Blog 10

Blog #10!

Observation: Ways to explain division to students in simple form

 Reflection: Last week in math class I was introduced to the idea that division is essentially separating a given number into equal parts. This can be said a couple different ways. Either 15 divided by 3 can be said as either, "separate 15 into 3 equal parts" or, "how many times does 3 goes into 15".  We demonstrated this by using the chocolate chip cookie idea on the board. Although I thought I already knew how to explain this concept, Professor Antosz explained a new way for us to teach children how to divide. This way, although very different from the way I was taught when I was in grade school, it is a lot more useful for teaching young kids who are learning how to divide for the first time.

 

Reflection on Reflection: Personally, I believe I will make all efforts to adapt to this new way Professor Antosz showed us on how to divide when I am able to teach my own classroom division. It is difficult for children to understand division the way we were raised learning how to divide (example, by carrying 1's etc.) This is difficult to teach and essentially more difficult for the child to grasp. However, this is an alternative way to teach division should the child not understand the first way. It is nice to collect different ways to teach a topic in math so that all children find what is best for them to grasp the concept. This new way of division for me, I believe, will get a positive reaction from students and allow them to learn better. For example, let’s use the example, how many times does 6 goes into 875. A child who is first learning division in a primary classroom, might initially start by using small numbers and continue going up, as in the following illustration:

However, like adults, children are lazy by nature as well, and soon they will figure it out for themselves to immediately start with a large number, for example:

Although it will take some time to teach myself this new concept in order to be able to explain it to my students, I believe it will be effective and ultimately help them learn to the best of their abilities, which is the main goal. I never thought I would have this much difficulty grasping grade school math at an adult age, however, I am quickly learning how difficult it actually is. Taking math again after so many years is allowing me to learn new concepts and preparing me even more for placement. 

Blog 9

Blog #9!

Observation: Understanding why teaching fractions with geometric shapes instead of learning how to write it works better.

Reflection: After leaving class today, on October 22^nd, 2012, I kept thinking about what Professor Antosz was discussing in class about teaching fractions with geometric shapes rather than with terms such as “lowest common denominator”. Prior to this class, I always assumed that I would teach math the same way I was taught throughout grade school. I did not understand the professor’s idea when he said he thought, “fractions without rules is a good thing”. However, after listening to his reasoning, I have a better understanding as to why this might be a good pedagogy of teaching.

Reflection on Reflection: I think the reason why it was so difficult for me to grasp the concept of teaching fractions without rules is because I do not fully understand fractions. This is something I will have to work on, because I strongly believe that teaching math using physical manipulative is a good idea. We have learned all year thus far that we should try to incorporate using differentiated instruction into our lessons. By using the math manipulative, this allows students of all types of learning to fully understand the lesson. After leaving today's math class, it taught me that there are many different ways to teach students math and that there are other ways to cover the required curriculum without doing basic math. We were also taught this year that children learn a lot faster and understand better when “doing” rather than being shown. By using the geometric shapes the students are not simply listening to the teacher explain how to solve the problems, but they will be able to pick up the concept a lot quicker because it allows them to be hands on. 

Blog 8

Math Blog #8!- Grading Systems 

Observation: Usefulness of rubrics for mathematics

Reflection: After discussing the purpose of math rubrics in class on Monday, it really made me realize just how difficult it is to distinguish between a level 3 or 4 student through solving certain math equations. If the student gets the problem correct and both of them took the same steps to get there, what distinguishes them from a level 3 or 4? It is difficult in the sense that a rubric should only act as a guideline for math and should not be the sole factor in determining a student’s grade.  I understand that there needs to be some form of formal grading for math, however the more I read the provided rubrics in the courseware pack, the more I think they do not do a good job of justifying what is expected of students to reach a certain grade level.  This might often leave students frustrated and discouraged because they never really understand how to take the next step and receive a higher grade.

Reflection on Reflection: After exploring all the pros and cons of a math rubric, it made me wonder what the point of them really was in regards to math. I always assumed they were a useful way to give students grades until actually discussing it more in depth. Do teachers have a premeditated idea about a student before they even grade their work?

On page 50 of the courseware pack, the rubric for a level 3 student reads “shows complete understanding of the problem”. A level 4 student reads “shows complete understanding of the problem and has insights beyond the problem”. If the problem is a simple math equation, what is the difference between the two different grade levels? If teachers have premeditated grade levels for students, certain students will never be able to excel in math as there no noticeably difference between the two aforementioned levels.

I have certainly experienced teachers like this, and this is one of the major issues I see with a rubric for the subject of math. It is also something that I will have to continuously be conscience of while grading student’s work.

            Due to the fact that math is such a unique subject to have a rubric for, I think it would be helpful if the students and teacher created their own assessment for this subject together. This way the students know what is expected of them to be able to reach certain grade levels, and they feel included and fully understand what is expected of them.