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Thursday, November 10, 2016

Catching Up: A Program for Students Who Struggle in Math

There's a lot of discussion in the school house about what to do with students who struggle in math. These are students who are one or more years behind with regard to math grade-level standards. We know who these students are from standardized assessments, observation, conversation, and more.

Now we have a program that provides extra support through a differentiated core program, preview program, and response to intervention. While all three programs have merit, they don't offer the consistent, daily developmental math program that strugglers need. As Khan suggests in his Ted Talk, we need to help these students catch up by mastering early math skills which provide a child with a strong number sense foundation and mastery for later learning.

Jo Boaler would suggest, in part, using meaningful math projects that naturally help a child to learn these skills in engaging ways. Her "floor to ceiling" explorations allow all students to learn in meaningful, collaborative ways--ways that don't separate those with strong skills and those with weaker skills.

I really like this idea, but right now with our tight grade-level standards expectations that's difficult to employ at all times. Instead, I think what we should do is provide a two session a day program including a differentiated core program for all that employs lots of meaningful math projects and differentiated learning events and a five-day a week number sense program.

Core program time would equal about 45-minutes a day while number sense programming would equal another 30-45 minutes. During number sense grouping, students would mostly stay in same groups with those who struggle the most with number sense assigned to smaller groups with highly qualified educators and those with stronger skills assigned to larger groups with teachers and/or teaching assistants. Those that struggle would begin at their level of need. For example, if a child could not make combinations of 10, then that's where that child would start and build from there. I would use the list of number sense skills, concepts, and knowledge below to lead the assessments and groups. I created this list from research.

This two session a day math program would meet both the need for students to engage in meaningful, heterogenous math groups while also providing sensitive teaching and coaching related to developing students strong number foundation which is essential for more sophisticated math learning. This kind of programming would provide the consistency, daily practice, and successful coaching that allows students to build one skill on top of another as they move forward in math. The change to the current program would be to combine the preview program and RTI into one five to six day a week number sense developmental program. In this way students would have the chance to develop skill in a brain-friendly way, a way that allows them to see how once concept, skill, or knowledge point leads to another. This kind of learning develops a strong math disposition because math learners are pattern seekers and relationship finders. Programs that are less consistent and coordinated do not naturally match the ways our brains work to gain depth, fluency, and mastery over topics.


Ladder One - Counting
Write out the numbers in each level, then practice counting forward and backward.  Let a family member test you by listening to you count the level without looking at your paper.
Level
(each level should be achieved forward and backward)
Notes/Date Passed
up to 25 

to 100 by ones

to 100 by 10's

to 100 by 5's

to 100 by 2's

to 20 by 1/2

to 20 by 1/3

to 20 by 1/4

to 20 by .1

to 20 by .5

to 1,000 using number booklet

to 10,000 by 1000's

to 10,000 by 100's

to 10,000 by 10's


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Ladder Two:  Math Facts, That Quiz:  http://www.thatquiz.org/
You pass a level when you can answer 50 facts in three minutes or less.

Fact Level
(students highlight fact set that they are currently working on)
List Time, Error #, and Date each Time you Take the Test.  Move to next level when you pass.
addition facts 1-12



subtraction facts 1-12



addition/subtraction facts 1-12



multiplication facts 1-12



division facts 1-12



multiplication/division facts 1-12



multiplication/division/add/subtraction 1-12



Ladder Three - Computation (paper/pencil tests)


Name:  _______________________________________________________________________

Large Number Computation
Test Date, Error Notes, Time
Large Number Addition including decimals, more than two addends, money, 4-digit by 4-digit, carrying, and checking with estimation.

Large Number Subtraction including decimals, money, 4-digit by 4-digit, borrowing, and checking with addition.

Large number multiplication including 2-digit by 3-digit, decimals, money, and checking with estimation.

Large number division including 3-digit divided by 1-digit and 2-digit and checking with multiplication.


Large Number Computation Test:  Addition

Exact Solution
Estimated Solution
75 + 89







129 + 2,357 + 6,890 + 24,679






2.9 + 4.08 + 3.45 + 12







6,789,234 + 6,789,235







$65.78 + $298.78 +$587








78,967 + 35,567 + 67,987











Large Number Test:  Subtraction

Exact Solution
Checking Solution with Addition
894 - 231





8,213 - 6,989





$295.78 - $198.39





7.8 - 2.12




758,221 - 679,989








Large Number Multiplication Test


Exact Solution
Estimated Solution
78 X 5





67 X 29





129 X 87






$45.67 X 8





7.8 X 2.31








Large Number Division Test

Exact Solution 
Check with Multiplication
89  -- 3







78/4







389 -- 8







6,789 -- 9








879 -- 23







_________________________________________________________________________________
Ladder Four
Essential Fourth Grade Skills
That Quiz:  http://www.thatquiz.org/

Skill
Time
Time/Error/Date/Teacher Sign
Integers: Number Line L4
50 - 10 minutes or less

Place Value L3
50 - 10 minutes or less

Place Value L6
50 - 10 minutes or less




Integers: Inequality L3
50 - 5 minutes or less

Integers: Inequality L5
50 - 5 minutes or less

Integers: Inequality Add L12
50 - 10 minutes or less

Integers: Inequality Subtract L12
50 - 10 minutes or less

Integers: Inequality Multiply L12
50 - 10 minutes or less

Integers: Inequality Divide L12
50 - 10 minutes or less

Integers: Exponents L2
50 - 5 minutes or less

Algebra L2
50 - 10 minutes or less

Algebra L3
50 - 10 minutes or less

Measure L2 Both inch + cm
50 - 10 minutes or less

Measure L3 Both inch + cm
50 - 10 minutes or less

Money L7
50 - 10 minutes or less

Time: Simple Clocks L4
50 - 10 minutes or less

Time Passed L2
50 - 10 minutes or less

Graphs: Bar and Line L2
25 - 10 minutes or less

Geometry Shapes L3
50 - 10 minutes or less

Geometry Triangle
Perimeter L10
25 - 10 minutes or less

Geometry Perimeter
Rectangle L12
25 - 10 minutes or less

Geometry Cube Volume
L5
25 - 10 minutes or less

Fraction Identity L 10 
50 - 10 minutes or less

Fraction: Inequality L3
50 - 10 minutes or less

Fraction: Simplify L3
50 - 10 minutes or less

Fraction: Arithmetic add L1
50 - 10 minutes or less

Fraction: Arithmetic subtract L1
50 - 10 minutes or less

Place Value: Decimals L3
50 - 10 minutes or less

Probability - level 1
15 - 3 minutes or less