article

Casillas, Robert I.
MTED 6314

Flores, C. (2006). How to buy a car 101. Mathematics Teaching in the Middle School, 12(3), 161-164.


The article deals with a concept called Problem-Based Learning (PMB). This is where you relate the curriculum to real life situations and use technology. The teacher gave the students criteria for a man who wanted to buy a car. Some of the criteria consisted of only spending $450 a month for car expenses (including gas), a car that is good in gas mileage since the owner was going to have to drive a lot, didn’t want a minivan nor sports car, and only wanted an interest rate of 5.85%. Students searched manufacturer’s websites, asked questions to car dealers the teacher was able to get to visit, and sat in various new vehicles that were brought in (some of the students had never sat in a new car). The teacher is more of a coach than a teacher with PMB by guiding students as they search for information. Before the project began, the teacher let some classes get involved in making a rubric so students knew exactly how they were going to be evaluated. Finally, the students made a power point presentation on the car they felt best met criteria. The author adapted to special needs students with a smaller number of requirements, and adapted to ESL students by allowing them to research websites from their country so other students could see how things are different, yet similar in various countries. The author concludes by recommending the teacher do a model so students know what the final product should look like and so the teacher is aware of struggles the students may have, and most importantly do not do the project for the kids (it is very easy for the teacher to want to take charge).

Casillas, Robert I.
I love the idea of PMB. I feel it meets criteria of problem solving we have learned: students get engaged in a task; draw from prior knowledge; requires effort; includes complex problems; communicates ideas; variety of methods to use. This allows students to see how math is used in real life because at one point in their life they will purchase a car and have to think about these things. The only thing I am concerned with is the time it will take to do the project because there is so much material to cover and only so many days we have before the TAKS test. But I guess as long as the teacher plans accordingly, students should be able to have time for the PMB and still get the rest of the curriculum covered. The teacher must also make sure he shows how the PMB relates to what they just learned so students can see the connection. Finally, teachers needs to make sure they cover the material first with a little TAKS assessment versus trying to get the kids to draw from last year’s knowledge to do the project. I must admit that my brain is going and I’m going to see if I can do something like this in May once we are pretty much done with the curriculum and the TAKS test is over.
















Casillas, Robert I.
MTED 6314

Grover, B., & Moss, L. (2007). Not Just for Computation: Basic Calculators Can Advance the Process Standards. Mathematics Teaching in the Middle School, 12(5), 266-273.


The article discusses ways non-graphing calculators can be used to make students better problem solvers because the use of calculators will make students think to a higher level. This is done by not only having students use a calculator but also giving them the opportunity to interpret what the answer on display means and by discussing limitations of various calculators. While the intention of calculator use is mentioned above, a hidden benefit is how students become confident in their ability to “solve” math and become more comfortable in contributing to classroom discussions since they have an “answer.”
The authors start off by giving the students a real world problem. The students then work the problem with paper and pencil. Next, the students share their solutions and problem solving while the teacher has a “neutral” look on his face. Then they have the students solve the problem with the calculator and at the same time keeping track of the strokes used. Finally, the students share what was done on the calculator, discussing similarities and differences with what they got on display for a final answer and what was keyed to get the final answer.
The authors conclude their article by mentioning the following results on student development: broad foundation of problem solving strategies by observing the multiple strategies used; respect for other student’s abilities and ways of thinking; ability to analyze the mathematical ideas used instead of analyzing the person speaking;
ability/desire to collaborate with a diverse group of peers; confidence in their ability to do
Casillas, Robert I.
mathematics; ability to achieve when a task is difficult.
I never thought of using calculators as a discussion to deepen the understanding of mathematics. To me calculators were a way to do calculations quickly to get a final answer. I have to wonder if what the authors are really trying to do is have the kids learn how to use calculators instead of doing a problem through paper/pencil (but the article is suppose to be about having students develop a deeper understanding of problem solving through the use of calculators). I say this because the authors seem to have the kids do the math on paper, then check the solution through calculator use and compare what they have and reasons for the possibility of differences among classmates from the calculator. It seems the checking among peers is being done on why different solutions appeared on the calculator and not why different solutions appeared on paper. I can understand how the authors are trying to train the students to use a calculator to problem solve (we are at a time where a lot of what we do is through technology and math is no exception). To make better use of the calculator concept and deepen understanding, I think teachers need to go over the answers from the paper/pencil method, and instead of having a “neutral” face as students are stating solutions discuss what made something correct/incorrect. Once that piece is understood, go ahead and show how the same solution can be given on a calculator and have kids practice using it and seeing what keys were used (and in what order) to derive the final solution wanted. If there were students who did not get the correct final solution on the calculator, peers can assist one another until the entire class knows how to use the calculator correctly.