The chapter by Abreu & Cline had me going down memory lane in a lot of ways. It reminded me especially of the time in Grade 3 when I was learning long division. I came home somewhat confused and asked my mum for help. She couldn’t understand why I was learning division in such an inefficient way; she then showed me how she learned it. It was certainly a much shorter way, but at the time I felt that I had to learn it the way I was taught in school. My mum did help me, but she thought it was silly. As I got older and more confident I used my mother’s way, but interestingly enough I still teach it the way I was taught in school. What does that say about schooling’s influence…?
I was also saddened to read that there still seemed to be a reluctance of students to bring in ‘home’ knowledge of mathematics into today’s classroom. Actually, I think a better word is surprised. I have seen in different schools how teachers do encourage their students to share their methodologies with the class, and I wondered if this was the exception as opposed to the rule? It also made me go through the Ontario math curriculum again because I was sure that it was written that teachers are encouraged to foster different ideas. However, after reading through several different passages, I found that the idea of using diverse methods was implied as opposed to explicitly stated, such as quotations I have listed below:
Page 12 Curriculum Expectations, para 6 (Grade 11/12 Math curriculum)
“Some examples and sample problems may also be used to emphasize the importance of diversity or multiple perspectives.”
Page 35 Antidiscrimination para 2 (Grade 11/12 Math curriculum)
“Learning activities and resources used to implement the curriculum should be inclusive in nature, reflecting the range of experiences of students with varying backgrounds, abilities, interests, and learning styles.”
I then searched through the IB document I need to use because the IB really fosters the idea of internationalism, and again nothing was stated explicitly:
Page 5 Internationalism (IBO Math SL Study guide)
• students are to learn how the attitudes of different societies towards specific areas of mathematics are demonstrated
It was clear that it is up to teachers to be proactive in the idea of showing students that ‘home’ math could definitely have a place in the classroom. I guess a possible concern that I would address if a student did want to use another method would be that they could demonstrate how the method works. For me, math/tricks without understanding, whether they come from the home or the classroom, will not lead to long-term mathematical understanding. There is absolutely value for learning different ways, but I feel that the students need to understand it, not just memorise it.
With respect to Martin’s chapter, I felt this again reiterates the need for teachers to be very aware of how they treat students when they walk into their classroom on the first day; to ensure that preconceived notions do not enter the room and I find this particularly challenging when we have meetings at the beginning of the year that articulates the strengths/weaknesses, the good/bad of students. For me, this can be somewhat detrimental because then you could walk into the classroom with low or high expectations, which is unfair for the students and yourself. I have discovered that students do change tremendously with various teachers, and year to year. I also agree that we need to remember, “that parents and adults are, along with teachers, the most significant influences on the formation of student attitudes, dispositions and beliefs about mathematics” (p. 148). There may be times when we forget how much influence we have especially with students that may be particularly challenging to us as teachers.
Gina brought up the point that she felt that she did poorly in math because she had “no cultural connections with them [teachers]” (pg. 155). I found this point particularly poignant as I have discovered over the many years how detrimental it can be for both student and teacher if this connection is not made. The challenge then becomes how can we ensure this connection is made? Should the connection be based on culture or on emotion? Can it be one or the other, or should it be both? I am fortunate that I have relatively small classes, but for the larger groups, how can we ensure this connection is made? How can we make sure that a student is not lost when there is so much mathematics needs to be covered?
These are some initial thoughts. I will be back.
Hi Leslie;
ReplyDeleteI've been thinking about your last point about Gina's comment for while now. Earlier this year, I read a study by Kathryn Au and Karen Blake (2003). They had this to say:
.....teachers of diverse backgrounds play an important role in improving schooling, especially for students who share their cultural backgrounds. This appears to be the case because these teachers' backgrounds enable them to empathize with students and to overcome the barriers typically posed by cultural and linguistic differences. (p. 193)
So I wonder if a connection is made when students recognize that their teacher know the realities of their lives and are aware of the inequities in public schools. I think sometimes we get so caught up in making sure things are equal in our classrooms or covering the curriculum, that we ignore the identities of our students.
I wonder if this is what Gina was referring to in her comment. I wonder if an African American teacher, who herself probably went through similar inequities in school, would have served as a role model to Gina and possibly led her down a different path.
I also wonder if this connection is made when the teacher and student share the same cultural identity. Is this even possible?
Those are my thoughts right now but I still have questions about this topic. For example, if identity is a negotiated social construction, then how do we get to know the identities of our students?
Au, K. & Blake, K. (2003) Cultural Identity and Learning to Teach in a Diverse Community: Findings from a Collective Study. Journal of Teacher Education, 54, 192-205
I have (sort of) mixed feelings about bringing in the kind of math that is done at home. While I was reading, I found myself agreeing with Abreu and Cline and feeling sad that students did not value their families' ways of solving math problems.
ReplyDeleteAt the same time, I have had students come in with an easy trick that someone at home taught them for doing the kinds of questions that we were working on in class. Usually the trick was a formula that we were in the process of deriving or something like that. By skipping ahead to the formula, I felt that they were missing out on a lot of learning, both with content and with the process of figuring something out mathematically.
I think that what I experienced was probably very different from what Abreu and Cline are talking about. I certainly don't think that students should be forbidden from using their own ways of solving problems just because some families are quick to supply a formula. However, I'm not sure how to keep that door open while addressing the problem that I had.
Hi Ruthie,
ReplyDeleteI can understand why you would feel distant from the idea of valuing the math the way it is taught at home into your classroom.
I feel that all teachers feel the worry of keeping all the students in the class on the same page. The anxiety of having students who have learned it earlier and asking questions pertaining to that can be dreadful as we struggle not to confuse the other who are not famliar with the concept yet.
There is always a way to deal to with this situation, personally, i would complement the child of having known the formula already but now give them the job to teach there fellow mates how and when it can be applied. If they get stuck somewhere maybe that will be the starting point of explaining how important it is know where the formula comes from rather than just knowing the formula itself.
If they are successful at describing their stance, commend them at their capability and there you have a confident, smart student with leadership qualities.
I feel that studnt success can sometimes occur at small steps and they should be encouraged. If they have learned something that moves them forward in their process of learning, it is only for the best.
It is difficult to lose the power of the "knowledge provider" for a while but at the same we do not want to lose the inqusitive student who does math at home and studies ahead of time because those good skills to posses.