# Foundations of Education and Instructional Assessment/Performance Assessment and Rubrics/Secondary Math

Changing the A+B=C mentality of Math Assessment
By Michael Piper

## Learning Targets

-The reader should be able to describe written, oral, observation, and portfolio assessment.
-The reader should be able to recognize examples of written, oral, observation, and portfolio assessment.
-The reader should be able to describe what factors are important when creating an assessment.

## Introduction

Mathematics can be a dangerous subject to teach. It carries with it the connotation of being a cold and objective subject, with black and white answers. People rarely tend to think of math as an art form or an adventure. Teachers and students alike are guilty of this impropriety, neglecting math's mysterious and elegant nature. The glory of math bravado and intense mental gymnastics gets traded for cold methodologies and mindless repetition. Students fail to exclaim eureka and great scott as they conquer concepts and self. Teachers fail to glow or shed tears when whispering delicious formulas and sacred teachings. The goal of the math teacher must be to once again move the student to tremble with awe and excitement over this great subject. But with growing pressure to meet the rigorous demands of quantitative standardized testing, how can one achieve this end? How can one implement assessments so that they kindle a passion for math instead of smothering it? The goal of this article is to help equip the motivated secondary teacher with tools that promote the understanding and appreciation of mathematics.

## General Guidelines for Creating and Using Assessments

Before going into specific methods and strategies of assessment, it is important to make a few notes. Effective assessment does not come about by throwing together random assessment events as an after thought to lesson planning. Assessment is an integral part of the teaching and learning process, and should be deeply interwoven into all classroom processes. It can be used before, during, and after units and the course in general. The vast majority of assessment need not be graded and may even given without the student ever having been aware of it.
Specific methods and strategies of assessment are also not beneficial in and of themselves, but are tools that require the teacher to develop skill in both administering the assessment and using its results. Assessments should be developed from defined purposes and with specific goals for their outcome. They can be used not only for evaluating student progress and understanding, but also to get students to think critically about what they are learning. They can be used purely for gaining feedback so that a teacher may adjust their instruction. And if one desires, they can even be used to make students recognize their own personal biases and misconceptions about mathematics. One should clearly define what is being assessed and how this may be done efficiently and accurately for a diverse collection of students.

## Specific Methods of Assessment and their Related Strategies
### The Importance of Writing Assessment in Math Class

This tends to be a form of assessment that gets neglected in math classes. Because it seems irrelevant or time consuming, many teachers dismiss it without considering its benefits. But there have been numerous studies that show a distinct correlation between strong math performance and the consistent use of reflective writing assessment (Evans 2008). The process of writing about math requires students to critically think about specific concepts and to organize them into a coherent flow. This helps the student to internalize specific ideas and promotes long term retention. It also allows them to evaluate their own understanding of concepts (Stepanek 1997). And since the students will have a better ability to express math verbally, they are likely to see improvements in reading math problems as well.
There are a variety of ways to implement this method. There are a wide range of topics. The students could be asked to write what they had learned at the end of the day, to explain how the concepts being discussed are used or reflected in every day life, or to compare and contrast current lessons with previous ones. They could also be asked to reflect on what they enjoy about the material, what they find difficult about it, or to describe areas where the teacher is being effective or ineffective. The style of writing can vary. Journals, essays, and some open-ended questions are a few of the ways this can be administered (Stepanek 1997).
When using this method, it is important to be consistent and to provide feedback. Consistency will help students become efficient in the writing process as well as promoting the processing of material as they learn since they will expect to have to write about it later. Feedback is important to show that you are reading their articles and that you care about their opinions and ideas (Stepanek 1997).

### Making Math Practical

Math has many practical and real-life applications. There are two ways that this understanding can be beneficial to student learning and interest. Many students already do math operations subconsciously in their daily lives without realizing it. By expressing math concepts in everyday situations that students encounter, some of the fear that is tied to unfamiliar math terminology and symbols can be diminished by providing associations that will encourage retention. Also, by polling students to find out common interests, lessons can be adjusted to present material in light of subjects that interest students. Examples presented in this way develop an appreciation of the usefulness of the subject as well as improving interest and retention (Stepanek 1997).
One of the challenges of teaching math is that one must overcome stereotypes such as math isn't useful in the real world. Encouraging students to think about their future careers and explaining the usefulness of math within those fields can help combat a mentality of doing math simply to pass and graduate. Math has applications in every field, including art, sports, the military, and most white and blue collar jobs to name a few.

### Observation

Observations within the classroom setting can be very useful for getting feedback on student strengths and weaknesses. This can be done in a variety of ways, such as checking individual students as they work, observing group work, and having students perform problems in front of the class (Stepanek 1997).

### Oral Assessment

Oral assessment is strategy many teachers use, consciously or unconsciously. Often it is simply asking students in a class for guidance while performing a problem in front of the class. Oral assessment has the advantage of providing more information than a standard test normally will. It gives real time feedback of student comprehension, helps diagnose misunderstandings and misconceptions of the material, reveals students' attitudes towards the subject, and effectively shows student comprehension of the material (Stepanek 1997).
Teachers can perform oral assessments through class discussions, individual interviews, focus groups, and student presentations to name a few methods. Topics can include those listed for writing assessments as well as a range of questions with quick or obvious answers. The teacher should have an idea of the questions that will be asked ahead of time, while leaving room to expand more into specific areas that prove valuable. It is important that students feel comfortable and safe to speak openly and make mistakes. The more routinely this style of assessment is administered, the more comfortable students will be with it. Common mistakes to avoid when performing this assessment are giving students answers or suggestions, posing leading questions, excessive talking/teaching by the teacher, and interrupting the student(Stepanek 1997).

### Homework

* Links to Resources on the Net
* National Council of Teachers of Mathematics-Article
* It's Just Good Teaching publication
* Assessment Strategies Article***Good Overview***
* Math Assessment Articles
* Assessment Strategies Handbook
* Portfolio Assessment Strategies
* Math Practice Tests/Tutorials
* Math Tutorials
Getting students to do math homework has always been difficult. One strategy to encourage students to complete homework is having open-homework quizzes, where students may use homework assignments as help on quizzes. Without announcing which quizzes will be given this way, students are more likely to complete random homework assignments they might not do otherwise.

### Computer Administered Assessment

Some schools administer the SOL test on computers only. Students doing math problems on the computer for the first time tend to experience a great deal of difficult compared to solving the same problem on paper. It can be extremely helpful to get students familiar with doing math problems on the computer before this kind of complication occurs.

### Portfolio Assessment

Portfolios are collections of student work demonstrating student comprehension of material. They can be put together from existing assignments as a sample demonstrating student strengths and weaknesses. Or they can be a selection of works from among a number of assignments for the purposes of grading. Portfolios may be done as a supplement to normal classroom grading systems but can also be done in place of them (Stepanek 1997).

### Non-Standard Grading Techniques

Another method of math assessment involves modifying the common grading system. Graded tests require that material on the test is such that the student will recognize and be able to complete the problems given. Unique and challenging problems that push students abilities too far would be unfair. Also, if a student does poorly on a few tests, even if by the end of the course they comprehend the material they cannot get a good grade in the class. Since the goal of the course is for the student to learn the material, some modifications can be made to the grading system that can have a variety of effects. For example, if students know they can retake a test they did poorly on, there will be less testing anxiety to get a high score the first time around. Testing anxiety can cause a student to do poorly on a test they are actually capable of doing well on. Another option is flexible grading, where students are graded on different assignments that they can choose from to accommodate different learning styles. This type of system could also accommodate self learning because students would have more freedom to work far ahead of the rest of the class (Murphy 1999).

## A Sample Math Assessment

Intermediate Algebra Final Exam
The sample provided is a final exam for intermediate algebra. It consists of almost all short answer questions, allowing for partial credit based on work shown. At the end it provides several problems from which the taker can choose three. This is a good assessment because it tests accurately whether or not the student knows the information. If this were not a final and it was being given back before the end of the course, the teacher would be able to provide useful and specific feedback to the student, as well as being able to shape lesson plans based on how the class had done as a whole.

## Review Questions

1. Which of the following is not a type of assessment? A. A Math Journal B. A Teacher Observing a Student Working C. A Math Formula Sheet D. An Individual Interview
2. Math is useful in which job field? A. Sports B. Art C. Military D. All of the above
3. Ms. Ima Mathner asks John what step she should do next for a problem she is demonstrating on the board. This is an example of: A. Oral Assessment B. Written Assessment C. Portfolio Assessment D. None of the above
4. John is asked to choose from samples of his classwork over the semester and put them together for a grade. This is an example of: A. Oral Assessment B. Written Assessment C. Portfolio Assessment D. None of the Above
Answers:(1-C)(2-D)(3-A)(4-C)

## References

Evans, L. (2008). The Aha! Moment: Making Math Concepts Stick. Principal Leadership (Middle Sch Ed), 8(9), 17-20.
Murphy, T. (1999). Changing Assessment Practices in an Algebra Class. National Council of Teachers of Mathematics, 92(3), 247-249.
Stepanek, J., & Jarrett, D. (1997). Assessment Strategies to Inform Science and Mathematics Instruction. Northwest Regional Educational Laboratory, June, 1-31.