Department of Science Education

Why we need to consider science forteaching mathematics.
Klaus Rasmussen

APEC8Dias 1

Department of Science Education

Mathematics and science in “emergencypreparedness education”
Two perspectives:• Why we need to consider science as a discipline (and atransposed discipline to be taught) when teaching mathematics(Chevallard, 2004)• Why we need to consider the teaching of mathematics as ascience.
Taking a moment to review and reflect on the interplay between the(teaching-)disciplines of science and mathematics.
• Maybe we just do it – it is so “obviously” a good idea!
The obvious connections between math and science in relation to theconference theme.
• Nature (and to some extend cultivated nature) presents us withsome challenges which are well suited as basis for good lessons• Intrinsic motivation (close to, or far from students world)• Clear relevance to society• Patterns and regularities
APEC8 – Overview and reflection
Dias 2

Department of Science Education

Different epistemological frameworks
When we look at the lessons we have seen and the textbook materials wehave produced, what will the students have opportunity to learn?
Is topics related to volcanic eruption and fire “just” a convenient thematicin which to learn so called real mathematics?
Is science “just” a convenient starting point to leave behind when we enter
mathematics, after we have done the mathematizing? (e.g. Formatting
reality to become suitable for mathematical modelling)Some characteristics of mathematics
as a discipline:•Hypothetical-deductive•Proofs are possible

APEC8 – Considering the teaching of two disciplines
Dias 3

Some characteristics of science asa discipline:•Empirical-inductive•Falsifiable (in principle)

Department of Science Education

The ambiguities of interdisciplinary teaching
Educational research has not reached consensus (in terminology)• Inter disciplinary
Borders more or lessA mix with visible
cancelled betweendisciplines• Multi disciplinary

boundaries

a cooperation withclear delimitation of
the individual
disciplines (Andresen &Lindenskov, 2009)• Integrated

No clear distinction
between disciplines(Matthews, Adams, & Goos,2009)

••
•
•
•

Cross disciplinary
Trans disciplinary
Thematic
Blended
Etc...

APEC8 - Considering the teaching of two disciplines
Dias 4“Anthropologists' first rule:
Do not be mislead by names”

Department of Science Education

Constraints and affordances to teaching in aninterdisciplinary fashion
Institutional constraints:• Teachers alone in the classroom• Teachers educated in disjoint disciplines

Affordances (some of them more believed than known):• Synergy (“why”)• Efficient (“Faster”)• Effective (“Better”) (Dorn et al. 2005)• Meaningfulness (“why”)• “Real life” relation• Utilitarian meaning• ...others• ...others
APEC8 - Considering the teaching of two disciplines
Dias 5

Department of Science Education

What knowledge should the interdisciplinaryteacher posess?
A science acquires knowledge ofthe world• Objective → inter subjective →consensus•That is verification should be•Repeatable•Across different methods•Generally accepted•Lesson Study might qualify as ascience (or a scientific method toacquire knowledge about theworld of teaching)•Some lesson studies are bynecessity interdisciplinary• MKT, PCK, in the moment
pedagogies, etc. (Mason & Davis, 2013,Shulman, 1986)• Knowledge from the sciences• Knowledge of math and science
ontology and epistemology
There seems to be too many “forms” ofknowledge involved- And this leads me to consider and introduce
praxeologies

APEC8 – Considering mathematics teaching as a science
Dias 6

Department of Science Education

An example of considering science andmathematics teaching together••

From the Advanced Science Teacher Education-project
Described using the levels of didactic codetermination fromthe Anthropological Theory of Didactics (ATD) (Winsløw, 2011)

Praxeologies:•Task•Technique•Technology•Theory“Anthropologists' first rule:
Do not be mislead by names”
APEC8 – steps to be scientiffic about interdisciplinary teachingDias 7

9. Civilisation

9. Civilisation

8. Society

8. Society

7. School

7. School

6. Pedagogy

6. Pedagogy

5. Discipline

5. Discipline

4. Domain

4. Domain

3. Sector

3. Sector

2. Theme

2. Theme

1. Subject

1. Subject

Levels of co-determination for a bi-disciplinary ecology

Department of Science Education

Considering science and mathematics teaching together –GIS, data analysis and modelling in geography•

Bridging Concepts (Wake 2011)• Flow (of many kinds)• (Maps)•The codetermination can be usedto trace how bridging concepts
actually work (and thus becomes
the bridge enabling a teaching
meaningful to both disciplines(Rasmussen & Winsløw, 2013)

APEC8 – steps to be scientiffic about interdisciplinary teaching
Dias 8

Department of Science Education

Bringing it together•Math and science can be utilised to justify each other, if
suitable “connections” are identified. (e.g. Bridgingconcepts)•Each teaching discipline should genuinely benefit from theother, or else nothing is gained.
• “Emergency preparedness education” appears well suited
to act as an interdisciplinary “field” in which (curricularitems from) mathematics and science can be taught.
•If “Emergency preparedness education” is to be taught aspart of math or science, we must be able to point out which
curricular items it helps cover.
•We can use Lesson Study “scientifically” to investigate if,
and how, the above outlined holds any truth.

APEC8 – some slightly normative “conclusions”
Dias 9Department of Science Education

References
Andresen, M., & Lindenskov, L. (2009). New roles for mathematics in multi-disciplinary, upper secondary
school projects. ZDM, 41(1), 213-222. doi: 10.1007/s11858-008-0122-z
Chevallard, Y. (2004). La place des mathématiques vivantes dans l’éducation secondaire: transposition
didactique des mathématiques et nouvelle épistémologie scolaire.’. In C. Ducourtioux & P. L. Hennequin(Eds.), La place des mathématiques vivantes dans l’éducation secondaire (pp. 239-263). Paris: APMEP.
Dorn, R. I., Douglass, J., Ekiss, G. O., Trapido-lurie, B., Comeaux, M., Mings, R., . . . Ramakrishna, B.
(2005). Learning Geography Promotes Learning Math: Results and Implications of Arizona's GeoMath
Grade K-8 Program. Journal of Geography, 104(4), 151-160.
Mason, J., & Davis, B. (2013). The Importance og Teachers' Mathematical Awareness for In-the-Moment
Pedagogy. Canadian Journal of Science, Mathematics and Technology 13(2), 182-197.
Matthews, K. E., Adams, P., & Goos, M. (2009). Putting it into perspective: mathematics in theundergraduate science curriculum. International Journal of Mathematical Education in Science andTechnology, 40(7), 891-902. doi: 10.1080/00207390903199244
Rasmussen, K., & Winsløw, C. (2013). Didactic Codetermination in the Creation of an Integrated Math andScience Teacher Education: The Case of Mathematics and Geography. Paper presented at the CERME 8,Antalya.
Shulman, L. S. (1986). Those Who Understand: Knowledge Growth in Teaching. Educational Researcher,15(2), 4-14.
Wake, G. (2011). Modelling In An Integrated Mathematics And Science Curriculum: Bridging The Divide.
Paper presented at the CERME 7, Rzeszow, Poland.
Winsløw, C. (2011). Anthropological theory of didactic phenomena: Some examples and principles of its use
in the study of mathematics education. Paper presented at the III Congreso Internacional sobre la TAD,Barcelona.

Thank you for your attention.
Dias 10