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Happy Monday!

As always, I hope you are happy, healthy, peaceful, and loved.
I have been spending time with upper-grade students lately and I am CONCERNED. Why are so many fourth-graders still using circles and sticks as a strategy to solve problems?

What skills do the students in the images below need to move towards more sophisticated and efficient strategies for problem-solving? Where would you start?

Algebraic Thinking

In kindergarten through third grade, students can solve almost all of their problems by memorizing their facts or drawing quick pictures. However, these same strategies are less effective when students get to fourth grade and have to solve multi-digit problems.

Consider a third-grade student who is taught to use skip counting by 6 or memorization to solve 48/6.

Now imagine this same student in fourth grade. What strategy might they use to solve 486/6?

You are going to need strong number sense to solve the above problem.

While skip counting and memorization might get students through third grade successfully, students will need number sense (algebraic thinking) to solve problems with multi-digit numbers efficiently.
They will need a deep understanding of place value and the base ten number system before advancing to more sophisticated strategies.
They will need to practice composing and decomposing numbers every day.

If kinder through third-grade students are not highly skilled in all of the above, fourth grade is going to be a real challenge. Memorization, skip counting, and circles and sticks will only get them so far.

I wonder might the lack of number sense, composing and decomposing, and the use of place value as a strategy be the cause of fourth-grade scores hitting a wall and going down.

Can they really count?

I am running into too many upper-grade students who sound like this when counting and using tools.

Fourth graders are not struggling with fourth-grade concepts. Students are grappling with kinder, first, second, and third-grade concepts.

So, let’s ask ourselves:

Do my students have good number sense?

Can they independently compose and decompose numbers using place value?

Do your students have adequate access to tools that help them count, compose, and decompose groups?

Can they round to a ‘friendly’ number to solve more efficiently?
7 x 0.19

Can they count by tens and ones, fives and ones, and hundreds and ones?

When they look at the equation 100-97 = ___, what do they see?
Do they see 100 – 97 or do they see 97 + ___ = 100.

Tools are for all kids. Too many ‘high’ kids have memorized facts, and cannot show their thinking conceptually or with a variety of models. All kids need number sense, conceptual understanding,  equations, and ultimately procedures.


What’s wrong with memorization?

 Nothing, if students also understand how to use algebraic properties to solve problems. We must build mathematicians, not memorizers.
Memorization is good, but it is not enough to meet grade-level content standards, proficiencies on state assessments, or to become a mathematician.Let’s help all of our kids experience success in fourth grade.
Where will you begin?

Begin your CGI journey. You can learn more about your students’ mathematical thinking.

Enroll in my online Cognitively Guided Instruction course through the University of San Diego.
You can enroll at any time, take up to 6 months to complete the course, and earn up to 3 graduate-level units.

Go to today!