Renee Jagodzinski							2/28/07
MED308/Cushman							Journal week #4

Date: 2/26

	Today, I learned that you have to make clear to students the different ways of 

looking at situations.  For example, when looking at the area of a square, rectangle, or 

rhombus, the area can be base multiplies by height, or height multiplied by length, etc.  

Also, with a rectangle and a square, you could have length multiplied by width.  But, a 

rhombus does not have this area formula because you have to include the height.  So, 

even though you are using different variables and names for different measurements, it all 

means taking the area of something.  It can just be worded in different ways to make the 

students think.  Many students weren’t clear with this concept because they didn’t 

understand that using the same variables or wording the question differently using 

different vocabulary, can really mean finding the same thing.  For example, they didn’t 

understand the length could mean the same thing as the base, or the width could mean the 

same thing as the height.

	I tried to connect this topic to their prior knowledge by looking at the shapes and 

making comparisons and contrasts between shapes.  This is basically using the van 

Hiele’s beginning level.  Like, what’s different and the same when comparing and 

contrasting a rectangle to a square by just looking at the shape.  

	I also tried to engage them actively in the lesson by asking them questions and 

having them look at the choices that they have.  They need to pick which one they 

thought was the correct answer.  But, we were mostly lecturing to the students because 

they tended to get stuck a lot on most of the formulas and didn’t really know what to do.

	I could engage them more in the lesson by having them answer and give an 

explanation for their answer.  If the answer is incorrect, I will tell them the correct answer 

and ask them what is the difference between their answer and my answer.  Then I will ask 

them what they think is the explanation for this particular answer being the correct 

answer.  

	Some things that I would change about the lesson is not do the Anticipatory set as 

long as I did for this one.  It’s important for students to know the basic formulas, but it is 

also important to see practice questions using these formulas and we weren’t really able 

to get to that point.  We were basically trying to get them to understand the formulas for 

different shapes and figures.

	To prompt their thinking, I wanted to show them different ways of looking at 

different shapes and how the formulas for the shapes were created.  For example, when 

looking at the triangle formula, we showed them how you can make two triangles to 

formulate a square or rectangle.  If you know the area of a rectangle and square and 

students can see that two triangles can formulate a square or rectangle, then you can see 

that a triangle is half a square.  Therefore, the triangle formula is half of the formula for 

an area of a rectangle or square.   

Date: 2/28

	Today, when doing the lesson similar polygons, I learned that many students are 

having troubles with the main operations, like subtraction, multiplication, division, and 

addition.  This can really make learning the content complicated for them.  Much content 

revolves around main operations and if students don’t understand the basics, they surely 

aren’t going to learn new content easily.

	When teaching the lesson, I would’ve liked to make the concept of proportions 

clearer.  They seemed like when we were teaching them the lesson, it was something they 

had seen for the first time.  They didn’t really understand what was going on during the 

lesson.  I think part of the reason was because they had troubles with the main operations.  

When doing proportions, you need to know simple operations to look at the different 

ratios and recognize when two figures are proportionate or looking at the scale factor.  I 

believe that students should get calculators.  This way, they won’t be concentrating on the 

simple operations throughout the entire lesson.  Of course, main operations are important.  

But, learning the concepts for the Math A are also important and they are able to use their 

calculator on the exam.

	We tried to connect the material to their prior knowledge when we were looking 

at the anticipatory set examples.  When we looked at the first example that compared a 5 

by 7 picture to a 7 by 8 picture, we asked the students what would happen to the objects 

in the picture if we extended it too far or the other way around being too small.  They 

responded that the face would be stretched out or it would be shrunken.  So, this is why 

we need to make things proportionate.

	There were some misconceptions that the students had when putting the proportionate figures together.  For example, when looking at the example of comparing a 

5 by 7 picture to a 10 by 14 picture, they were confused about where to put the numbers 

on the two different figures which represented the pictures.  By not being able to figure 

out where to put the numbers, they had a hard time creating these things into proportions.  

For our example when writing the proportion of the two figures, they would 

write 5:14 and 7:10 where it’s supposed to be the other way around.

	By engaging them into the material, we asked them questions and then asked them 

how and why they believe those were the correct responses to a particular problem.  After 

going over a few examples together, they were given a problem to see if they were able to 

understand it on their own.  When they seemed to get stuck, we helped them through it 

giving them little hints on how to get through the problem.

	However, we could’ve engaged them more in the content by having them get into 

groups and help each other work out a particular problem.  Sometimes teachers can be 

intimidating and by working with their peers, they are able to converse with each other 

and learn from one another.  Sometimes this kind of learning is better in some situations 

like this one.  

	We had to modify our lesson by basically just being able to work on the 

anticipatory set of the lesson.  Throughout the entire anticipatory set, we were trying to 

get the students to understand the main concepts by looking at practice problems that they 

use those concepts with.  But, I think for the next lesson, we should just concentrate on 

the main concepts first before looking at practice problems.   the main concepts are very 

important.  Once they understand the main concepts, they can look back at them when 

doing the practice problems.