Algebraic Thinking
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Algebraic Thinking

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Rubin_diffalgebra.pdf

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This document helped to remind me that algebra is made up of more than just solving for unknown quantities. When we do algebra in my classroom, that is primarily what we focus on and teach in an explicit manner. However, I can teach generalizations and equalities to also help my students with their thinking. My students are learning these skills to some degree, but I can focus on making my students think about their own thinking with these skills by teaching them in a more explicit way. Teaching what the "=" means is such a basic thing, but could spark conversation and expand student thinking on math as a whole. I will be sure to take my time when teaching algebraic thinking, and will create a conversation-based classroom to cover all of these topics instead of just having my students 'solve for x'.

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Kevin J. Reins :: Mathematics Education

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This article focuses on how students who are in elementary school are capable of handling algebraic thinking. I have seen this myself- my students who are in fourth grade have already learned what variables are and how to use expressions to show indeterminate numbers. In the article, many of the algebraic questions are posed as open ended problems, yet the students seem to have no problem with coming up with answers, even when they are in third and fourth grade. I believe that this study article shows just how capable children are when it comes to learning algebra. In my future teaching, I will be sure to not underestimate my students and expose them to basic algebraic thinking as early as possible. This study also provides some useful practice problems to begin to have students think algebraicly and shows how different students represent their thinking, which is useful for a teacher to see so she can show her students the many different ways of thinking.

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Hands on Equations

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Hands on Equations is a great way for students to think about algebra. It is something that we use in our classroom often to teach algebraic thinking in a concrete way, which is an important step in helping students understand a math topic. Once the children set up visual problems they have created on the balance, they can solve and then share with their peers. When I learned algebra, I never was taught to represent it concretely, but it is helpful to students who are unable to think about algebra in an abstract way. Hands on Equations is a reminder to me that manipulatives are a great way to teach any kind of math!
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Developing Algebraic Thinking through The NBT Standards

Connor Reilly's insight:

These students seem much younger than my students, so I was very surprised to see how they were able to work and use algebraic thinking in this activity. I think that this would be a great way to introduce algebraic thinking strategies to my students. The activity starts with students using manipulatives, but eventually they are able to create rules and use generalizations to solve the problems mentally. I think this would be useful for me as a teacher to see if my students can formulate rules on their own, or if this is something that I need to teach a little more explicitly. I also now see that I should not underestimate my students when it comes to algebraic thinking. Many times the brain thinks algebraically on its own, so it is my responsibility as a teacher to foster that thinking instead of squishing it and simply teaching students 'rules'.

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Thinking Blocks Ratios

Get Thinking Blocks Ratios on the App Store. See screenshots and ratings, and read customer reviews.
Connor Reilly's insight:

This is a great app that can be used to encourage algebraic thinking in all grades. Using manipulatives first is a smart way to get students, particularly younger students, thinking about algebra. It is also important to note that our students are the students who are growing up in the 21st century with technology all around them. Therefore, incorporating technology such as apps into curriculum can assist student learning. Algebra and the use of letters in a subject that is predominantly numbers can be very intimidating to children, so including these manipulatives as a step one can be beneficial to your students' learning.I think that I would use this app with my students who are still struggling with algebra as a remedial lesson.

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