Teachers’ beliefs about improving transfer of algebraic skills from mathematics into physics in senior pre-university education

Figures & data

Figure 1. How a teachers’ belief system is affected by the social context of teaching (adopted from Ernest, 1991).

Table 1. Semi-structured questionnaire, which was based on the transfer problem in the case.

Question number	Rationale
	Case: during a physics lesson a student does not recognize that the physical formula (formula in short) for displacement, , has a similar algebraic structure as the mathematical equation (equation in short), . This student is also unable to express t in terms of s. However, earlier that day during mathematics, the student managed to express x in terms of y, implying that besides a lack of recognition, the student is not able to apply algebraic skills from mathematics to physics successfully.
	Now we want the same student to recognize that in both cases a similar algebraic structure is used.
1.	Is this a familiar problem?
2.	Do you consider it an important problem?
3.	What may be the reason?
4.	As a physics (mathematics) teacher, what would you do a about it?
5.	What may the mathematics (physics) teacher do about it?
6.	What does it mean for the formal physics (mathematics) curriculum?
7.	What does it mean for the math- and physics textbooks?
	We also want this student to be competent in the application of algebraic skills from mathematics into physics. In this case, to express t in terms of s: .
8.	Do you consider it an important problem?
9.	What may be the reason?
10.	As a physics (mathematics) teacher, what would you do a about it?
11.	What may the mathematics (physics)teacher do about it?
12.	What does it mean for the formal physics (mathematics) curriculum?
13.	What does it mean for the math- and physics textbooks?
14.	To what extent do you follow textbooks during teaching?
	In the above-mentioned case, it can be seen that math- and physics are closely related to one another. Teachers appear to have different ideas about their relation.
15.	How do you see the relation between math- and physics?
16.	Do you have any cooperation with your mathematics colleagues?
17.	How do you see the optimal cooperation with your mathematics colleagues?
	Our pre-university physics education is permeated with algebraic problems from mathematics, such as the case above.
18.	How can the application of algebraic skills from mathematics to physics be improved for solving algebraic problems that occur in our pre-university physics education?

Table 2. Teachers’ beliefs about aspects influencing students’ transfer and aspects about CME.

Core theme/subtheme	Mathematics teachers	Physics teachers
1. Coherence	126	135
1.1 Alignment	2/1^a	10/6
1.2 Collaboration and cooperation	85/10	75/10
1.3 Ideal collaboration and cooperation	39/10	50/10
2. Curriculum	65	86
2.1 Curriculum (general)	25/9	10/7
2.2 Mathematics curriculum	23/10	31/10
2.3 Physics curriculum	17/10	45/10
3. Education	7	26
3.1 Junior pre-university education	7/5	26/7
4. Pedagogy of algebra	82	72
4.1 Algebraic skills	40/10	26/7
4.2 Algebraic techniques	7/4	8/5
4.3 Practice (general)	21/9	30/9
4.4 Practice within mathematics	9/5	3/3
4.5 Practice within physics	5/3	5/3
5. Relation between scientific subjects	87	52
5.1 Mathematics and physics	27/10	15/10
5.2 Mathematics within physics	35/10	23/10
5.3 Physics within mathematics	25/10	14/10
6. School subjects	30	20
5.1 Mathematics	19/7	13/6
5.2 Physics	11/6	7/4
7. Teacher	193	112
6.1 Mathematics teacher	97/10	48/10
6.2 Physics teacher	96/10	64/10
8. The use of textbooks	143	139
8.1 Following textbooks	31/10	43/10
8.2 Mathematics textbook	66/10	31/10
8.3 Physics textbook	37/10	45/10
8.4 Textbook general	9/5	20/7
9. Transfer	144	89
9.1 Activating prior knowledge	8/5	10/4
9.2 Affordances (specific)	34/10	8/5
9.3 Constructing relations (general constraints)	27/10	23/9
9.4 Constructing relations (specific constraints)	75/10	48/10
9.5 Focus on students	1/1^a	1/1^a

^aThis subtheme turned out to be an outlier.

Ernest, P. (1991). The philosophy of mathematics education. London: Falmer.

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