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From Math to Relationships

After a  year of using Judith Gould’s Four-Square Writing strategies, I started to connect the scientific model to the 4 square and the problem solving “method.”

Step 1 Determine what the problem is asking.

Step 2 Gather the facts relevant to that problem.

Step 3 Use the facts to try some strategies.

Step 4 Make sure your solution solves

the problem.


Please note:  If you search "4-square problem solving"  You will see some people use different

versions of the same idea.  You can see that understanding how to teach students to break the

problem-solving process is:

1) improved over the last 15 years

2) Still being invented in classrooms after classroom across the country.  

3) being taught to many, many children without certainty of effectiveness.

Yet,  this is a start, folks.

Some problems with a more linear model: It can feel overwhelming to students with developing executive functions because it appears long.

The ‘problem’ is far away from the solution which does not encourage the connection between what the problem is asking and what the final solution is.

The good thing about the 4-square model is that the solution is actually touching each of the other quadrants.


But this model has a LOT of holes.  And if we alter the ideas just a little, then we can use this model to sort out so many types of authentic concerns that people encounter from math to friendships.

I implore focusing more instruction

  • Step 2 (below)

  • Labeling

  • calculator use while teaching the problem-solving process.


Alter Step 2.

Step 1.  Consider what the problem could be.

Step 2  Predict a reasonable solution.  (even going to far as to write the prediction in that bottom right quadrant.)


Seriously.  Predicting a reasonable solution . .changes the game.  It requires a person to refer back to the problem. To ensure the context is fully understood.  It also begins to frame the steps one might need to take in order to solve it. Predicting a reasonable solution, also helps a problem solver filter through the facts to extract those most relevant.


When novice problem solvers gather information, initially,

they bring all of the facts.  Even those that are irrelevant.  

If they perceive that the solution will include complex computation, their brain's default to either the easiest operation or the one that results in any number that is not overwhelming.


Specific Labeling

Spend much time improving and encouraging specific labeling of numbers.  

It is imperative that the numbers are labeled. 

Labeling requires the ‘language’ part of the brain to participate. The ‘math brain’ is powerful. It just wants to play with numbers. It does not care what the numbers mean.  So, a student can enter numbers into a calculator and use any operation the math brain desires, often leading to inaccuracy and always reduces the chances the student is successful.

Instead, invite the language side of the brain.  Label each number. No number can have the same label.


The specific labeling increases the chances the student will choose the appropriate operation because the numbers have context.


You can infer what the problem was asking by looking at the example with specific labels.

In fact, this type of labeling suffices for any ‘explain how you got your answer’ prompt.


Many teachers have a misconception that students have to write out a narrative of the process. You can see by the example on the far right, that even letters or pictures could suffice.  Specific labeling is more than adequate AND helps the learner make good decisions. It is proven that we make better decisions when there is disfluency in a process. (1) One reason that when you GIVE someone digested data, they do not get as much out of it as the person who initially processes the data to share it with others.


That is not to say students WANT to label the numbers.  The math brain really does NOT want to work with the language side.  The math side, like order, binary, black and white. We all know that with language things begin to get more complex. You have to teach the students that it is normal not to want to label.  It takes longer.


Additionally, I do not let them erase or scribble out attempts that did not have the desired result.   They may draw one line through it.  It is important for problem solvers to learn to value their attempts.  And that their is value in their first attempts.  There is important information learned in the first attempts that may provide useful information later.  AND as a teacher, I'd like to see the progression of their attempts.


Calculator use


I advocate for teaching novice problem solvers how to use a calculator in order to scaffold their learning.

This is not fluency time or algorithm instruction time.


It leads to better decision making.   When students are learning to manage a great deal of information, it reduces the cognitive load, to have the computation left to the calculator.  It ensures greater accuracy which makes it likelier that the student will have success.


It is not ‘easier’ to use the calculator.  Calculator use is a skill in and of itself.


Additionally, I require the students to write the numbers and operation and  specific labels down first.  

Students do not typically want to write the numbers down until AFTER they use the calculator.  That leads to less impressive outcomes.

They do not want to write the numbers down FIRST because they may not be sure their attempt will be 'right' the first time.  Because they are still building their understanding of what operations actually do to the value of the solution.


{more to come}


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