Having taught in a couple of different school districts over the past couple of years and after conversations with teachers in other school districts, I have really started to wonder about the appropriate placement of Geometry in the high school math curriculum. I have seen many approaches, but I am not sure any of them is ideal.
My previous school district took on the most traditional approach: Algebra 1 first, Geometry in the middle, and Algebra 2 last. The idea is that students need a solid Algebra foundation (mostly equation solving) for many of the concepts that they see in Geometry. Some see breaking up the two years of Algebra as a pro as well. They feel that students that dislike Algebra will become more interested in math when they see Geometry in year two.
At my present district, though, the stance is taken that students will benefit from taking the two Algebra courses successively. It is also reasoned that students receive enough equation solving exposure in junior high to be successful in a high school Geometry course. In my first two months teaching freshman Geometry courses, though, I have had a couple of concerns. Some students’ algebra skills are weak enough that I do feel it interferes at times. I find myself taking for granted that my students will have a certain algebraic skill only to find that I have to back-track and slow down. The more advanced students pick up on it quickly, while others tend to struggle. It is still early, so I am keeping an open mind to see how this plays out the rest of the year. Another concern of mine is that my freshman are not always mature enough as learners for the challenges that Geometry presents. In this course, there is so much application and visual/spatial reasoning. This seems to be a huge transition from junior high mathematics.
Yet another sequence I have heard about in a nearby district is to “sandwich” Geometry in the middle of Algebra 1. Their students take the first term of of Algebra 1, then take both terms of Geometry, followed by the second term of Algebra 1. Algebra 2 comes last. The rationale is that in the first half of Algebra 1, the focus is generally on equation solving and linear functions, which is primarily what is needed for Geometry. Then, the more difficult concepts in Algebra 1 would come after students complete the full Geometry course. While this would seem to address my concern about students’ lack of Algebra skills, I still wonder if they would be lacking some cognitive maturity.
So this brings me to the question that has been in the back of my mind for a while... would it be appropriate for students to take Geometry last? The more I think about it, the more I like it! I like that students would take Algebra 1 and Algebra 2 successively. I like that they would have very solid algebra skills at the onset. I like that they would be more mature learners and would be seeing the most intense proof content later in their career (and closer to college). So then, why is this not a common practice???
I would love to get some feedback from fellow math teachers. What is happening at your school? What are the pros and cons? What do you think about the “Geometry last” idea? Do you know of any research done on this topic?
My previous school district took on the most traditional approach: Algebra 1 first, Geometry in the middle, and Algebra 2 last. The idea is that students need a solid Algebra foundation (mostly equation solving) for many of the concepts that they see in Geometry. Some see breaking up the two years of Algebra as a pro as well. They feel that students that dislike Algebra will become more interested in math when they see Geometry in year two.
At my present district, though, the stance is taken that students will benefit from taking the two Algebra courses successively. It is also reasoned that students receive enough equation solving exposure in junior high to be successful in a high school Geometry course. In my first two months teaching freshman Geometry courses, though, I have had a couple of concerns. Some students’ algebra skills are weak enough that I do feel it interferes at times. I find myself taking for granted that my students will have a certain algebraic skill only to find that I have to back-track and slow down. The more advanced students pick up on it quickly, while others tend to struggle. It is still early, so I am keeping an open mind to see how this plays out the rest of the year. Another concern of mine is that my freshman are not always mature enough as learners for the challenges that Geometry presents. In this course, there is so much application and visual/spatial reasoning. This seems to be a huge transition from junior high mathematics.
Yet another sequence I have heard about in a nearby district is to “sandwich” Geometry in the middle of Algebra 1. Their students take the first term of of Algebra 1, then take both terms of Geometry, followed by the second term of Algebra 1. Algebra 2 comes last. The rationale is that in the first half of Algebra 1, the focus is generally on equation solving and linear functions, which is primarily what is needed for Geometry. Then, the more difficult concepts in Algebra 1 would come after students complete the full Geometry course. While this would seem to address my concern about students’ lack of Algebra skills, I still wonder if they would be lacking some cognitive maturity.
So this brings me to the question that has been in the back of my mind for a while... would it be appropriate for students to take Geometry last? The more I think about it, the more I like it! I like that students would take Algebra 1 and Algebra 2 successively. I like that they would have very solid algebra skills at the onset. I like that they would be more mature learners and would be seeing the most intense proof content later in their career (and closer to college). So then, why is this not a common practice???
I would love to get some feedback from fellow math teachers. What is happening at your school? What are the pros and cons? What do you think about the “Geometry last” idea? Do you know of any research done on this topic?
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