First, read the article on instructional strategies for incorporating algebraic reasoning into an elementary classroom posted under the week 5 documents.
In at least 250 words, please respond to the following:
Peer Response 1
Craig
Several obstacles exist that limit exposure of algebraic concepts to elementary students, most of which have already been touched upon by my classmates: teacher limitations, student understanding, and curriculum scope included. Being real here about elementary teachers (I am one), most of us are not mathematicians by trade. I took a couple of college-level math courses but never went beyond that and never with any real purpose. When I completed coursework in Algebra and Algebra II roughly 25 years ago, I never anticipated teaching algebraic concepts.
One of my biggest pet peeves as a teacher—of 5th and 6th grade students—is when students have learned that quotients are always less than their dividends or divisors, products are always greater than their factors, sums greater than their addends, and differences are always less than the subtrahend and minuend. As a teacher I fear teaching a “rule†that turns out not to be a rule. I do not want to further add to student misconceptions. Reading the article this week, I kept waiting for the teacher to ask the students if the equation they developed would be true for all values of n. If n were 0, would there be two people sitting at 0 tables? While the equation may have been true for all positive integers, it was not true for 0, fractions, or negative integers. Personally, I am conflicted about using this example to generate a discussion… but I appreciate the activity for its power to get students to recognize patterns.
In week 1, I discussed the 6th grade standard of factoring algebraic expressions using the distributive property and how we use area models to facilitate student learning. I supposed this is an elementary algebra topic and doesn’t really fit into what we have discussed this far with regard to patterns and linear equations. A new activity I could work into this conversation would be Sierpinski’s Carpet from Illustrative math. This is math task that I often give to my honors students as it deals with exponential patterns and rational numbers. The first few steps of the pattern are given to the students, who then work to determine the area of the carpet at the 9th iteration.
Link to the task: https://tasks.illustrativemathematics.org/content-standards/tasks/1523
Peer Response 2
Jennifer