teacher in a dialogue by generating follow-up turns to guide the student towards learning and solving the problem. In the following subsections, we compare different finetuned and prompted language models on the task and evaluate how much detailed information that can be given to the model, such as step-by-step solutions of the MWP, influence performance.
5.1 Training details
We use neural conditional language models that given a tutoring dialogue history uf'. grounding

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MATHDIAL KFI
MATHDIALenn sBLBU
MATHDIAL
sBLEU BERTScore
BERTScore (1)
Uptake (
KFI
sBLEU (*) KFI (t)
Model
(uy=1; d1
(#r+1. MWP)
(wy, myy-1)
BART
4.5
52.0
15.0
46.3
86.6
5.2
16.0
3.3
13.5
BART
5.7
52.8
16.1
47.2
87.9
6.5
16.1
4.3
16.1
TSI50
7.2
51.1
27.2
54.3
94.8
8.4
27.7
5.2
26.3
T5raM
9.0
53.8
23.0
51,4
91.6
10.7
23.1
6,3
23.7
Flan-T52som
8.2
52.9
23.5
52.0
92.0
9.6
24.2
5.7
22.4
9.7
55.0
22.1
51.5
91.7
11.3
22.5
6.9
21.6
Flan-T33a
7.8
54.8
17.7
48.4
88.8
8.9
18.1
5.9
17.0
3.9
51.9
12.3
44.4
81.7
4.4
13.1
3.4
11.2
OPTi an
3.8
52.1
11.5
44.2
82.6
4.4
12.5
2.9
9.9
ChaiGPT (0-shoo)
2.2
47.7
22.6
50.3
92.7
2.1
22.8
2.3
22.2
Table 3: Results of finetuned and zero-shot prompted models the tutor response generation task. We find that i) models finetuned on our dataset can outperform much larger prompted models, ii) there is still gap in terms of generalization, iii) simply scaling the same pretrained model does immediately improve results.
information XC and teacher move A, we wish to generate continuation of the dialogue #1 C V Here 7* denotes all strings that can be constructed from the model vocabulary V using Kleene's s clo- sure. K. is string composed of information anno- tated E MATHDIAL, namely the MWP, step-by- step solution, and the students' solution attempt. We study locally-normalized models of the form
based on it, and therefore constitute our 'seen' split. The remaining 10% are unseen during training and test the ability of the model to generalize to new problems. The dataset split is published with the dataset.
Metrics We assess our models using the sacre- bleu (Post, 2018) implementation of BLEU (sBLEU) (Papineni et al., 2002), well BERTScore (Zhang al., 2020) between gen- erated response (uT+1) and annotated response (üT+1) for each teacher response in the conver- sation. Furthermore, in line with previous works (Dziri et al., 2022; Daheim et al., 2023), we report BERTScore and the token level FI (KF1) between generated utterance and math word problem as a proxy for faithfulness. However, we note that an increase in these metrics can be caused by an in- crease in overlap, which may also indicate more telling and can be undesirable. However, finding good evaluation metrics for assessing the faithful- ness of dialogue tutors remains an open problem. Finally, we measure the Uptake of the generated response (Demszky et al., 2021).
po(uT+1 u A)
Nr+1
II
po (IuT4Iba
[uT+il] "- of A), 111
where O denotes the parameters of the model and T is moved throughout the dialogue evaluate each intermediate teacher turn. We either optimize these parameters by finetuning for 10 epochs zero-shot prompting an LLM. When finetuming, we use an initial learning rate of 6.25e and linear learning rate decay without warm-up, and optimize the neg- ative log-likelihood of the ground-truth response using the AdamW optimizer (Loshchilov and Hut- ter, 2019). We experiment with satte-of-the-att pre- trained Transformer (Vaswani al., 2017) models and make of the checkpoints provided by the transformers library (Wolf et al., 2020). particu- lar, we finetune BART (Lewis al., 2020). Flan-T5 (Chung et al., 2022) which is based on T5 (Raffel et al., 2020) and was finetuned on the instruction- following flan collection (Longpre et al., 2023), well as OPT (Zhang et al., 2022). Finally, we zero-shot prompt ChatGPT (Brown et al., 2020).
We propose two evaluation metrics for end-to- end tutoring, where tutor model is evaluated inter- actively by using it to teach an LLM that simulates student. Success @k measures the percentage of conversations where the student reaches the cor- rect final answer at least once within the first k turns (equivalent of % solve rate prior work). Telling @k measures the percentage of conversa- tions where the teacher explicitly tells the final answer before the student has reached it on their own within the first & turns.
Data split We split data into training split containing 80% of the conversations and set containing the remaining 20%. Around 60% of the problems in the test set are also found in the training data, where at least one conversation was
We use the deberta-largo-mnii checkpoint

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SBL.BU (1) BERTScore(f)
logue tutors trained on it. Table 4 shows results obtained with Flan- when giving different information. The results show that the step-by-step solution is crucial for the model. Question and incorrect solution are not as crucial but are also often repeated by student or teacher throughout the dialogue. Future work can explore this information in more detail to improve tutoring models.
(WT+1, üT-1)
137MM
8.0
$3.0
question
8.6
53.2
incnrrect solution
8.3
53.5
ground-truth
9.5
55.0
all
9.7
35.0
Table 4: Ablation the influence of grounding informa- tion, which shows that the ground-truth -ruth solution gives the model the most valuable information.
6.3 Human Evaluation
6 Results
Model
Coherence (?)
Correctness (f)
Equitable (f)
6.1 Tutor Response Generation
3-point
I/1
3-point
Flan-T378M
2.85
0.89
2.19
Table shows our main results for the task of tutor response generation on MATHDIAL. first gen- eral observation is that automatic metrics appear low when compared to state-of-the-art models on other dialogue data. This might be explained by two main challenges that tutoring models face: high level of ambiguity when it comes to sound teaching strategies and complex problems that the models need be able correctly assess. contrast, the data that ground responses in other dialogue tasks often needs a lesser amount of interpretation. Scaling models in terms of their parameter size is not directly reflected in improved metrics. This indicates that just using larger models might not be enough to build meaningful tutors MATH- DIAL. Still, as shown in BERTScore and lexical overlap between response and grounding informa- tion, smaller models appear to rely more on the grounding information and might paraphrase less which might make teaching less engaging for stu- dents. Instruction tuning seems to have largely positive effect in tutoring, well. This is exhibited by the improvements that 1 yields over T5,
Flan-T53p
2.84
0.91
2.18
OPT
2.61
0.72
1.95
CharGPT
2.89
0,43
1.43
Ground-truth
2.94
0.98
2.42
Table 5: Human evaluation shows that finetuning mod- els E MATHDIAL increases their performance in terms of correctness and equitable tutoring.
Finally, we conduct human evaluation accord- ing to three criteria: 1) Coherence: how coherent the teacher's response is with respect to the preced- ing dialogue, 2) Correctness: whether is in itself correct, and 3) Equitable tutoring, Equitable tu- toring describes how well the model provides the student with room for exploring the problem and solution space. We use three expert annotators that each annotate 50 responses. We obtain agree- ments of 0.29, 0.69, and x 0.34 for the three categories. We find that the ground-truth data that we have collected shows high scores all three criteria which confirms its quality. Then, we find that small fine-tuned models perform much better in terms of correctness and equitable tutoring than prompted large language model (ChatGPT), though the latter is pretrained much more data and has significantly larger parameter count. This shows the importance of high-quality data for training meaningful tutors. The automatic metries are only partially confirmed. For instance, Flan- T5 is rated slightly better than Flan-T5780M correctness despite lower automatic scores.
In order to be used in real-world settings, dia- logue tutoring models need be able to generalize new problems. However, we find that there is still large gap in the performance of all finetuned models between seen and unseen problems. This indicates a clear need to build models that can gen- eralize better. Uptake on the other hand is generally high and for different models even higher than the ground-trutt annotations. Finally, finetuned mod- els tend outperform zero-shot prompted GPT in terms of automatic metrics but the validity of them for evaluating such models may be questioned.
6.4 Interactive Evaluation of Dialogue Tutors
Good tutoring models need to maintain high quality not only when viewed per-utterance but especially over an entire conversation. In order assess this, we use them to tutor an InstructGPT student and measure their success (Success @k k), as well as the rate of telling (Telling@k). The tutor models are
6.2 Influence of grounding information
MATHDIAL provides provides a large set of annotations that can be used to ground the responses of dia-

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IdiaacK
Nonlim
0.0
CluceT
EG8
Harl3
61-
04--
625
04-
013
050
50
16
Skg connt
Sup couat))
Skip ovaath
Success
Telling @5
Success
Telling 10
Success @
Telling @
Success @ 10
Telling 10
Model
Model
6
10
NextStep
25%
0%
25%
0%
Problems with 2 step Solutions
ChatGPT 29%
16%
53%
32%
Flan-TT5uum 65%
0%
68%
2%
Mlan-T57amx
39%
4%
ChatGPT
57%
14%
77%
20%
Ground Truth
59%
<1%
82%
4%
Problems with 3 step Solutions
Flan-T5yum
18%
30%
7%
Figure 5: Performance our tutor model and 3 base- lines interactive tutoring of the student model. We find the model trained on E MATHDIAL to have simi- success@5 rate with less telling.
ChatGPT
17%
19%
43%
38%
Problems with step Solutions
Flan-T5yaum
27%
1%
34%
2%
ChatGPT 29%
20%
52%
32%
Figure 6: Performance of our tutor model and ChatGPT student model on problems with solutions of different lengths (r is the number of steps in the ground truth solution). The performance of all models drops for problems with more than step solutions.
used as outlined in the previous subsections and the student model uses the same settings as during data collection. We compare our Flan-T5780M model with simple baseline that repeatedly asks "What is the next step?" (NEXTSTEP), ChatGPT, and the ground-truit truth conversations.
on interactive tutoring
Figure 5 shows that NEXTSTEP has the lowest success rate, but never tells solutions by construc- tion. ChatGPT, on the other hand, has a high suc- cess rate but also the highest rate of telling. This is a crucial shortcoming because high telling coun- terproductive to effectively teach students. Flan- T5780M achieves balance between the two and shows similar amount of telling as the ground truth.
We benchmark open-source models on the task of tutor response generation and show that smaller models finetuned can significantly surpass the performance of much larger prompted LLMs. Moreover, in our pro- posed interactive tutoring simulattio,, the finetuned model achieves similar student-solving success as prompted LLM while keeping the direct telling rate lower. Nevertheless, models still require better reasoning over student solutions and better gener- alization to unseen problems.
E MATHDIAL
We note that the gap in success rate between Flan-T5780M and ChatGPT, at least in the initial steps, stems mostly from longer problems, as is ev- ident from Figure Overall, no model can match the success rate of the ground-truth annotations. This indicates large room for future improve- ments and research.
Our dataset fills a crucial gap towards studying effective dialogue tutors at scale by providing a significantly larger amount of dialogues than other available corpora in one-on-one tutoring and pro- vides a tough testbed towards better tutoring mod- els. We hope that it can spark more research in this mcaningful but understudied area of NLP.
7 Conclusion
We introduce a new framework for semi-synthetic dialogue dataset collection. We use it to collect pedagogically rich dataset for tutoring math word problems that follow equitable tutoring practices and learning sciences research scaffolding stu- dent understanding, called MATHDIAL. Our dataset consists of ca. 3k tutoring conversations grounded in math word problems from GSM8k.
8 Limitations
In this work, we used LLM to simulate stu- dent confusion. However, we acknowledge that these models have a limited understanding of hu- man learning and this is key limitation in our dataset certain kinds of student confusions may be under- or over-represented our dataset. Future

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work can focus on addressing this limitation.
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Tsung- Meing Wen, David Vandyke, Nikola Mrkšić, Mil- ica Gašić, Lina M. Rojas-Barahonn Barahona, Pei-Hao Su, Ste- fan Ultes, and Steve Young. 2017. A network- based end-to-ens trainable mask-oriented dialogue system. In Proceedings of the 15th Conference of the Euro- pean Chapter of the Association for Computational Linguistics: Volume I, Long Papers. pages Valencia, Spain. Association for Computational Lin- guistics.
Tianyi Zhang, Varsha Kishore, Felix Wu, Kilian Q- Weinberger, and Yoav Artzi. 2020. Bertscore: Eval- uating text generation with bert. In International Conference on Learning Representations.
Yizhe Zhang, Michel Galley, Jianfeng Gao. Zhe Gan, Xiujun Li, Chris Brockett, and Bill Dolan. 2018. Generating informative and diverse conversational responses via adversarial information maximization. Advances in Neural Information Processing Systems, 31.
Rainer Winkler, Sebastian Hobert, Antti Salovaara, Matthias Söllner, and Jan Marco Leimeister. 2020. Sara, the lecturer: Improving learning in online edu- cation with scaffolding based conversational agent. In Proceedings of the 2020 CHI Conference on Hu- man Factors in Computing Systems, CHI '20, page 1-14, New York, NY, USA. Association for Comput- ing Machinery.
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A Dataset statistics
Sebastian Wollny, Jan Schneider, Daniele Di Mitri, Joshua Weidlich, Mare Rittberger, and Hendrik Drachsler. 2021. Are we there yet? a systematic literature review on chatbots in education. Frontiers in Artificial Intelligence, 4:654924.
For NCTE, uptake is calculated on the teacher- student dialogue pairs while bigram entropy cal- culated on all teacher utterances. For TolkMoves and TSCC, bigram entropy is calculated on all teacher utterances having more than three words, while uptake is calculated on teacher utterances immediately following student utterances if both have more than three words.
Jing Xu, Da Ju, Joshua Lane, Mojtaba Komeili, Eric Michael Smith, Megan Ung, Morteza Behrooz, William Ngan. Rashel Moritz, Sainbayar Sukhbaatar, Y-Lan Boureau, Jason Weston, and Kurt Shus- ter. 2023. Improving open language models by learning from organic interactions. arXiv preprint arXiv:2306.04707.
B Problem and confusion selection
While the problems in GSM8k are simple enough to be understood quickly by teachers, they remain challenging for students, who among others have to deal with equations or percentages. We follow the GSM8k reasoning format and prompt ChatGPT (gpt-3.5-turbl 5-turbb) with a 2-shot prompt. Given a prompt and a math word problem, we sample n reasoning paths T; solutions from the model. We parse the first numerical answer a; after the model
Lining Zhang, Simon Mille, Yufang Hou, Daniel Deutsch, Elizabeth Clark, Yixin Liu, Saad Ma- hamood. Sebastian Gehrmann, Miruna Clinciu, Khy- athi Raghavi Chandu, and João Sedoc. 2023. A nec- dle in haystack: An analysis of high-agreement Proceed-
workers on MTurk for summarization. ings of the st Annual Meeting of the Association for Computational Linguistics (Volume I: Long Papers). pages 14944-14980 Toronto, Canada. Association for Computational Linguistics.

---

generated "#*##" which represents the final result. Most of the generated outputs have this format and we discard all generations not following sample N = 50 reasoning path candidates using the same settings as suggested by (Wang et al., 2023b). After sampling multiple reasoning pairs and corresponding answer pairs (ri, 0z) we use majority vote over which does not lead to ground truth answer arg max, Ei=1 (a; # a). We select problems with most four solution steps. Since our initial experiments show the occurence rounding errors, which related work finds to be more common LLMs than humans (Frieder et al., 2023), we limit them by discarding confusions that are within 0.1 of the original solution. Moreover, to filter out other simple calculation errors which are not interesting from learning standpoint parse all the intermediate equations which are in the format a c >> and use calculator to check for inconsistencies.
C
Student model
We
C.I
Prompt
We use InstructGPT (text-davinci-003) with the following prompt using temperature sampling with T 0,4 and no top-k truncation:
Student Persona: (STUDENT PERSONA) An'n Math problem: (MATH PROBLEM) \n\n
Student solution: (STUDENT SOLUTION) \n Context: (STUDENT NAME) thinks their answer is correct. Only when the teacher provides several good reasoning questions, (STUDENT NAME) understands the problem and corrects the solution. (STUDENT NAME) can use calculator and thus makes calculation errors. Send EOM tag at the end of the student message. An'nn (DIALOGUE HISTORY)
The full prompt used is:
Q: Natalia sold clips to 48 of her friends in April, and then she sold half as many clips in May. How many clips did Natalia sell altogether in April and May?
C.2 Student characteristics
To build a dataset that would reflect students of var- ious backgrounds, we use numerous student names associated with their given pronouns. List all stu- dent characteristics based on prior work studying misconceptions in learning algebra (Booth et al., 2017):
A: Natalia sold 48/2 <48/2=24x24 clips in May. Natalia sold 48+24 =48+24=72=72 clips altogether in April and May. IHHII 72
has a problem with understanding what steps or procedures are required to solve a problem.
Q: Weng earns $12 an hour for babysitting. Yesterday, she just did 50 minutes of babysitting. How much did she earn?
has a problem with understanding underlying ideas and principles and recognition of when to apply them.
A: Weng earns 12/60 = < x12/60=0.22 2.000....0.2 per minute. Working 50 minutes. she earned 0.2 50 = <0. 2=50=10>10. #### 10
struggle most with understanding what the problem is asking them do.
Of the problems in the GSM8k dataset, 5684 problems were queried after climinating problems with more than 5 steps in the solution. This yielded 2, 313 problems with at least one wrong solution. We then eliminated student solutions having fewer than 300 characters (having too few characters makes it harder to pinpoint where exactly the er- ror occurred) or more than 500 characters (longer solutions require annotators to spend more time understanding the error), leaving with 1,979 wrong solutions. Finally, eliminate problems where all or 49 out of 50 proposed solutions have the same (wrong) final answer, leaving us with our final set 1131 problems.
has difficulty determining which pieces of in- formation are relevant and which are irrele- vant to solving the problem.
struggle to put the numbers in the correct or- der in the equation or determine the correct operation to use.
struggle recognize the problem type and therefore do not know what strategy to use to solve it.

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C.3 Common error cases
Student is ready: Steven
We manually screened some conversations and teacher feedback to understand common of student model. The most common problem among them was the occurence of simple arith- metic errors (e.g. 7-2=9) and inconsistent student behaviour (e.g. student returning to the incorrect answer after figuring out the correct one in the previous utterance). These errors are captured in the teacher quality Likert seale rating of student behaviour. We acknowledge further analysis is needed to better understand the fine-grained stu- dent model behavior on problems with different numbers of steps e.g. by cognitive task analysis (Koedinger and McLaughlin, 2016).
common error cases
misetatd Eo addlr beaf
the mase dalss sehectio
He
Shadent
dan
Liim pur
Rubita cale ti Tooes Dable
D Data collection interface
Figure 7: Web interface of the tool for collecting dia- logue tutoring conversations. The left panel shows math word problem, correct solution, and student solution. The right panel contains conversation history, panel for selecting the category of response, and a text area to send response the student. After clicking Send, the student model is immediately invoked using internal API call.
We use Prolific for data collection and hire annota- tors with teaching experience. To ensure the data quality we filter only annotators with 100% com- pletion rate with more than 500 total submissions. All the payments to the annotators exceeded the US federal minimum wage and the final batch of annotators were paid the equivalent of $12/hour. The data collection interface is shown in Figure Annotators were restricted to having maximum of five conversations in one annotation session. One conversation takes ca. minutes. Data collection took place over a period of 2 months.
Calculation error easily solved by calculator
Missing / Wrong factual knowledge
Misunderstanding of question
None of the above
D.1 Annotation pipeline
Tutoring conversation Next, the teacher has a conversation (see Figure 7) with a student and uses scaffolding moves help the student understand the problem. The conversation ends when the stu- dent correctly solves the problem if the total conversation time exceeds 10 minutes.
For each annotator, we randomly assign a student and math word problem. Teachers were instructed to first analyze the student homework solution and then start the conversation to scaffold student prob- lem understanding. Post-conversation question- naire is filled out by teachers to rate the conversa- tion and get feedback on the type of student error.
Post conversation questionnaire Teacher fills the post conversation questionnaire as shown Figure 9.
Comparing solutions As shown in Figure 8, the teacher first analyzes and compares the correct so- lution with the incorrect student solution (student confusion). The teacher marks the exact line of first student error and categorizes the problem into the following categories:
D.2 Annotators training phase
We let annotators read best practices on how to have productive conversation with students (cf. Section D.3 and D.4) and tested them on their un- derstanding of our task afterwards. We started the data annotation with all the annotators able to suc- cessfully pass the test. Moreover, improve the training phase we manually checked several con- versations by cach annotator terms of the quality and usage of diverse scaffolding questions.
Reached correct solution but proceeded fur- ther
Extra quantity or Missing quantity
Unit conversion error

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Study progress
Da eacoedin reading stuckeis corlaco"""""
Math Problem::
sinding song sinpers. remaining singers preacle jarted werse tigirher?
You soreed aarver
Correct Solution:
alaludent arao.
Cacuoplute nu derin
Analynn the student anower first by compuiing it the connuct
Remercal rebb vn cobetces
Student Solution: (mark the exoot step of the first anror)
302 aiger
Thees Nili a singins paine in seooed venss
nut sing
were
Describe
Thus these ware 15-5 10 angges who did ang saceed varsa.
Thenefore the final th vere, whele cheir serge logether, of nowr 30-1 people jired
mutripycn
Select
sicencd
Whet prioriuue calagoyy oighht
Shatent confiction other chadents.
Figure 8: Teacher first compares student solution with the correct solution and marks the exact step of the error.
D.3 Annotation Guidelines
Stadent interaciinnccioonn.oooo
staden:
Teachers were instructed to have a one-on-one tutor- ing session with different 6th-grade students. They were told that students received math word prob- lem for homework and submitted their solutions beforehand. In tutoring conversation, teachers were asked to go through the student's solution and try to let the student understand using a se- ries of sensemaking questions to support student reasoning and learning. Specifically, they were instructed to not just correct student solutions by telling what's 's correct/incorrect, but give students the opportunity to explore the problem with focus on core aspects, such as their chosen strategy. How- ever, as the goal is focus on conceptual errors, they were allowed to let students use calculators or correct their arithmetic mistakes.
Sborggy caages
Sacap)
Figure 9: Post questionnaire.
giving out the partial or full answer to the student and should be mostly used when a student is stuck.
D.5 Background for teacher moves
Scaffolding (Reiser, 2004; Anghileri, 2006) assists students succeed in tasks that would otherwise be complex and differentiates between guidance (e.g. decomposing problem, clarifying) from cognitive activation (c.g. causing cogmitive conflicts, activat- ing prior knowledge (Limón, 2001)). The effective teacher moves to scaffold students" understanding have been studied extensively by analyzing and an- notating real human tutoring conversations (Nye et al., 2014; VanLehn, 2011). Experienced teachers can through natural language guide students' fo- cus and uncover misconceptions (Nye et al., 2014). The teacher moves the form of scaffolding to sup- port student understanding by asking open-ended questions, activating their prior knowledge, or caus- ing cognitive conflicts (Limón, 2001). ). A teacher asking scaffolding questions provides learning op- portunities for students to actively construct their knowledge. However, at the same time asking only difficult questions could lead motivation and potentially the end of the dialogue. On the other hand, only constantly revealing an- swers does not lead to long-term learning.
D.4 Teacher moves taxonomy
Table 2 refers to the details of teacher moves used during annotation. In summary, Focus comprises of all conversation elements that direct the student towards the solution without actually giving out any of the solution, while Probing attempts to develop reasoning skills and world knowledge relevant to the problem, but not necessarily specific to the given problem. Telling is giving out parts of the solution, either calculations or strategy or both. All other conversational elements, including trying to understand what the student has already tried, fall under Generic.
loss of learner
Most importantly, scaffolding questions that are productive for long-term learning are Focus and Probing. On the other hand, Telling represents

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D.6 Postprocessing
so students themselves.
can solve the problem
As we are interested in real educational use cases for our tutoring system, apply safety filter to filter out conversations with any sensitive content. particular, we use the Perspective API' to filter out conversations containing toxic content (<1%).
Human Evaluation Protocol
The following dimensions were rated by annota- tors:
D.7 Initial pilots
"The response naturally follows up on the previous ulterance and context and has no logical conflicts with the context."
Coherence
We initially explored two additional approaches data collection: i) human--ummn conversations, and ii) synthetic generation by LLMs. The frame- work we used in the final data collection enables to scalably create data since are only reliant user who quickly create entire conver- sations with the LLM, taking ca. minutes per 7+ turn conversation. We found this more efficient and performant than both human-human conversations and synthetic data generation. Specifically, the human-to-human collection is too time-consuming (on average 15 minutes per conversation in our pilot experiments) and requires waiting times to synchronously connect participants (Choi et al., 2018), and synthetic generation has proven to be error-prone (see example in Figure 10); for exam- ple, models fail understand student solutions and themselves make arithmetic errors that are not expected from teachers.
Correctness "The response is factually and mathematically correct and respects the learn- ing concepts being taughu."
"The response gives a learning opportunity for the student by provid- ing space for reflection, explanation, pointing follow-up challenge, or engaging the stu- dent in other ways.
Equitable tutoring-
We use 3-point Likert scale ranging from (poor) and 3 (very good) for coherence and equitable tu- toring and a binary scale for correctness.
ChatGPT prompt is the same as the interactive tutoring scenario (Section E) with an additional section containing student solution.
E Interactive evaluation of tutoring
The student model all cases an InstructGPT model
as defined in Section C.I, with the student name fixed to "Kayla". The first utterance of the teacher is hardcoded to "Hi Kayla, could you walk me through your solution?". For Flan-T5780M teacher model decoding, we used sampling without beam search. For the Chat- GPT teacher model (gpt-3.5-turbal 5-turbo), the follow- ing prompt used:
A tutor and a student work together to solve the following math word problem. \n Math problem: (MATH PROBLEM) \n The correct solution is
follows:
(CORRECT SOLUTION)\n
Your role is tutor. The tutor is a soft-spoken empathetic person who dislikes giving out direct answers to students and instead likes to answer with other questions that would help the student understand the concepts
"https://perspectivvap..

---

Context
Conversation
Q: Sam memorized six more digits of pi than Carlos memorized. Mina memorized six times as many digits of pi as Carlos memorized. If Mina memorized 24 digits of pi, how many digits did Sam memorize?
T: (probing) You outlined that Carlos memorized
18 digits of pi where did you get this figure from?
S: I got this figure by taking the number of digits that Mina memorized (24) and subtracting the number of digits that Carlos memorized more than Mina (6). So 24 6 18.
Ground Iruth: Carlos memorized 24/6=4
digits of pi. Sam memorized 4+6=10 digits of pi.
Final Answer: 10
T: (probing) If the question says that Mina memorised six times as many digits of pi Carlos memorised, and she memorised 24, what do you think that means for the digits of pi that Carlow memorised?
Student solution: Step 1:
Carlos memo-
rized 18 digits of pi. Step 2: Mina memorized digits of pi. Step 3: Sam memorized 6 more digits of pi than Carlos, so he memorized 24 digits of pi (18 + 6 = 24). Final Answer: 24
S: It means that Carlos memorized 4 digits of pi (24/6
T: (focus) That's brilliant really well done. So, if that means that Carlos memorised digits of pi, and the question says that Sam memorised six more digits of pi than Carlos, how many digits of pi has Sam memorised?
S: Sam has memorized 10 digits of pi (4 6 6 10).
T: (focus) That's absolutely perfect! So, based on that, how many digits of pi did Carlos, Mina and Sam each memorise?
S: Carlos memorized 4 digits of pi. Mina memorized 24 digits of pi, and Sam memorized 10 digits of pi.
T: (focus) Well done Luca! You got it right!
Table 6: Exxmmles of MATHDIAL conversations. T' refers teacher utterance, refers student utterance. Each conversation is grounded in the correct solution and student solution. Bold text is information for the reader indicating error categories.

---

Prompt:
proficient educator assists a learner by providing just a few clues to help hin/her in the correct direction. The student should take the lead in reasoning and conputations. Generate tutoring conversation between inath Teacher and 8th-grade
following
problen correctly.
Nath Problen: Jereny decides to take Tylenol because of the pain he is experiencing. He decides to take 1880 every weeks. nany pills they they
ng?
Correct solution: He takes 0a00/000-c1100//0002220 pills each time He takes then 24/6=<<24/6=4bod times day. So he 4*2=<<442-8008 pills
takes for 2774s227-14<<14
he takes 8*14wcc@"14-112>>112 pills
InstructGPT:
Teacher: Hi Leslie, looks like having trauble with this math ward problen. you tell what you's struggling with?
Leslie:
Yeah, I'm
how figure how pills Jereny needs take.
Teacher: Alright, let's break down the problen and see if we can solve it step by step. First, let's think about how much Tylenol Jerent needs take each day. He's taking 1688 day?
hours, how tines does he need to take each
Leslie: He needs to take it times day because
Teacher: That's correct! Now let's figure out how much Tylenol he takes each day in total. If takes 1898 mg each time, and he takes times day, haw nuch does he take in total each day?
Leslie: He takes 3888 ng each day because 1698 3 3680.
Teacher: Excellent! Now let's figure how nany pills he needs take each Each pill 508 nany pills does need take day get
ng?
Leslie: He needs to take pills each day because 3660 588
Teacher: That's a correct! Now let's as think about how nany pills he needs to take in total over the weeks. If he needs to take pills each day, and there
in week, how pills does need take in total over 2 weeks?
Leslie:
He needs to take 84 pills in total because
84.
Teacher: job, Lealie!
fantastic breaking
problem solving step step.
Figure 10: In our initial pilot study we observed that synthetic data generation by InstructGPT strictly followed the same structure of only asking next-step questions (highlighted yellow) and was prone inconsistencies in factual correctness and order of steps (highlighted in red).


Reviews:
[{"review_id": "k1VvKPjg7H", "reviewer": "Reviewer_pp3K", "summary": "", "questions": "I wonder how much “teaching skill” can LLM learn from this dataset. After being trained on this dataset, can the model learn to educate students in other domains? For example, can the LLM use the teacher's moves to help a student with physics problems?", "limitations": "", "rating": 3, "confidence": 4, "soundness": 3, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their comments. We are encouraged by the reviewer valuing the *data collection framework, teacher moves, analyses, and usefulness of the dataset for developing better LLM tutors*. We try our best to respond to their queries hereafter:\n\n**Responsiveness of InstructGPT Student**: We acknowledge that we cannot simulate real students perfectly, but we have incorporated several methods to mitigate this problem and we will highlight them better in the paper.\\\nFirstly, we prime the student model with a prompt encouraging them to stick to their original (incorrect) answer unless convincing guidance has been provided by the teacher.\\\nSecondly, we would like to reiterate that the dataset is intended to model teacher behavior in diverse teaching situations.\\\nFinally, we asked teachers to rate conversations with students, and the majority of the conversations were rated rather positively as shown in Figure 3.\\\nWe are releasing the teacher ratings of how realistic the student confusion and student behaviors are, making it possible to train only on more realistic cases by filtering out those with low scores, should one choose this.\n\n**Transfer to Other Subjects**: In this work, we study the transfer to unseen math word problems and point out (in Section 7.1) an already significant gap in the performance. The teacher moves in our study and decomposition to the subproblems could be applied across a variety of learning subjects, given a set of problems. However, transfer to other subjects remains an open research problem and we believe our dataset could enable more research in this direction. We plan to analyze and address the transfer to other subjects in future work.\\\nWe would like to emphasize that our dataset is the first to allow studying this problem at such a scale.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "1.\tThe proposed data collection framework can effectively collect dialogues and is reproducible.\n2.\tDetailed and insightful analysis on the collected dataset.\n3.\tThe collected dataset is potentially useful for developing a LLM teacher.", "reasons_to_reject": "The major disadvantages have been discussed in the limitations section. One concern is that the “student” played by LLM might be more active than real students, and the humans teachers might not be able to maintain a high teaching quality during the data collecting procedure, which could bring more challenges to apply this dataset in real-world applications.", "questions_to_authors": "I wonder how much “teaching skill” can LLM learn from this dataset. After being trained on this dataset, can the model learn to educate students in other domains? For example, can the LLM use the teacher's moves to help a student with physics problems?", "paper_topic_and_main_contributions": "This paper proposed a dataset of 3k one-to-one teacher-student tutoring dialogues grounded in multi-step math reasoning problems. The dataset is collected under the WOZ framework, where the human teachers are paired with LLM students to generate dialogues. The dataset also defines different teacher moves and student characteristics, which are valuable for further analysis and larger scale data collection. The authors conduct detailed analysis and evaluation on the dataset to reveal the challenges of LLMs in tutoring students.", "excitement": 3, "reproducibility": 4, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "5x2PLVNAtF", "reviewer": "Reviewer_jaAZ", "summary": "", "questions": "1. Why there are three settings  (MATHDIAL, seen, and unseen) in Table 3?\n2. In Appendix E.1, the model is finetuned given the teacher's move as one of the inputs. However, is it should be decided by the model itself?\n3. Other questions in reasons to reject.", "limitations": "", "rating": 3, "confidence": 4, "soundness": 3, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their comments. We are happy the reviewer shares the *motivation to address this important and valuable problem of studying effective dialog tutors at scale*. We apologize for any difficulty the reviewer faced due to the placement of figures and will improve their placements to make the camera-ready version easier to understand. We try our best to respond to their queries hereafter:\n\n**Figure 2 Relevance**: Figure 2 aids the reader by providing a quick overview of our data collection methodology.\n\n**Figure 3 Meaning**:  We do not focus on the gap between the red and blue bars for our conclusions. Replacing students with LLMs leads to 2 possible sources of non-realism in our model: first, the student confusion may be unrealistic, and second, the behavior of the student while the teacher explains their error to them might be unrealistic. The red and blue bars represent how well these two have been mitigated respectively. The best case scenario, therefore, would be to have the entire weight on 5 for both bars. \\\nBased on the data in Figure 3, we can see that the distribution is skewed towards the highest Likert rating of 5 (with an average of 3.45 and a median of 4 for both measures), indicating that the majority of simulations are assessed to be realistic by the expert annotators. To put our message across in a better manner, we will complement the Likert distribution figure with corresponding summary statistics in the camera ready.\n\n**Evaluation clarifications**: We study the continuation of the dialogue $u_{t+1}$ given a preceding set of turns $u_{1:t}$ and follow standard dialogue evaluation protocols used in [1], where $t$ is moved throughout the conversation, such that we evaluate each teacher turn in the dialogue. Therefore, evaluation contains intermediate situations. We train our models to predict the next response using cross-entropy to the ground-truth response. During inference, we use beam search with 4 beams. Thanks a lot for pointing this out, we will clarify the notation used in Section 6 and Appendix E.1 in our next version. \n\n**Why there are three settings (MATHDIAL, seen, and unseen) in Table 3?** To compare the generalizability of models to unseen math problems. This is a first step to studying the generalizability of tutoring models before evaluating on other subjects. As a reminder, our dataset consists of 1131 math problems. The test set contains around 60% of seen problems, where the model has seen at least one conversation on it during training, and 40% of unseen problems, which the model has not encountered. Our results in Section 7.1 indicate that generalization to unseen math problems is one of the open problems for the community to address that is enabled by our collected dataset. The setup is described in further detail in L434-438.\n\n**In Appendix E.1, the model is finetuned given the teacher's move as one of the inputs. However, is it should be decided by the model itself?** Yes, that's indeed an important variant of evaluation more closely following real-world scenarios as indicated by [1]. Our dataset allows this evaluation scenario and we will be happy to add this experiment to Table 3 in the camera ready. Most importantly, we will encourage the community to follow it.\n\n[1] Jakub Macina, Nico Daheim, Lingzhi Wang, Tanmay Sinha, Manu Kapur, Iryna Gurevych, and Mrinmaya Sachan. 2023. Opportunities and Challenges in Neural Dialog Tutoring. In Proceedings of the 17th Conference of the European Chapter of the Association for Computational Linguistics, pages 2357–2372, Dubrovnik, Croatia. Association for Computational Linguistics.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "1. The motivation is very straightforward and the targeted problem is very valuable.\n2. The dataset can fill a crucial gap in studying effective dialogue tutors at scale by providing a significantly larger amount of dialogues than other available corpora in one-to-one tutoring.", "reasons_to_reject": "1. The paper is not well-organized and hard to follow. For example, Table 1 is presented on Page 3 and introduced on Page 5. Also, Figure 2 does not bring any understanding improvements to the paper.\n2. The collection methodology relies on using LLMs to simulate students, which is crucial that the model can do so realistically to create high-quality data as claimed in Section 4.1. However, according to Figure 3, it seems can not lead to the conclusion that LLMs can simulate students since the percentage gap between red and blue is relatively small. In addition, as LLMs are tuned to follow instructions, a real human student may not strictly follow the instructions and there are other problems that may occur in practice.\n3. The experimental details are not clear. For example, the details of input and output during finetuning and the loss functions, also the inference details.\n4. The evaluation is not suitable or not clear. According to Lines 439-454, the metrics are evaluated between generated response and annotated response at the end of the dialogue session. However, intermediate tutoring processing is also very important in this situation, and sometimes even outweighs the final answer.", "questions_to_authors": "1. Why there are three settings  (MATHDIAL, seen, and unseen) in Table 3?\n2. In Appendix E.1, the model is finetuned given the teacher's move as one of the inputs. However, is it should be decided by the model itself?\n3. Other questions in reasons to reject.", "paper_topic_and_main_contributions": "The main contributions of this paper are the introduction of a novel framework for the creation of semi-synthetic dialogue datasets, wherein genuine experts collaborate with LLMs to emulate plausible students. Furthermore, a comprehensive tutoring dataset consisting of 3,000 dialogues is built based on the framework. This dataset is augmented with extensive grounding annotations. The experimental results are effective and extensive.", "excitement": 3, "reproducibility": 3, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "tgMLgTYmLP", "reviewer": "Reviewer_i8Bf", "summary": "", "questions": "Did you have multiple teachers judge LLM student interactions in Figure 3?  Do you have an IAA metric to report?\n\n389: “88.29% of the time they were able to do so” <- when the confusion was not able to be resolved, how did this interact with the teacher judgments on the simulation ability in Figure 3?\n", "limitations": "", "rating": 4, "confidence": 4, "soundness": 4, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their insightful comments. We are encouraged that the reviewer appreciates *the value of exploring this task as a community, incorporating past educational work, and thorough analysis and evaluation*. Please find our responses to the points raised below:\n\n**Annotators agreement**: Regarding section 4.2, a moderate agreement between human annotation of probing vs. focus has been observed in previous works. It reflects the mental state of the tutor and the effect they expected to achieve with the utterance. Since the post hoc annotators do not have access to said mental state, the agreement is expected to be low.\\\nRegarding section 7.3, we agree both better training of annotators and refining the specificity of the annotation task might have mediated some of these issues and improved the robustness of these findings.\n\n**Did you have multiple teachers judge LLM student interactions in Figure 3?** We had every teacher self-report whether or not they were able to resolve the confusion of the student immediately after the completion of the conversation, hence we have one annotation per conversation. The same math problem and confusion may have been encountered by multiple teachers (55.7% of math problems have been annotated by more than 3 annotators), but since the student and teacher behaviors are different for each conversation, we cannot compare annotations across this. \n\n**When the confusion was not able to be resolved, how did this interact with the teacher judgments on the simulation ability in Figure 3?** We thank the reviewer for suggesting this interesting analysis. For conversations that the teachers could successfully resolve, the mean of the teacher judgment of student behavior is 3.59, while it is only 2.34 when the conversation was not resolved. The difference is even more stark for the teacher judgment of student confusion, where successful conversations had a mean rating of 3.54 but 1 on unresolved conversations. This seems to indicate that teachers felt that all confusions that could not be resolved were unrealistic, while student behavior was also less realistic than the ones they were able to resolve. We shall add this analysis to the camera-ready version.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "Authors propose a novel framework to collect tutoring data by capturing common LLM errors, which capture student misconceptions in the majority of cases.  A LLM to interact with a tutor conditioned on the error.  This approach incorporates past educational work on pedagogical tutoring strategy.\n\nThis dataset is an exciting contribution to the dialogue tutoring community and could encourage more work in this area.\n\nAnalysis of different models trained to produce tutoring responses is comprehensive and insightful.  End-to-end evaluation with a trained tutor model and the LLM student is an interesting finding and shows there is value to exploring this task as a community.", "reasons_to_reject": "While the authors conduct human evaluation, there is low-to-moderate agreement among annotators for multiple tasks.  I wonder if more training of annotators or a more specific annotation task might have mediated some of these issues and improved the strength of these results.\n", "questions_to_authors": "Did you have multiple teachers judge LLM student interactions in Figure 3?  Do you have an IAA metric to report?\n\n389: “88.29% of the time they were able to do so” <- when the confusion was not able to be resolved, how did this interact with the teacher judgments on the simulation ability in Figure 3?\n", "paper_topic_and_main_contributions": "This paper produces a novel dataset of 3k math tutoring conversations, collected by having teachers interact with a LLM.  Once the data is collected, the authors benchmark several baseline approaches, finding fine-tuning approaches perform better.  The authors also have the student LLM interact with the trained tutoring models, showing a gap between current methods and human tutors.\n", "excitement": 4, "reproducibility": 4, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "GUEm6ztzzU", "reviewer": "Reviewer_q15M", "summary": "", "questions": "1. Why is the construction of a dataset more powerful discussion on this topic, rather a model based comparison approach? Is it to set a ground truth that is different from existing WoZ datasets? How do you manage to show this difference in the current work?", "limitations": "", "rating": 5, "confidence": 3, "soundness": 3, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their insightful comments and references. We appreciate the reviewer *highlighting that our work could highly impact the use of LLMs in education*. Cognitive task analysis is an interesting perspective and our dataset could be potentially (with smaller additional annotation of knowledge components) used to study how teachers break down math problems into smaller subproblems and guide students. We will add these sources to section 2.2 and use quantitative cognitive task analysis in future work.\n\n**Why is the construction of a dataset more powerful discussion on this topic, rather a model based comparison approach?** We decided to focus on the data collection methodology because there is a lack of datasets available in the dialogue tutoring domain. Data is the most important asset in this domain and without it no experimentation could be done. Our work opens a new avenue of modeling approaches for the understudied domain of educational tutoring, and allows for building new models on a larger scale (due to the significantly larger size than previous corpora) and extensive grounding annotations.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "## Reasons\n1. The work explores a more cognitive aspect (with relevant citations) to the use of dialogue in tutoring systems. This allows to discuss the idea that there are aspects to learning for the student from working out a problem step-wise. Using this dataset, it is possible to analyze and produce better models fine-tuned for this task.\n\n2. Unlike the standard user study based approach, this work focuses on analyzing the closeness to human tutoring with GPT models. This could have pedagogical implications with the use of LLMs in Education.\n\n## Contributions\n\n1. A dataset for further analysis / discussions with the rise and use of LLMS  in Education\n\n2. Promoting the use of AI agent instructors who can assist human instructors in helping students with a learning task, using grounding cognitive theories and applied cognitive theories in the use of dialogue based tutoring systems.", "reasons_to_reject": "## Reasons / Weaknesses\n\nI don't find strong reasons to reject, however a strong potential exploration which could be added to this paper is the idea of cognitive task analysis in Math\n\nKoedinger, Kenneth R., and Atsushi Terao. \"A cognitive task analysis of using pictures to support pre-algebraic reasoning.\" Proceedings of the twenty-fourth annual conference of the Cognitive Science Society. Routledge, 2019.\n\nKoedinger, Kenneth R., and Elizabeth A. McLaughlin. \"Closing the Loop with Quantitative Cognitive Task Analysis.\" International Educational Data Mining Society (2016).\n\n", "questions_to_authors": "1. Why is the construction of a dataset more powerful discussion on this topic, rather a model based comparison approach? Is it to set a ground truth that is different from existing WoZ datasets? How do you manage to show this difference in the current work?", "paper_topic_and_main_contributions": "# Summary\n\nThis is a dataset paper that discusses the step-wise reasoning to solving math problems. These steps are generated in textual formats using models such InstructGPT and Flan-T5 (750M). The dataset contains 3k tutoring conversations. The purpose of this work is to understand the performance of GPT models as tutors instead of problem solvers, because of their tendency to solve the problem before tutoring a student. The goal is to analyze the generated dataset to build faithful, verifiable and equitable systems.", "excitement": 5, "reproducibility": 4, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"Missing_References": "N/A", "Typos_Grammar_Style_and_Presentation_Improvements": "N/A"}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper introduces a novel dataset, MathDial, featuring 3k tutoring dialogues centered around multi-step math reasoning problems. The dataset was collected using a framework where real teachers interact with a Large Language Model (LLM) scaffolded to represent common student errors. The authors propose a taxonomy of teacher moves that promote student learning opportunities, and demonstrate the potential of MathDial to fine-tune language models into more effective tutors. The paper is submitted for consideration in the Resources and Evaluation and Dialogue and Interactive Systems tracks.

Reviewers largely agreed on the significant value of the proposed dataset to the community, particularly in the context of dialogue-based tutoring systems. They appreciated the paper's novelty, the potential impact of the work, and the depth of the analysis provided. Several reviewers pointed out that the dataset can fill a crucial gap in studying effective dialogue tutors at scale, and it could encourage more work in this area. However, the reviewers also raised several concerns and questions which were tried to address in rebuttal. These include the role of the LLM as a student, the realism and quality of the collected dialogues, and the clarity of the experimental details. The consensus among the reviewers was that while being an interesting field of study, the paper could significantly benefit from addressing these concerns and questions in the final version. The authors are strongly encouraged to take these comments into consideration to further improve their paper.

Overall, this submission is seen as an important contribution to the field of dialogue tutoring and has the potential to stimulate further research in this area. In addition, I encourage the authors to address the reviewers' feedback to further strengthen the paper.
Decision: Accept-Findings