Abstract
Learner disengagement is a familiar problem for teachers of mathematics. The abstract nature of mathematics is one contributing factor, but a more significant factor relates to the pedagogical practices commonly used by teachers. This is the area of focus in this chapter. The empirical research reported here is part of a PhD study which concentrated on the contrast between teachers’ perceptions of what they called ‘disengaged’ students, and the perceptions and behaviours of the students themselves. The evidence points to both engaged and disengaged behaviours by all the students sampled. The teachers’ practice of labelling students as ‘disengaged’ is exposed as a self-fulfilling practice which effectively excludes them from the mainstream activities of the class. This chapter asks the question: Could a focus on inclusive approaches to the pedagogy change the engagement situation positively?
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Appendices
Appendix 1
Question 1
How often do you do these activities in your mathematics lessons?
Tick one box in each row
Always in every lesson | Often in some lessons | Sometimes in few lessons | Rarely or not at all | ||
|---|---|---|---|---|---|
1a) | Talk about your work in small groups | ||||
1b) | The whole class talks about your work together | ||||
1c) | Do mathematics problems in the real world | ||||
1d) | Use models and materials | ||||
1e) | Practise mathematics skills | ||||
1f) | Solve problems | ||||
1g) | Do investigations | ||||
1h) | Do mathematics projects | ||||
1i) | Explain your ideas to other students | ||||
1j) | Make posters and displays | ||||
1k) | Play mathematical games | ||||
1l) | Explore mathematical puzzles |
Question 2
Mark an X on the line to show how much you prefer one activity over another one at the other end of the line.
Talk about your work in small groups | Do problems in the real world | |
Practise mathematics skills | Do investigations | |
Explaining to other students | Play mathematical games | |
Talk about your work to the whole class | Use models and materials | |
Solve projects | Do mathematics problems | |
Make posters and mathematical displays | Explore puzzles |
Question 3
Please write a number in for each statement (‘1’ indicates your first choice, ‘2’ indicates your second choice, ‘3’ your third choice, etc. down to ‘6’ your last choice).
I like mathematics because….
3a) | We get to discuss with each other | |
3b) | We do lots of practical work | |
3c) | We try to solve problems we have | |
3d) | We get to discover new ideas | |
3e) | We get to show the other how we do things | |
3f) | We learn about important mathematical ideas |
Mathematics is important for my future because:
3g) | It helps me to think | |
3h) | It is about solving problems I have | |
3i) | It teaches me lots of useful things | |
3j) | It helps me to be creative | |
3k) | I learn to tell other about my ideas | |
3l) | It shows me that all kinds of problems are interesting |
Question 4
Rate 5 (Strongly agree)–1 (Strongly disagree) (Tick one box in each row)
5 | 4 | 3 | 2 | 1 | ||
|---|---|---|---|---|---|---|
4a) | Mathematics is one of the most worthwhile and necessary subjects to study at school | |||||
4b) | I am no good at mathematics | |||||
4c) | In mathematics class, I listen carefully and pay attention | |||||
4d) | Girls often have to work harder than boys to do well in mathematics | |||||
4e) | I get confused and frustrated when I do mathematics | |||||
4 f.) | As an adult I will not use much mathematics in everyday life | |||||
4 g) | I study mathematics because I know how useful it is | |||||
4h) | Mathematics is a subject I need to study so I can get a good job in the future | |||||
4i) | I give up trying to work on mathematics when I cannot understand it | |||||
4j) | Mathematics problems should always be solved by following rules | |||||
4k) | To learn mathematics you do not need to explain what you are doing | |||||
4l) | In mathematics, it is possible to have more than one right answer | |||||
4 m) | In mathematics, there should always be one right answer | |||||
4n) | My teacher is good at explaining mathematics | |||||
4o) | During mathematics, we usually work on our own | |||||
4p) | Mathematics is like a different language to me | |||||
4q) | We use lots of materials (resources to learn mathematics) | |||||
4r) | My mathematics teacher thinks some problems are too difficult for me | |||||
4 s) | My teacher encourages me in mathematics |
Question 5
Rate 5 (Excellent)–1 (Weak) (Tick one box in each row)
5 | 4 | 3 | 2 | 1 | ||
|---|---|---|---|---|---|---|
5a) | How good are you at mathematics? | |||||
5b) | How good would you like to be at mathematics? | |||||
5c) | Where would your teacher put you on this scale? | |||||
5d) | Where would your mother put you on this scale? | |||||
5e) | Where would your father put you on this scale? | |||||
5 f.) | How good do you think your mother would like you to be at mathematics? | |||||
5 g) | How good do you think your father would like you to be at mathematics? | |||||
5h) | Where would your friends in class put you on this scale? |
Appendix 2
Stages of Mathematical Well-Being
Stage 0: Awareness of mathematical activity At this first stage the learner is aware of mathematics, not as a coherent body of knowledge but as a collection of mathematical activities. There is an awareness of the different nature of these from other school activities |
Stage 1: Recognition and acceptance of mathematical activity The learner recognises mathematics as a coherent activity, different from a language or a sport activity and it is accepted as a similarly worthwhile pursuit. The learner feels comfortable in the mathematical learning context, although having a passive acceptance of such experiences and being disinclined to seek them out |
Stage 2: Positively responding to mathematical activity At this stage, mathematical activity invokes a positive response. More than just acceptance of the activity, here there is a welcoming of it and some pleasure in its pursuit and in its achievement. This pleasure develops feelings of self-confidence and positive self-esteem, which reinforce the acceptance and worthwhileness of mathematical activity in general |
Stage 3: Valuing mathematical activity At this stage the learner appreciates and enjoys mathematical activity to the extent that there is an active seeking out of those activities, and of people with whom those activities can be shared. The learner reaches acceptably high (to them) levels of mathematical competence |
Stage 4: Having an integrated and conscious value structure for mathematics At this stage the learner has developed an appreciation of mathematics, of how and why they value it, and where that valuing might lead them in the future. An awareness grows of the human development of mathematical knowledge, and of one’s place in the mathematical scheme of things |
Stage 5: Independently competent and confident in mathematical activity At this stage the learner is a fully independent actor on the mathematical stage. Sufficiently independent to be able to hold one’s own in mathematical arguments at various levels, the learner is able to criticise other’s arguments from well-rehearsed criteria |
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Bishop, A., Kalogeropoulos, P. (2015). (Dis)engagement and Exclusion in Mathematics Classrooms—Values, Labelling and Stereotyping. In: Bishop, A., Tan, H., Barkatsas, T. (eds) Diversity in Mathematics Education. Mathematics Education Library. Springer, Cham. https://doi.org/10.1007/978-3-319-05978-5_12
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