Math Curriculum

Writing a proposal very rough draft:

Format:
Background (why I'm writing this proposal)
Introduction (what I'm planning on doing/changing)
Content (I, II, and III)
Summary

Background:

I have been teaching the maths and sciences for nearly ten years.  I've taught in small classes, large classes, and individual one-on-one stufff.....  I've also taught students of all ages, but there are certain things that I've noticed a trend in...  Nearly all of my math students claim to hate fractions.  Even those good at math tend to prefer decimals over fractions.  There's no reason to hate fractions because they make things very accurate, but even good math students hate them.  Maybe it's because they never learned it correctly or something...  I've also noticed that many students that start to need outside help in math start in Algebra 2 or PreCalc when they start learning about logarithms.  Logarithms isn't very hard to learn.  It's just the opposite of an exponential, like taking a square root is the opposite of a square.  But I understand why they find the subject difficult.  It's because they're first introduced to the concept in high school and taught like it's a completely separate thing.  And lastly, I also noticed that Algebra class in high school is the make or break for a lot of students when it comes to learning more STEM-approached stuff later in life.  They'll either make it through Algebra

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Challenge of the month

Jake is looking at Anna.  Anna is looking at George.  Jake is married.  George is not married.  Is a married person looking at a not-married person?  Yes, no, or can't tell?

Answer is yes.  Doesn't matter if Anna is married or not.  If she's not married, then Jake is looking at Anna so yes.  If she is married, then she's looking at George so yes.
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...  so they'll either make it through Algebra fine and go on to Calculus and study science-y related things in college, or they'll completely despise math and go into Statistics to fulfill the math requirements of graduating and will resolve that they will never touch the subject again in college.  The goal of this proposal is to teach math in such a way while the students are in grade school that they will not have to go through these hurdles during their math career and will see STEM subjects in a different light.  Basically they won't be scared shitless of math and science.

Introduction:

How to teach fractions in a way that is less scary?  Well first introduce the fraction notation when kids are learning division.  One of the biggest issues that I see is that kids, even when they're in 10th or 11th grade aren't able to understand that division is the same is fractions.  They see fractions, and in their mind fractions are in a completely different category.  Resolve this issue by having students associate fractions with division early on.  Knowing the terminology such as 'numerator' and 'denominator' are not important at this stage, and can come later on.

How to teach logarithms that won't have kids hating their class?  Teach logarithms when teaching square roots and cube roots.  They know what exponents are in 5th or 6th grade, and they know what square roots and cube roots are by 6th and 7th grade.  Why wait another three or four years before teaching about logarithms?  There's no real difference between logarithms and roots, so just teach them simple logs along with roots.  Of course, students learn about more properties or roots as they mature in math, and so they can learn more about logs later as well, but introduce the subject early on, so the topic isn't scary.

How to change the way students feel about math, particularly algebra?  Start by integrating Algebra concepts very early on, with Algebra notation, so that the Algebra notation itself wouldn't be a shocker when they get to 5th or 6th grade.  Kindergarten students know 2 + 3 = 5.  That means __ + 3 = 5 and __ is 2.  So x + 3 = 5 then x = 2.  and show that 2 = 5 - 3.  (Now I'm getting too much into detail and this should be in the content section).  Instead of having the answer to a word problem be the main focus of the lessons, possible writing them in algebraic notation be a main focus and solving be more of an afterthought.  Because word problems also tend to be a bane of a student's existence.  If kids are learning division and multiplication and fractions, have Algebra with fractions and multiplication and division.  Basically the idea is don't suddenly teach Algebra as a fresh topic in 6th grade, but rather have all of 6th grade Algebra 1 be integrated throughout the 1st through 5th grade material.


Other random shit:

Why keep the multiplication as the 'x'?  Ex:  2x3 = 6.  But what about 2(3)?  This is lost on so many student entering Algebra, although it shouldn't be.  It's the notation.  Notation itself is such a source of confusion, why can't we introduce the notation early on?  If we give the students the association between the multiple notations there wouldn't be any confusion.  So a math worksheet with lots of multiplication for 1st graders could look like a combination of multiple notations with problems that are more or less exactly the same.  Same thing with division...  Use division symbol and fraction symbol as different notations of the same thing.  Introduce parenthesis in kindergarten even!!  They can add multiple numbers already by counting on their fingers.  3 + 5 + 2 = 10!!  But what happens when you do 3 + (5 + 2) =?  Well we do parenthesis first!  It's not a difficult introduction.  It doesn't even make anything more complicated.  Kids can understand these things.  But why wait for 5 more years before parentheses are introduced?