Gender issues in Mathematics

Gender in Mathematics presentation

Algebraic Thinking in the Early Years

In Carolyn Kieran’s reaction article on theories of algebraic thinking, she discusses a model with 3 components:

1. the generational activities of algebra-rules governing numerical relationships, variables and unknowns, the equal sign and the equation solution.
2. The transformational (rule-based) activities-collecting like terms, factoring, expanding, substituting, etc.
3. Global, meta-level, mathematical activities-problem solving, modeling, change, relationships

In the examination of different approaches on preparing students for algebra, Kieran goes on to note there is no international consensus on what is algebraic thinking and how best to teach it. She mentions the Chinese curriculum, where its goal is to understand quantitative relationships as well as the Singapore primary mathematics program which focuses on problem solving and relationships. The Korean curriculum focuses on relationships and structure as well as problem solving. The U.S. seems to stand a bit apart, instead focusing on number patterns and generalizations.

Kieran does point out the commonalities between the programs in the development of algebraic thinking: relationships, generalization, justification, problem solving, modeling and structure.

I found Kieran’s article to be insightful and agreed with many points. I found it interesting that many of the curricula in Asia were similar, in that they focus on problem solving and relationships. I have certainly noticed a difference between the mathematical abilities of students who have used the textbook I’m most familiar with, Singapore Math, and students who have come from schools using different texts, such as Math Makes Sense, without such a strong focus on operations and understanding.

I also didn’t consciously realize that there could be students operating with an arithmetic frame of mind and those with an algebraic way of thinking in my classroom. After Kieran’s description of the difference, I feel I could confidently identify most of my students as one or the other.

In several sections of the article, Kieran mentions the importance of the equal sign and that students understand its meaning. It reminded me of an activity another teacher once did with a group of elementary teachers: 11 + 4 = ____ + 3 = _____ + 7 = _____. Most teachers said the answer is 25!

Kieran mention 5 items that should be focused on to succeed in algebra: relations, operations and their inverses, representing and solving problems, numbers and letters together and the meaning of the equal sign.” In your experience, do you think students have a good understanding of these concepts? Or do you find you need to review/re-teach some of them?