Performing well below grade level

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

Comments

mcavanaugh said…
I was a high school dropout who later majored in engineering at UT-Knoxville. I struggled somewhat with math since I never took trig or pre-calculus.

The one thing I always wanted was some kind of test that would pin-point what topics I had missed or needed to strengthen. I felt like I had weaknesses and was motivated to work on them. My time was at a premium (I was a single mom of 4) and I wanted my study to count!

Somehow I feel a teen might feel the same way!

I was amazed to see how quickly I picked up math in college (I was a struggling high school student.) I now know it was due to several reasons:
1. I became a Christian after dropping out of high school and put a lot of effort into memorizing and reviewing scriptures.

2. I quit trying to grasp the theory and I did homework like crazy whether I understood it or not (getting a professor or T.A. to "unstick" me so I could keep solving problems. Later I realized this coincided with my learning style.

3. I think I was smarter than I realized and that was why high school math bored me so much. I went to southern rural public high school and we were expected to do tons of boring problems over and over again with no practical application. Calculus was interesting without the tedium.

4. I learned how to program computers - that skill translated well to setting up word problems.

I would have done even better if I could have tested to pinpoint my weaknesses and concentrated on those.

I just found your blog and I love it!
Susan said…
About kids who aren't performing up to grade level, and that teens should be able to learn all their math in a year...
Yes, IF the child does not have some specific disability. My youngest struggles mightily to learn math. It's just part of the territory that comes with her heart defects and her cleft palate. I agree completely with your suggestion of starting with addition and working up from there. But somebody who's trying to teach teachers how to deal with "behind" kids should remind them that some kids are just going to be behind.
I've found that these below-grade level students often get stuck with the same curriculum as the other kids in the class. That only leads to frustration with math and further lagging behind.
Mommy2Lots said…
Excellent tips. I have one child who's extremely ahead and one who's extremely behind. The one who's behind is behind due to basic math operations. Problem is, it's been gone over with her in the correct order several times by me and 2 different teachers. She seems to understand better after I've done it with her in the correct order, which leads me to believe that the teachers may not have been completely honest about their methods with me. I believe that doing this one more time with her will finally make it sink in because she is so close. We will be homeschooling again this fall, due to my bad experience with the school system (a second go-round). My hope is that I can catch her up before school starts so that I will not have to hold her back a grade level.
Anonymous said…
My question would be how to move ahead while still catching up?? I am a hser and know that my child with numerous memory issues isn't on grade level and yet I am stuck between trying to catch up and keep up.
Maria Miller said…
Hi Anonymous,
I don't think there is any exact "formula" you would go by. But you can't do a great deal of "keeping up" if the foundation is hazy.

Maybe you could email me and tell more about your situation.
Anonymous said…
Hello
I just read your comments seven months after you posted. I want to share with you how I learned to add, quickly, and how I attempt to help others learn it. I teach high school and am amazed at how many students still need to use their fingers to add.

I learned to add in the sixties. How? I was a bowler, and there were no automatic scorekeepers. In fact, as a ten year old I used to go the bowling alley and keep score for bowling leagues at $.25 per bowler for three games. Came out to $2.50 per league, not bad for a 10-year old in 1963. I could buy all my comic books myself.

And, you learn to add quickly, because any mistakes will be caught by the bowler and he or she could be very mean to you if you messed up.

You learn to add any numbers together since spares and strikes can make it quite interesting.

You can do this with your students. Use soda bottles and a softball on the playground, or buy a plastic bowling set at a toystore. Make up some bowling score sheets and have students first keep just there own score, and then increase the tension by having them keep several scores. Have two different students keep the same set of scores and then compare.

Make it fun and it will last them a lifetime.

Regards

Don Winterhalter
Visalia, California
El Diamante High School
clanmama said…
I have some children that were homeschooled, and this year are going to start public school. We were using an old mennonite curriculum, that was very complete, but repetitive and I think may hve waited to introduce some concepts. From trying different things and other circumstances two of my children are in math grades lower than what they should be. My oldest going into grade 7 finished a grade 5 book, and my grade fiver a three. Do you think it will be very difficult for them to adapt? Also, do you have any suggestions to help them? Thanks in advance for your time.
Maria Miller said…
I think it's a good possibility they will have some difficulties, but then again, it might not be too awfully bad. You might just want to wait and see and help them understand the concepts that they do have difficulties with, as they come up in the curriculum they use in school.

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