I want to preface this blog entry by saying it will be longer than usual and contain more math-specific content. I will try to elaborate as best I can for the non-math teachers out there to understand.
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As many of my readers well know I am definitely what some would call an "independent spirit" when it comes to my pedagogy. Others might call that "rebellious" but I choose to think of myself as one who can be swayed by a valid, reliable argument.
With that in mind I would like to share a recent frustration that I have with the School District of Philadelphia in the context of the Algebra 1 course that I am teaching. From my understanding and short experience (although 3 years teaching is already more than a lot of folks out there), the progression at the beginning of the course is something like the following:
1) Review pre-Algebra topics including the order of operations (PEMDAS)
2) Connect these topics to patterns in nature and the world to analyze
3) Discuss algebraic representations (the variable x, etc) and apply to these situations
4) Connect patterns and algebraic representations to create a linear graph
There are obviously more things to do inside each topic but this is what I think makes sense for the start of the class.
Now, contrast that with the most recently updated Planning and Scheduling Timeline from the School District of Philadelphia. I will quote the "eligible content" here:
1) A1.1.1.1.1: Compare and/or order any real numbers. Note: Rational and irrational may be mixed.
2) A1.1.1.1.2: Simplify square roots
3) A1.1.1.2.1: Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.
4) A1.1.1.3.1: Simplify/evaluate expressions its equivalent forms. involving properties/laws of exponents, roots, and/or absolute values to solve problems. Note: Exponents should be integers from -10 to 10.
5) A1.1.1.4.1: Use estimation to solve problems.
6) A1.1.1.5.1: Add, subtract, and/or multiply polynomial expressions (express answers in simplest form). Note: Nothing larger than a binomial multiplied by a trinomial.
7) A1.1.1.5.2: Factor algebraic expressions, including difference of squares and trinomials. Note: Trinomials are limited to
the form ax2+bx+c where a is equal to 1 after factoring out all monomial factors.
8) A1.1.1.5.3: Simplify/reduce a rational algebraic expressions.
I completely agree and have been focusing on teaching the first five points they suggest. But at point 6 I respectfully and wholeheartedly disagree with their plan.
For those uninitiated folks, a "polynomial" is something like 5x^2 + 2x - 1. What the District suggests we do is emphasize those types of expressions before we help kids understand the concept of simpler ideas like a "linear equation" (ex. y = 2x + 3). Then they go on to request (at point 7) that we teach the kids to factor these expressions when the kids don't know how they were created in the first place!
I definitely do not understand the rationale behind all of this and wish I could discuss this with the person (or people) who created it. Maybe they could explain to me why this progression is pedagogically sound. In the meantime, if I don't teach this content in the "proper order" then my students will perform poorly on benchmark assessments this year. Since we do not want that to happen, I am being forced to teach according to a plan that I fervently think has little relation to proper pedagogy.
-----
As many of my readers well know I am definitely what some would call an "independent spirit" when it comes to my pedagogy. Others might call that "rebellious" but I choose to think of myself as one who can be swayed by a valid, reliable argument.
With that in mind I would like to share a recent frustration that I have with the School District of Philadelphia in the context of the Algebra 1 course that I am teaching. From my understanding and short experience (although 3 years teaching is already more than a lot of folks out there), the progression at the beginning of the course is something like the following:
1) Review pre-Algebra topics including the order of operations (PEMDAS)
2) Connect these topics to patterns in nature and the world to analyze
3) Discuss algebraic representations (the variable x, etc) and apply to these situations
4) Connect patterns and algebraic representations to create a linear graph
There are obviously more things to do inside each topic but this is what I think makes sense for the start of the class.
Now, contrast that with the most recently updated Planning and Scheduling Timeline from the School District of Philadelphia. I will quote the "eligible content" here:
1) A1.1.1.1.1: Compare and/or order any real numbers. Note: Rational and irrational may be mixed.
2) A1.1.1.1.2: Simplify square roots
3) A1.1.1.2.1: Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.
4) A1.1.1.3.1: Simplify/evaluate expressions its equivalent forms. involving properties/laws of exponents, roots, and/or absolute values to solve problems. Note: Exponents should be integers from -10 to 10.
5) A1.1.1.4.1: Use estimation to solve problems.
6) A1.1.1.5.1: Add, subtract, and/or multiply polynomial expressions (express answers in simplest form). Note: Nothing larger than a binomial multiplied by a trinomial.
7) A1.1.1.5.2: Factor algebraic expressions, including difference of squares and trinomials. Note: Trinomials are limited to
the form ax2+bx+c where a is equal to 1 after factoring out all monomial factors.
8) A1.1.1.5.3: Simplify/reduce a rational algebraic expressions.
I completely agree and have been focusing on teaching the first five points they suggest. But at point 6 I respectfully and wholeheartedly disagree with their plan.
For those uninitiated folks, a "polynomial" is something like 5x^2 + 2x - 1. What the District suggests we do is emphasize those types of expressions before we help kids understand the concept of simpler ideas like a "linear equation" (ex. y = 2x + 3). Then they go on to request (at point 7) that we teach the kids to factor these expressions when the kids don't know how they were created in the first place!
I definitely do not understand the rationale behind all of this and wish I could discuss this with the person (or people) who created it. Maybe they could explain to me why this progression is pedagogically sound. In the meantime, if I don't teach this content in the "proper order" then my students will perform poorly on benchmark assessments this year. Since we do not want that to happen, I am being forced to teach according to a plan that I fervently think has little relation to proper pedagogy.
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