Weekly Blog #7

This task is asking the students to color in the fraction that is given. The students have to understand what the fraction says then color in the corresponding checkers. The big idea of this task is to see if students understand fractions and what certain fractions look like by coloring in the fraction that is given, so they were asked to color in 3/4 so the student colored in 3 checkers of the 4. This is correct. But, when the students moved on down the page to questions 7-10 they became much more confused. This particular student ended up coloring the right checkers after some help and errors at first. At first this student, along with more than half the class, did not understand this particular set. Let's take number 7 for example. It states 1/3 are red. The students understand that, oh one of these 3 should be colored in so they colored in one checker out of all 9 that were there. The student saw the fraction as 1/3 so one should be colored in but did not understand or recognize until after further help that one whole set of three checkers should be colored. I helped explain this to the student by drawing a square split into three parts. I drew three checkers in each part for a total of 9. I then asked, "how many parts do we have?" The students responded with 3. I then asked how many checkers are in each part, again they said 3. I then helped them understand what the problem was asking by explaining, "ok we have 3 parts and it is asking us to color in one of those three parts. So if I want to color in ONE part, how many checkers and what part would I color?" The student(s) then understood and said to color in the one part that had three checkers. I helped them further their understanding by explaining that when there are sets like this pretend a line splits them into parts, when it asks to color 1/3 we know to color one part of the three parts total.
The students current mathematical thinking about this problem reveals to me that she understands fractions as a whole but not as part-whole. She understands that if there are 4 pieces and it says to color in 2/4 she would color in 2 of the 4. But she is struggling with understanding that if there is a set, then you will have to color in ONE SET of the total amount of sets, like problems 7-10.

The Questions I have about this problem are:

1. The student understands the parts and fractions now, but if this were to pop up in another worksheet or on their math test will she understand how to do it? If a similar thing showed up will this student realize the problem is dealing with parts and not just a whole pizza or 4 checkers total?
2. Why did the teacher not explain this to the students before about the parts? Was it not in the content dealing with fractions?
3. How can we teach students about fractions without simply having them color in 2/5 of a group of objects? How can we further their understanding into a deeper meaning of what fractions are?

Ways I might answer them:

1. I suppose the only way I could find out this answer is by observing other worksheets or seeing what the test will look like for them. I have no other way of seeing if the student will remember this information unless I provide them with a similar worksheet to assess their understanding or experience them completing another page similar to this one.
2. I could find the answer to this question by asking my mentor teacher if she taught them about fractions and dealing with parts of a group. 
3. I think that the answers to this question can vary. We can further their understanding by having them complete word problems and creating their own drawings and fractions from the numbers within those problems. Students will then be solving a higher level task because it is not just simply saying, "color 1/4." The students will have to see what numbers are in the problem, what numbers are placed in the numerator, the denominator, and how they know that. This will aid in their mathematical thinking about fractions and help them understand more to them.