"I don't get it!"

Now I consider myself a person with a very high tolerance level but when I'm in the classroom, I find that few things are tolerable to me and one of them is the cop-out phrase "I don't get it!" You may think that's unacceptable for a teacher to hate the typical 'cry-for-help' phrase, but hear me out.

I always challenge my students to think positively rather than negatively. So I set up a standard at the beginning of the year. I suggest that we use the phrase, "Could you help me understand?" in place of "I don't get it!" Why? Well one phrase is often used to justify why they've given up. While the other suggests that I'm not willing to give up, if you can show me another way, I want to "get it".

Today, my (intervention) small group had a silent "I don't get it" moment. Let me set the stage for you:

So you've taught your whole group lesson on Perimeter and Area, fully equipped with hands on models, foldables and pair-share thinking questions. All of this lasted its full 30-45 minute time (since you're a 5th grade teacher and these concepts are review anyways).
Now you're in small groups with your 4-5 students and you're diving deeper into the concept. You come upon a problem that is a bit more rigorous and your goal is to hammer through it piece by piece via open discussion.

The problem goes like this:

Ms. Kim has a backyard with the dimensions 60ft by 40 ft. She has a flower garden in the corner of her backyard with the dimensions 15ft by 20ft. How much of Ms. Kim's backyard does NOT include her flower garden?

What do you do?

Let me share with you my journey through this rigorous discussion. To me this was the easier of the two questions I wanted to discuss. Based on the level of these students at my table, I was not shocked by their blank stares. My students were mentally numb and no matter of discussion was bringing forth a solution for this problem. So of course the obvious move was to switch into "INTERVENTION" mode and help students understand:

A. What the problem was asking us to do (find the grassy part of the backyard (minus the garden)).

B. Figure out a process by which to calculate this leftover section.

C. Chart out all of the steps (in correct order)...utilizing their Math Reference (STAAR) charts.

The discussion was quite toilsome. Below is the approach we took.

1. We looked at a piece of rectangular construction paper.

I asked "How does this piece of paper represent our backyard?"

2. Then we analyzed the problem by re-reading and pulling out components like "does NOT include her flower garden" that need interpreting. Using the construction paper, we drew a section to represent the garden and asked,

"What should we do to isolate the garden from the yard?"
STUDENT RESPONSE: Cut it off!!!

So we did. Then we discussed what the left over represents.
STUDENT RESPONSE: The part of the backyard that is NOT the garden.

3. We went back to the problem to make a connection.

"How do we demonstrate using math language, cutting the garden away from the backyard?"
STUDENT RESPONSE: Subtraction!!!

"Subtract what?", I followed up!
STUDENTS RESPONSE: Subtract the garden (area) from the backyard (area).

From here, we were able to decide what formula we needed.

Area (rectangular backyard) - Area (rectangular garden) = Area (leftover backyard)

 

I had students identify what formula they would use and justify why!

*This was very important with the smaller rectangle, because some of them thought we would use the AREA (square) formula simply because it LOOKED LIKE a square.

 

"What do we know about the sides of a square?", I asked. (That they are all the same)

"Are the sides of the garden the same?" (no)

"So what can we conclude?" (its a rectangle)

 

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The next problem was even tougher for them to think through. But I could be a bit more understanding. Here's what it looked like:

 

A rectangular wall had a window in the middle of it. How will you determine the area of the window?

 

 

I wasn't even mad at one of my students who said, "Get a ruler and measure it!!"

That's the logical think to do, right? She got my vote but I'm sure everyone else at the table was mad when I shot down her idea with my response, "We would totally do that if they instructed us to use a ruler to measure it, but since they didn't, what other method should we use?"

 

No amount of THINK TIME was helping these students figure out a solution. So we took to a hands-on model to get their juices flowing.

 

So we used a series of linking cubes and a part-part-whole mat. I asked them to identify the "whole" from the linking cubes.

 

Then I related the linking cubes to the length of the wall. I had the students discuss how we could separate the yellow section (the part) from the purple section.

 

 

 

STUDENT RESPONSE: Cut off two purple ends!!

*and we did!

 

We translated our actions into a mathematical number sentence:

 

Whole - part = part

 

From here they were able to see the length of the wall as the "whole" and the window as the part that needed to be separated.

 

They discussed as a table, that they should:

 

A. Subtract 7 from 20, then subtract 7 again to find a leftover of 6. (20 - 7 - 7 = 6)

 

Then someone said, "Couldn't we just..."

 

B. Subtract 20 - 14?

 

So I posed their question to the group to vote! The we justified why these two approaches were similar.

 

Finally, the students were able to ascertain the length of the window. Now, in the original problem, the window was a square, so we were essentially done.

 

We labeled the lengths and widths of the square and calculated the Area of the window.

 

One young lady said, "why did they give us all that information if all they wanted us to do was find the area of the window?"

 

After we all had a good chuckle from her pertinent question, a student replied, "Because it was the information we needed to find the information we didn't have!"

 

WOW!!! What a learning moment! Now, could I expect them to do problems like this on their own? Not for this small group, but with more practice, they would eventually grasp the idea.

Here's the take-away. Don't expect all of your students to apply perimeter and area immediately! Students with slower processing skills need a more concrete association as they think through word problems. Be patient and open enough to build the bridge to their understandings.

My philosophy is, "Your light bulb may not go off when others' go off, but it WILL go off!"

 



 

 



When Teaching gets Frustrating...

Have you ever been standing at your dry erase board waiting for the class to give the answer to your math question? Waiting, in the intolerable silence; begging them by rehearsing the question in different ways almost literally giving away the answer. Not even your usual 'quick arm shooters' have their hands raised. You feel your blood boiling and you're moments away from giving up.

Later, in your small group you are asking students to decompose a number and the 5 students are sitting with linking cubes in front of them yet starring at you like a deer caught in headlights. Finally, you scream, in frustration, "COME ON GUYS, DE.COMP.OSE THIS NUMBER!!!!!!!!", as if that will somehow provoke them to spew out the right answer.

Yes, teaching (imparting knowledge into someone's brain) can be difficult and even frustrating. But when you're facilitating learning, the process is a bit more meticulous. Let's explore the process:

Let's say you ask your students to explain to you how they can mentally add $19 + $28.

1. First let's analyze the question I presented. I didn't start the lesson by telling them that we would learn how to add these two numbers. Rather I had them explain to me what they THINK they could do to add these two numbers without pencil and paper.

My objective (later) is to teach them the algorithm, but not without asking them to draw on their prior knowledge (hopefully of base ten and/or decomposing numbers, making ten, counting on, etc.). The idea is that I want them to explore the various strategies they may already be aware of.

2. After hearing their explanations (and hopefully you gave them opportunity to discuss with a partner or table of students so they can draw on the thinking of other students), you want them to share out. This allows you, THE FACILITATOR, to both correct their thinking and informally assess where they are.

If this step isn't taken seriously and intentionally planned, frustration can easily enter. You must KEEP CALM and allow various incorrect approaches!

3. Most importantly, you must be prepared for these incorrect approaches (answers). They must be premeditated. In other words, you should know all the responses that will be given and be ready for them. Yes, especially the incorrect ones!

So really, step 3 is pre-step 1! When you're lesson planning, you must think of how you will handle the responses-what intervention will be needed? You must think through how you will group your students based on their responses.

This step involves intervention planning (intervening when strategies aren't working).

A. If the students started at one and counted to nineteen then added 28 more...DON'T FUSS!!! This simply tells you that the students struggle with COUNTING ON and REASONING.

B. If the students counted on from 19...CELEBRATE THEM! That wasn't the best strategy but at

least you know they can SEQUENCE and COUNT ON! Their next step then is to help them apply UNITIZING and CONSERVATION of numbers.

C. If the students are able to decompose the 19 into 1 ten and 9 ones ...then decompose the 28 into 2 tens and 8 ones for a combination of 3 tens and 17 ones--well they are in a different and more advanced place! They may not know how to regroup the 17 ones but at least they understand DECOMPOSING!

*There are other answers that you could expect, such as:

MAKE TEN STRATEGY

Taking a "one" from the 28 and adding it to the 19 to make 20 (this is called the MAKE TEN strategy). This would restructure the problem to 20 + 27. Regrouping, then wouldn't be necessary.

The idea is to cut down on frustration on your part, by understanding the various places your students can and may be in their level of development. This can occur by reading articles on Numerical Development such as Subitizing by Douglas Clemens, 1999. You may also check out Teaching Student Centered Math by John Van de Walle.

Be prepared to take them to the NEXT level in their cognitive development.

"The best defense is a good offense!"

"Be proactive, rather than reactive!"