Reflecting on Tuesday and Thrusday

This week went by so quickly for me. It's hard for me to remember what happened because it has been such a blur. However, there are some things I need to hash out.

Tuesday
I taught a lesson on factoring trinomial squares. I think what is working is showing them multiple examples to try to cover as many possible cases as possible. This works for my students that are still concrete thinkers. It works for them because they will not get distracted or discouraged by the abstract ideas of trinomial squares. What is not working is getting my students to understand the importance of the relationship between factoring trinomial squares and FOIL. The way they are related is that FOIL checks the solution of the factoring. In other words, factoring is the reverse of FOIL. The reason this is important to realize is because my students have a tool they can use to check all their solutions. However, they do not check and they end up missing points on tests because of that.
For my next lesson, I do plan on explaining the concept of trinomials. The concept is that a trinomial represents the area of a rectangle and the factors represent the dimensions of the rectangle. By using Algebra tiles, I can connect the procedure of factoring trinomials to a visual representation.

Thursday
I taught a lesson on factoring trinomials directly and using Algebra tiles. The Algebra tiles worked really well. By the end of the period, almost all my students were understanding the lesson. The tiles helped my concrete-thinkers see the factoring in an abstract way. It is abstract there are many ways to configure the tiles, but there is only one way that will form a rectangle and lead you to the solution. Unfortunately, this method did not work for my students who prefer the direct way to factor trinomials. However, I taught them the direct procedure as well. Although they cannot picture how to arrange the tiles, they can work with the numbers and still get the right answer.
I think I could have done more to connect the procedure to the concept of factoring trinomials. In order for them to see the connection, I should have explained the correlations between the arrangements of the squares and how to factor the trinomials. For the next lesson, I plan on having my students reflect on the correlations by asking them guiding questions to see if they can discover it on their own. Either way, I think they will gain a deeper understanding of the concept of factoring trinomials.