I don't know if I will be able to write all that I have been ruminating on in one post or not. This might have to be done in parts, as I am rev-ing up to begin school here on the 29th.
I also am not sure that this is wanted or needed. But I have felt that I needed to post this for a while now…so here it is.
I am going to divide math education into three parts.
Arithmetic (Basics)
Algebra and Geometry (High School)
Calculus and beyond
In Arithmetic we have the four operations addition, subtraction, multiplication, and division ...henceforth referred to as asmd(also-Add, Subtract, Multiply, Divide).
And as I mentioned in a previous post, we learn this in deepening levels. We start learning about just regular whole numbers and we first add, then subtract, etc.
I have checked in on the other posts. I agree that we want to understand concepts...but these are tools. You do not want to build a screwdriver or a hammer before starting a project. You do not want to have to go to an encyclopedia each time you need to use a wrench to build an understanding of it in order to use it. Before the building project, you need to know the how and why of the use of the tools. Same with the asmd. They are tools. So, YOU MUST KNOW THEM or they can't be tools. They will be stumbling blocks without memorization. Balance here is key. Memorization without understanding is as meaningless as knowing a screwdriver and a screw go together but having no clue that they can screw two pieces of wood together to make a birdhouse. However, without memorization (w/the understanding in place) you will never be fluent in the language of mathematics. Can you imagine if you had to look up the definition to just about every single word you read? I know I wouldn't read any more than I absolutely had to. Yikes. Can you imagine a child who in Algebra has to calculate every single basic addition or multiplication fact and who stumbles over every single division...4 divided by 2. Or how many 9's are in 36?
It is painful to think about. Success (in that and related subjects) would be denied that child. I am not saying that one can not live a valuable and productive life and not know their math facts. I AM saying that one can not have success and feel successful in math and the related subjects w/o the tools or the components of the language. 2+4=6 is a definition of 6. Just like each word in English has a definition. It would be crippling to not know our basic definitions. Same in Math. 9x4=36. No thought required. Understanding complete. Put in toolbox! Next.
Almost all of Arithmetic is ASMD. Of whole numbers, fractions, decimals, percents--and even neg and pos numbers.. We also have the vital ingredients of place value, units--like inch, kg, oz., etc. measuring, and parts and whole, problem solving, etc. But the main math dish here is comprised of those four fundamentals ASMD applied across the different expressions of numbers.
This is pretty much all of arithmetic. Yes, children learn to recognize shapes. A young child recognizes a triangle. And there are many things that have been added in to this stage, even introduction of variables, equations, geometry, etc.
I have nothing against adding all that in. My 7 y/o does know the difference between parallel and perpendicular lines. But I assert, that IF you and your child are struggling in math. The BASICS, as defined here, w/o the extras, are ALL that are required and needed!
Let’s talk math timeline.
Basics (Arithmetic) starts early in normal living...so we will say K or even earlier.
So from Kindergarten (or even Pre-School) to ??? are we learning the Basics?
SCM takes us all through the 12 years to come back to the beginning to plan. Let's do that here too.
If a child is bent to math and wants to be an engineer, architect, mathematician, scientist, computer scientist, businessman, doctor, etc. We are talking college with calculus.
If a child is wanting to be a nurse or non-technical field that requires a college degree...we are probably talking college algebra--and that will possibly be it.
There are also children who never plan to attend a university or do anything that requires a college degree. And then the undecided ones need to leave some options open.
Goal: College Calculus and beyond
Options:
1. Through Pre-Cal (Also called Trig/Pre-Cal) in HS. Can go into college algebra and then into college calculus or sometimes straight into college calculus.
2. Through Calculus in HS or Through AP Calculus w/concurrent college credit. If got college credit, can skip cal 1 and go straight into cal 2 if needed. If didn’t, can try to clep cal1 or just take cal 1 and get a feel for college and its requirements—the exact same things are not necessarily covered—depends on semesters vs. quarters, and other factors.
Grade Range to Begin Algebra1:
Algebra 1 needs to begin in 8th or 9th grade. 8th: Algebra 1, 9th: Geometry, 10th Algebra 2, 11th Trig/Pre-Cal, 12th Calculus or AP Calculus w/college credit. (Start in 9th if only going through Pre-Cal.)
Goal: College Algebra
Options:
1. Through Pre-Cal (Also called Trig/Pre-Cal) in HS. Can go right into college algebra.
2. Through Algebra 2. Can go right into college algebra. Might have to take a placement test, maybe.
Grade Range to Begin Algebra1:
By 9th Grade ideally. 9th: Algebra1, 10th Geometry, 11th Algebra 2, 12th Pre-Cal or whatever math credit required for your state or if three is enough…none or problem solving or business math, etc. If three major maths are enough for your state, you could potentially start Algebra 1 in 10th and still make it. But I like that extra year for room. What if it takes two years to conquer one of those subjects?
Goal: Maybe College
Options: Through Algebra 2. Leaves options open. Can go right into college algebra if desired.
Grade Range to Begin Algebra1:
By 9th Grade ideally. 9th: Algebra1, 10th Geometry, 11th Algebra 2, 12th Pre-Cal or whatever math credit required for your state or if three is enough…none or problem solving or business math, etc. If three major maths are enough for your state, you could potentially start Algebra 1 in 10th and still make it. But I like that extra year for room. What if it takes two years to conquer one of those subjects?
Goal: No College
Options: Through Geometry. So Algebra 1 and Geometry…Geometry is the language of builders, contractors, etc. It is necessary to many many jobs.
Grade Range to Begin Algebra1: This is going to depend on your state’s math requirements. But obviously, you could do other H.S. math and start Algebra 1 as late as 11th and then Geometry in 12th. I would personally give more leeway than that! What if it takes two years to conquer one of those subjects?
My own personal recommendation: Start Algebra 1 in 9th grade unless child is definitely math bent and needs all the credits he/she can get…then 8th.
If can’t start in 9th start as soon as you can—meaning mastery of basics has been accomplished and can now tackle Algebra 1. If this is 10th, don’t panic. If this is 11th, depending on above goals, don’t panic.
So the basics. From pre-k to ?? 8th? 9th? 10th? 11th?
You decide based on the above outline of goals and your own family’s make-up.
But the BASICS (w/o the extras—for you who are mathematically challenged)…go from pre-k to at least 8th or 9th or even 10th grade. Wow. We have more than 10years to teach ASMD in all its forms.
I wish we were in a room together. I am expecting to hear some sighs of relief. Take the pressure OFF! Master the basics. Spend the time. The curriculum’s schedule should not be your master or even your leader. Mastery should be the indication to move forward. AND put the tools in the toolbox…memorize the required definitions (math facts) so you don’t cripple your children. It doesn’t have to be stressful. Don’t get a whip out and beat it into them…but do get it done. There have been a lot of good suggestions offered in the other posts. I was proud to see the post from the mom who said it took 1 ½ years (I think) to master the multiplication tables…and then they moved on! YEAH! When she gets to grade 8, 9, or 10…her child will have a toolbox full of items to build with in Algebra. He/she will learn the language of algebra b/c they won’t be getting out the dictionary to define each three letter word they run across.
I pray that this has put some of the math race/pressure/issues/upsets/complications/etc. to rest. I pray this clarifies things so that you can focus on the important stuff.
I really do pray this is a blessing to you and leaves you peaceful instead of in turmoil.
God Bless,
Jo
Thanks again.
