1 Convincing you of your child’s teacher’s expectations.
2 Why does the teacher need that perfection?
3 Why does the easiest math, the foundation, get ignored every class?
4 Foundation taught always comprise of four elements, sometimes five.
5 Here’s how the foundational five, works with a new concept.
6 Did you see what just happened with the retention expectation?
7 Next step? Final two thoughts.
P.S.
1 Convincing you of your child’s teacher’s expectations
Math teachers expect your child to remember math taught in the past. There, I said it. Hmm, don’t think that sentence will move the needle or be enough of a wake-up call for you. Let me have another crack/swat at this and be miles more emphatic and clearer. Take 2: Your child’s math teacher will expect your child to remember 100% of past math taught. If you think about that, it’s ridiculous; who expects 100% perfection from anyone? My words may have moved you a smidgeon more, but I need a massive move, a paradigm shift. A home run with my words that will cause an instant pivot! I got it; here’s the game changer that tosses you upside down. Take 3: Your child’s math teacher is expecting perfection! Perfection, as in past math taught, should be remembered and must be retained. Recalled, in an instant! Okay, I feel better about my words, but less so, as the implication that your child has to look at a math concept and be able to regurgitate something about it instantly, is harsh. Yes, but it’s the reality of being a math student!
The most important part of math is? The foundation - the fundamentals taught each day.
2 Why does the teacher need that perfection?
For students to ‘get’ the new math concept they’re teaching that day, it requires that students remember math taught in previous years. The past math becomes part of the foundation of the new math and 100% recall helps to figure out the new math quicker. A weakness in the past foundation guarantees a weakness in the foundation of the new math.
The easiest part of math is? The foundation - the fundamentals taught each day.
3 Why does the easiest math, the foundation, get ignored every class?
Because it's not deemed important. I'm saying it's not important as it's too easy; well, it should be easy. And it's an emphasis in class, on here's a question and do the question, here's a question do the question, here's another question do the question. It's a focus on doing questions first, second, third … which is only 40% of the required foundation. But success in
doing questions with a know-how of 40% leads to a habit of continued focusing on and 'doing questions'! That 40%, 'question + do the question', is quick to do, and math students crave speed when it comes to math! In other words, the realization that the other 60% is very important, isn't there and in some ways is not on the radar.
What’s the 40%?
The Easy Question and doing that Easy Question (together called an example).What’s the 60%?
Meaning of math words, meaning of math symbols and visual of that question. Together, these five elements comprise the foundation of math taught each day, what I call the foundational five.
4 Foundation taught each day always comprises of four elements, sometimes five.
1) Easy question (usually the first example taught)
2) Easy question done
3) Math words in the question (know their meaning)
4) Math symbols in the question (know their meaning)
5) Easy question done visually (a picture)
Note: this fifth foundation, the picture, isn’t always taught ☹. I’d recommend your child find out the visual as the picture plays a big part in remembering - it acts as a quick review of much of the first four. An example would be if I say, rectangle, it’s a picture that first comes to mind!
These foundational five are the easiest math your child will be taught daily.
These foundational five are the easiest math your child will be taught daily. When I say easiest taught, I mean simplest, most uncomplicated, stress-free, and quick to know, as there is nothing less elementary. Nothing! This means they have to find it easy. But that ‘easiest math’ taught isn’t necessarily going to be easy for your child. If you’re thinking, Yeah, I agree, how can my child make this new foundation easy? Quick answer - by remembering 100% of the old foundation!
Your child has been taught hundreds of concepts, each of which have their own foundational five.
5 Here’s how this, foundational five, works with a new concept,
and I’ve mirrored a math class and made jot-notes on a grade 7 math question (student age 12):
Title of new lesson: Multiply Integers
Easy Question: Evaluate (+3) x (-2)
New math
Math words? none
Math symbols? none
Past math the teacher will expect your child to remember
Math words? Multiply, Integers, Evaluate
Math symbols? +3, -2, ( )( ), x (and knowing how to multiply).
Math words for the symbols, + (positive) and - (negative)
There are two methods to teach this:
Method #1: Understanding (slower), and Method #2 Memorization (quicker).
Method #1: What the teacher will do or should do in that first example is write all the steps and explain it in detail, with the intention to have it become easy.
Evaluate (+3) x (-2)
= (-2) + (-2) + (-2)
= -6
6 Did you see what just happened with the retention expectation?
#1 The (+3) x (-2) became (-2) + (-2) + (-2). The teacher assumed your child remembered that, multiplication is repeated addition.
#2 Teacher did not reexplain how to do the integer addition, (-2) + (-2) + (-2), which gives an answer of, -6. It’s a past foundation where 100% retention is expected.
#3 Math word, Evaluate, never explained and the meaning not given. Why? It’s a math word, students have seen over a hundred time, and the teacher is going to assume they remember what it means.
Review: The teacher expects students to remember 100% of the foundation taught in the past. Let’s say your child has been taught 400 math concepts then, yes, there is an expectation your child will be able to recall all 400! Yeah, that’s a high standard to hold a student to.
Next, the teacher will aim to create a rule out of example 1, as rules allow math to be done faster. They’ll take, example #1, (+3 ) x (-2) = -6, and voice the rule, “When you multiply a positive number by a negative number you’ll always get a negative number. With symbols, they’ll write, (+) x (-) = -
So, about 10% of this new lesson on Multiplication of Integers concept is new, as in, never been taught (the Rule). Everything else is the retention-perfection of past foundations your child’s teacher is expecting.
Then, after example 1, all other examples taught in that class, will use that memorized rule. The focus on the 40%, here’s a question do the question approach, is about to start with the upcoming examples. And that memorized rule will be also used on the homework too, so lost in the teachings is the importance of the meanings of the Word and the Symbol and the Picture - it’s like they get no respect.
In tomorrow’s class, all of this work around Evaluate (3) x (-2) becomes the foundation that has to be remembered. If you’re counting, your child is now at 401 concepts that they have to remember the foundations for.
401 concepts that they have to remember the foundations for.
FYI: The visual of the question, Evaluate (+3) x (-2) becomes a second way to do the question and may or may not be taught. It’s one of foundational five, so yes you child needs to know it. The picture is figured out using a second meaning of the multiply symbol, x, symbol, which is, ‘groups of’. So, (+3) x (-2) means, three groups of -2, which turns out to be a visual of, (-2) + (-2) + (-2). Picture below:
**Here’s Method #2 on, Evaluate (+3) x (-2), being taught, using the memorized rule:
The teacher speaks and/or writes the rule, “When you multiply a positive number by a negative number you’ll always get a negative number. Then with symbols, will write, (+) x (-) = -. Answer, (+3) x (-2) = -
7 Next step? Final two thoughts.
Next step?
I recommend that your child record the foundational five for each new math concept taught. It will help with their retention, they’ll have a resource of foundations for future use, and quick access to past foundations from the past.
Final two thoughts:
When your child only focuses on the 40% of the foundation (question and doing the question repetition), that gets them through the math quicker, but leads to memorization.
Then, when your child gets stumped on doing a question, that means the memorization using that 40% (question and how to do it) is not working. And that’s where that other 60%, the Words, Symbols and Pictures, most definitely can and will help your child get un-stumped, but only if they have not been ignoring them all along!
Knowing the foundational five, don’t ignore them! It makes math easier!
Edison
Edison Hopkinson
Learning strategist to math students and parents
Strategies that remind you why the foundation has to be remembered!
P.S.
Grade 7 math: Here’s a partial lesson of a concept taught for the first time.
Title of new lesson: Solving Equations
Easy Question: Solve x + 4 = 6
New math
Math words? Solve, Equations.
- Solve means find the value of the variable that keeps the equation balanced.
- An equation is when two expressions are equal to each other.
Math symbols? x
- x is called a variable. It means the value of the variable that keeps the equation balanced.
Past math the teacher will expect your child to remember.
Math words? none
Math symbols? x, +, 4, 6, =
In the definitions: Value, variable, balanced, expressions.
Doing the question, Solve x + 4 = 6
x + 4 - 4 = 6 - 4
x = 2
Teacher’s verbal explanation with that first step:
1. I take away four from the left side of the equal sign to get the ‘x’ on its own
2. I also take away four from the right side of the equal sign also, as the symbol, ‘=’, represents a balance.
3. The ‘=’ symbol represents a balance, which means whatever I do to the left side of the equal symbol must be done to the right side of the equal symbol.
Doing the question, Solve x + 4 = 6, visually.
Let’s start with the picture for, x + 4 = 6
Recap
In this question the foundational five are all taught.
It will now be your child’s responsibility to remember 100% of this foundation - all other examples taught in this class will build on this first example, as will all homework, and the next three to four classes.
Solve, Solving is the most important concept in Algebra and shows up in grades 7 to 12 and into university.
Solving shows up in all Word Problems.