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Problems with Common Core Math
I’ve written about the difficulties in helping students with math in a common core curriculum. One cause of these difficulties appears to be the number of skills required to solve just one math problem.
Due to the way Common Core Math is taught, it may require 10 or 20 specific skills to solve just one math problem. A weakness in ANY of these specific skills may result in student failure.
Furthermore, the complexity of these problems make it almost impossible to ‘diagnose’ with which specific skills the student is struggling.
Below is an actual common core third grade math problem.
“Jennifer’s Mom canned six jars of peaches. If Jennifer’s Mom cans three more jars of peaches and cans 45 peaches in all, how many peaches are in each jar?”
We'll skip over the fact that this is the 21st century--not the eighteen hundreds--and many children have no idea what canning peaches is, look at the steps required to solve this third grade math problem.
- Understand that the answer “Y” requires dividing the total number of peaches “N” by the total number of jars “X”.
Equation: Y = N / X or Y = 45 / X
- Understand that the total number of jars “X” equals the number of jars already canned “A” plus the number of jars she intends to can “B”. Equation: X = A + B
- Substitute A + B for X to get the Equation: Y = N / (A + B)
- Order of Operations. Solve (A + B): (6 + 3) = 9
- Y = 45 / 9
- Y = 5
Let’s take a look at the skills and concepts required to solve this third grade math problem.
- Reading Comprehension
- Reading Retention
- Grammar: statements and interrogatives
- Vocabulary: “canning”, “jars”, “more”, “in all”, “how many”, “in each”, “peaches”
- Deductive reasoning: understanding that jars canned in the past plus jars to be canned in the future equal the total number of jars.
- Math Concept: Addition
- Math Concept: System of Equations
- Math Concept: Variables and Constants
- Math Concept: Substitution Method
- Math Concept: Properties of Equality
- Math Concept: Order of Operations
- Math Concept: Division
This is a simple third grade math problem that requires six operations and 12 specific mathematical concepts to arrive at the correct answer.
Now, if that weren’t bad enough, several if these concepts are NOT even taught until the 6th, 7th, and 8th grades. So how is the third grade student supposed to solve this equation?
Well, I think the precise pedagogical term would be, magic.
I am not kidding. I specifically asked about this problem and the explanation from a common core teacher was that the student is NOT supposed to mathematically solve the problem. They are expected to intuitively (magically) solve the problem using trial and error.
I’m sorry, but in my opinion, this is NOT teaching math. It may make a nice theoretical discussion about math, but trial and error guessing is not math.
Most children, but especially Visually Dominant creating thinkers need to understand the principles underlying the solutions. Visually Dominant thinkers extrapolate the specific from the general.
Yes, most children do generalist from the specific. You show them two or three specific examples and they will generalize from those examples. This pedagogy works well for 85% of students so it makes sense that virtually every text book and every curriculum is set up so that students can generalize principles from specific examples. This is classic INDUCTIVE reasoning.
Unfortunately, Visually Dominant students, like those with dyslexia, ADHD, and Autism, are EXACTLY THE OPPOSITE. We learn by DEDUCTIVE reasoning. If you teach us the General Principles and we will Deduce the specifics.
Obviously, schools are NOT going to throw out their entire curriculum to accommodate 15% of students while alienating the other 85%. So, what’s the answer?
Students, especially Visually Dominant students need to be taught how to learn using their natural strengths and abilities—eidetic memory, pattern recognition, deductive reasoning, organization by patterns and relationships, etc. Once students have the skills to learn, the curriculum becomes irrelevant.
For more on dyslexia, education, and learning strategies, consider “Reading with Dyslexia” and “Finding Your FACE” and "Math Made Easy" as helpful resources.