Strategy to use in Mathematics Classroom

In researching for my Inquiry Project I came across a teaching strategy that I believe is worth sharing. In the article, Strategies For Teaching In Heterogeneous Environments While Building A Classroom Community by Hayley Lyn David & Robert M. Capraro () they discuss a strategy developed by Zemira R. Mevarech & Bracha Kramarski called IMPROVE. This strategy involves the following steps:

1)      Introducing new concepts: teacher introduces concept to the whole class.

2)      Metacognitive questioning: students are placed in small (2-4 students)heterogeneous groups to engage in metacognitive questioning (they take turns asking 3 kinds of questions: i)comprehension(articulate main ideas in problem, classify problem in appropriate category, and elaborate the new concepts; ii) strategic (questions that refer to appropriate strategies for solving the problem  and, iii) connection (questions that often refer to similarities and differences between the posed problem and other problems previously solved.

3)      Practicing: students cooperatively work to develop and agree on a working solution.

4)      Reviewing and reducing difficulties: through questioning the students review and reduce difficulties; students worked from different perspectives and checked their work to find the simplest solution.

5)      Obtaining mastery: as students practice cooperative learning through metacognitive questioning, each student mastered each concept at various rates.

6)      Verification: along with teachers’ observations and informal assessment, the students are given a formative test to verify mastery.

7)      Enrichment: students who master the concepts move on to enrichment tasks.

David, H. L., & Capraro, R. M. (2001) Strategies for teaching in heterogeneous environments

     while building a classroom community. Education, 26, (1), 80-86.

Girls/Boys/Learning Styles/Gender Equity.........

In chapter nine Boaler discusses Boys, Girls, and Learning Styles.  Boaler states that the ‘greatest disadvantages were experienced by the girls mainly because of their preferred learning styles and ways of working” (p.137). She contends that girls from the highest sets at Amber Hill underachieved because of the learning approach the school took. She stated that these girls “seemed to value aspects of mathematics teaching and learning that were not present in their school’s approach” (p. 149). These girls at Amber Hill wanted to ‘understand their mathematics’ (p. 153). Boaler stipulates that mathematics is being widely taught in a way that is not equally accessible to boys and girls, and this appears to relate to the preferences of pedagogy (p. 152).

According to Anthea Lipsett a writer of education issues, formerly for the Education Guardian, “Boys are not innately better at maths than girls, and any differences in test scores is due to nurture rather than nature”, according to researchers (Lipsett, 2008). She quotes research by Prof Paola Sapienza of Northwestern University in the US as saying “The so-called gender gap in math skills seems to be at least partially correlated to environmental factors, the gap doesn’t exist in countries where men and women have access to similar resources and opportunities.” According to data analysed by researchers in 40 countries, boys did tend to outperform girls in math, but in more ‘gender equal societies’ such as Iceland, Sweden and Norway, girls scored as well as boys or better. The research found a striking gender gap in reading skills. In every country girls performed better than boys in reading but in countries that treat both sexes equally, girls do even better.

Paul Blundin (2009) states that just about every scientific instrument in the world have come to a fairly inescapable conclusion that boys and girls learn differently because their brains develop differently. His article says that boys and girls use different learning intelligences to gather information but although it may take effort and stimulation for a brain that has a strong spatial bias to develop its more logical-mathematical abilities, but it can be done. Blundin claims that although boys generally are more capable in the logical-mathematical category this is changing and girls have been gaining ground in this area. He attributes this to how society is desiring to encourage girls in math. Blundin writes, “Cooperative learning experiences that involve more active tasks than just writing, show girls attending to the task more readily and socializing more productively. Boys want to get to the project and get moving and doing”. This comment compares to Boaler’s findings that Phoenix Park girls performed better than Amber Hill girls because at Phoenix Park the girls were free to develop their own styles of working, encouraged to think for themselves, discuss ideas with each other , and work at their own pace. (p. 148)

Blundin ends his article with “Those dedicated to teaching… must see every child as a potentially multi-intelligent child and provide as much stimulation in all the areas as possible.”

I don’t know if I grew up in a home, community, and school who treated boys and girls equally when it came to learning mathematics or not but I don’t remember ever thinking that I couldn’t or shouldn’t be better at mathematics than boys. 

http:www.guardian.co.uk/education/2008/may/30/schools.uk1

http://old.eduguide.org/Parents-Library/Learning-Intelligences-Gender-Behavior-150.aspx

Mathematical Identities

Reading through the text book up to and including chapter 8, I became intrigued by ‘mathematical identities’. It’s interesting how the attitudes and beliefs of the students at both Amber Hill and Phoenix Park influenced how they were able to use math in different situations. As I dug into the topic a little more, I came across a discussion article by Grootenboer and Zevenbergen (2008).

 Grootenboer and Zevenbergen state that it is important to have this discussion about mathematical identities because there is a developing problem with students not being engaged and not participating in mathematics and there is a concern about mathematical achievement as well as poor attitudes toward mathematics (p. 244). In this article the authors discuss how students learn mathematics and continue to develop a mathematical identity through a classroom context. They discuss the three main aspects of the classroom as being the student, the discipline of mathematics, and the classroom community.

The student brings to the classroom community an already developing mathematical identity that has been formed by engaging with family, peers, etc. This identity has already been influenced by ‘their previous experiences of mathematics education’ and these experiences will affect their future learning in mathematics (p. 244). The teacher is a significant feature of the classroom community (p. 245)  but the community also includes the other students and the physical environment.

The authors stipulate that ‘if the goal of mathematics education is to develop a strong mathematical identity, then the critical focus is the relationship between the student and the discipline of mathematics’ (p. 245) and the ‘facilitating context for the development of this relationship is the classroom community, and specifically the teacher’ (p. 245).

Grootenboer and Zevenbergen  discuss that the classroom community is only temporal , and the only thing that will last is the mathematical identity which is the connection between the student identity and mathematics.  The teacher is the bridge between the student and mathematics. The teacher must be knowledgeable in the area of mathematics and must have a well-developed mathematical identity himself/herself. The teacher should have ‘a positive attitude towards the subject, a sense of joy and satisfaction in undertaking mathematical practices’ (p.246). The teacher must also have a relationship with the students because it is the teacher’s role to facilitate the development of students’ mathematical identity thus bridging student and subject (p.246).

From reading this article and the text chapters in Boaler’s work (2002) I have a better understanding of how students develop their attitudes and disposition towards mathematics and how I (as the teacher) have a leading role to play in helping to develop my students’ mathematical identities. It is very important that I seek professional development in mathematics to stay on top of new learning trends and teaching ideas, to give my students a positive outlook on mathematics, and most important develop a relationship with my students as we learn and enjoy math together. I only have them for one year and then they take their mathematical identity with them to another community classroom where they will continue to develop their identity further.

Boaler, J. (2002). Experiencing School Mathematics: Traditional and Reform Approaches to Teaching and their Impact on Student Learning. Lawrence Eribaum Associates: Mahwah, New Jersey.

Grootenboer, P. J., & Zevenbergen, R. (2008). Identity as a lens to understand learning mathematics:

Developing a model. In M. Goos, R. Brown, & K. Makar (Eds.), Navigating currents and charting

directions (Proceedings of the 31st annual conference of the Mathematics Education Research Group of

Australasia, Brisbane, Vol. 1, pp. 243-250). Brisbane: MERGA

http://www.merga.net.au/documents/RP262008.pdf

Janna and I are responsible to lead discussion for the week of Nov. 9th  to 15th.