I am leading a training next week on how to introduce grade level concepts/standards when the students are performing well below grade level, and I am sure that math is going to be an issue. Any suggestions?
These are my 2 cents on teaching under-performing students.
Let's imagine we have an 8th grader performing on 3rd grade perhaps.
I would dismiss for starters geometry and measuring topics, and concentrate on this train of topics, in THIS ORDER:
addition
subtraction
multiplication
division
fractions
decimals.
... the goal being to cover the basic arithmetic up to pre-algebra.
Think of mathematics as a building. You need to have the foundation building blocks before you can go forward.
Maybe the child stopped understanding the math on 2nd grade or 3rd. We need to find the exact point after which he has not understood everything.
You can gauge this by the way by asking the child simple questions such as,
- I give you an addition 8 + 2 = 10, you give me a subtraction sentence (1st grade knowledge).
- How much do you need to add to 600 to make a thousand? (2nd grade place value)
- Draw a picture of 4 x 3 (3rd grade knowledge)
- There are 293 flowers and 145 are red. How many are not red - how do you find that? (using subtraction in finding parts)
- Draw a picture of 20 : 4. (division concept, 3rd grade)
etc.
So for such imaginary 8th grader, I'd make up a separate curriculum that goes through addition, subtraction, multiplication, division, fractions and decimals, in this order.
A teenager can go through those topics in 1 year, and understand it all, if he wants to. Obviously you'd want to show the student the train of topics too so they know what's coming next. You'd want to motivate them that hey, in one year I can learn all this basic math. You'd want to show them how the basic topics lead to the next ones.
Addition: you'd start at adding single-digit numbers, then memorizing addition facts, then 2-digit addition, then multi-digit addition.
If the student does NOT know addition facts, then spend a week practicing them! But not in random order. Like I do in my books (Addition 1 and Subtraction 1) you need to put those facts into contexts, study them in systematic, logical fashion such as sums of 5, sums of 6, etc. (using fact families). Or, adding to 9, adding to 8, etc.
Not knowing the addition facts makes the student SLOOOOOWWWW in doing simple addition problems, and makes it hard to get into subtraction or multiplication. So it is important, even if he's on 8th grade, and it is 1st grade stuff.
On to subtraction. Cover the three situations where subtraction is used, even if it is 1st grade stuff. Cover multi-digit subtraction. Shouldn't take many weeks.
Then multiplication concept. Times tables. Multi-digit. Absolutely remember to show what principles 23 x 38 is based on (multiplying in parts). Spend several weeks here.
And so on.
In a school year's time, it absolutely is possible to cover the basic arithmetic if the student is a teenager. I just would cover it all, including 1st grade topics, to make sure to catch those points where the student "dropped" off.
Any comments anyone?
Maria Miller
