This one goes out to all the algebra teachers; especially those in middle school. Anyone notice that kids “get it” in 7th grade and then act like they have never seen a variable once they hit algebra? Or am I the only one? We had nearly 70% of our 7th graders proficient and above on last year’s CST’s, but only 40% of our algebra students were proficient. If you take the advanced classes out of the mix, it is more like 60% to 30%. I know, I know, you can’t base what a kid knows solely on a standardized test. But, those numbers are pretty indicative of how the kids actually do in class. Some will say that algebra is just too abstract for most 8th grade kids. I don’t know if I buy that, especially when I read articles like this.

I am going to have some release time once testing is over in order to adjust our pacing guides and I would like to be able to develop some lesson ideas to help our teachers bridge the gap between number sense and algebraic thinking. Maybe some of you have already tackled this. I would love to hear what you have done. How have you sequenced your 7th grade curriculum and how have you helped move your students from numeric fluency to algebraic proficiency? I figure if I am going to lock myself in a room and try to hash this out, you may as well be there with me!

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Love the idea of company when you lock yourself away to work.

*sigh* I work with high schoolers, but I know exactly what you mean. (Currently tutoring an Algebra 1 senior who has flashes of insight and then lapses of memory.) Not sure I have any other ideas, though I do like what Mr. K talked about with solving equations.

Boy, those kids in Lebanon! I get the feeling that for some kids we’re forcing them into Algebra at the expense of their concrete understanding of numbers/quantities and measurements. How do you do Algebra without acing that stuff? I don’t think you do.

Dan Greene‘s school does an interesting thing in teaching a numeracy remediation for two years to many students – though I don’t think that’s the solution you’re looking for. I’m thinking of adding on a chunk of numeracy review to the beginning of my algebra class next year. It might even be a unit on measurements. Like measuring distances, areas, volumes, and speed. Making sure that students understand the units and are able to manipulate them, estimate with accuracy, and get some good fractions and decimals in.

That said, I haven’t started on this, so that’s my first reaction.

@Sarah

Yeah, working alone can be, well, lonely. I figure that I have gotten more great ideas from reading all your blogs that I should probably invite you to the conference room w/ me. I feel your pain when dealing with HS algebra students. I spent 11 years teaching HS before I took my current position. A senior in algebra is a different animal than an 8th grader…that’s for sure. Thanks for the link.

@Nick

I think we have decided that number sense is the place to start. It seems that if we can get kids to really understand not just fraction, decimal facts, but what they really mean. 2/3 isn’t just a number less than one. When one says 2/3, the first question should be “2/3 of what?” If we can get kids to ask that question, having them learn about 2/3 x won’t be so hard.

I think you are right when it comes to having them work with measurements. Measurements give concrete meaning to numbers and if we can help them make connections between the meaning of numbers within one set and how they relate to numbers in another set and maybe even make a generalization about that relationship, then we are on our way to teaching algebra.

Students at the middle-school level would benefit from remedial instruction for number sense, simple geometry, and measurements. Also, at the upper end of middle school and offered at the beginning in high school should be Pre-Algebra. Algebra in high school, which is really just a more generalized form of Arithmetic, is no more abstract than a student’s own natural language. In fact, much of the complicated human context found in other subjects (such as the social sciences and English literature) is removed or simplified – making Beginning Algebra simpler to study.