A key expectation of Grade 8 Algebra students is student note taking and teaching an adult what is learned daily. This cycle of note taking, student class room practice and student as teacher for an adult is designed to make learning visible and also make learning gaps visible. When the student knows what he or she knows or doesn't know, the student can take steps toward mastery. Visible learning gaps are the foundation blocks of building mastery.
In our first month, we have discovered that note taking and student as teacher can both improve. The objective of this post is to provide some constructive suggestions for note taking that can in turn help to structure the student-adult teaching interaction. We will continue to highlight and reinforce good note taking in class, mirroring the steps here.
1. Each classroom lesson has at least one big idea, or key point. A good example is the two day lesson in Algebra 1 on polynomial division. The first big idea was that the divisor determines the process we use in division. If the divisor is a monomial, looks like (3x), we use a fraction method. If the divisor is a binomial, looks like (x - 3), we use long division.
2. Beneath the big idea of the lesson there are process steps to follow in an orderly, methodical way. The process steps often have a key first step and also pitfalls to avoid. In the case of the fraction method noted above, we simplify the integers first, then the variables. A pitfall to avoid is forgetting to use the integer 1 when simplifying or canceling variables. In the case of long division, terms in the dividend must appear in order from greatest power to least and all powers must be represented. If a power is missing in the stated problem, we insert zero times that power when we set up the long division. For example, if the x term is missing, we include (+0x) in the dividend. A key step in long division is duplicating the first term on the subtraction line. Another key step is remembering to subtract, or distribute the negative, over both terms on the subtraction line.
3. Adults can help students with note taking by beginning the at home student as teacher lesson by asking the student to show the adult the notes and where the big idea and process steps appear in the notes.
A typical student as teacher lesson at home might begin this way:
a) Here are my notes from today.
b) We worked on polynomial division. The big idea is that the divisor determines the method. Let me show you the kinds of divisors we see. They look like (3x) or like (x - 3) for example. We use a fraction method for (3x) and a long division method for (x -3).
c) The fraction method was easier since we just simplify the fractions we create by making the divisor the denominator of fractions with the terms of the polynomial as the numerators.
The class lessons follow this general pattern of big idea, process steps, common pitfalls to avoid and guided practice that allows students to use their notes with sample problems. As the first few students complete their work on the guided practice problems, we begin doing the problem on the board to prompt the rest of the class through the problem. These prompting steps help students stay on track, overcome bumps that have them stuck, confirm good processes, and allow for additional note taking.
Another area where adults can help at home is showing the student where their gaps have become visible. For example, if the student is solid on the fraction method above, but is struggling to set up the long division process that specific topic needs to be a question posed by the student in class the next day. A good suggestion would be to say to your student, "Here is a long division problem I am unable to complete as the adult student. Please take this problem to Mr. Hawkins tomorrow so he can help everyone with it. If I am stuck, someone else probably is, too."
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