discussion post and 2 one paragraph peer response 7

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:

Discuss some of the difficulties of incorporating algebra into the elementary classroom.
Remind us of the activity you mentioned in the week one forum that you have used in your classroom.
Discuss how you would begin to adapt this activity or create a new one to fit the topics that we have covered in this course. In particular, how will it address the issues raised in this article.

Peer Response 1
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 doesnâ€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 Sierpinskiâ€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

One of the biggest difficulties in incorporating algebra into the elementary classroom that I have seen is the lack of understanding of the strategies and content by the teachers. When this happens, teachers fall back into using what the methods they learned or even skimming over the material to say they taught it and move on. It makes us uncomfortable to not have the understanding but we donâ€t always want to speak up. Then the students have gaps in their learning and they cannot make the connections that will allow them to build on the knowledge is future years.

The activity that I have used, is “Gifts From Grandma” from Illustrative Mathematics, https://tasks.illustrativemathematics.org/content-standards/3/OA/A/3/tasks/262. In the word problems, they need to find different unknowns using their understanding of patterns to help them. The three parts of the problem are about grandma and the grandchildren, but the information is different and not connected to the part before it. (Part a find out how much money grandma spent, Part b find out how many games were purchased, and Part c how much did each grandchild get.)

The first thing I would do to adapt this activity, I would make the parts of the word problem build on each other so that more patterns could be observed. This would allow for the use of a T-chart or function table to find the papers between money spent, grandchildren, and games they each get to play. The task as currently written uses multiplication with the unknown in a different place in each part. In using a t-chart, the teacher needs to be aware of how the students are using it and making sure that they are finding the patterns that lead to the equations.

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