Prealgebra Strategies- Math 1510

This week one of the topics we discussed was prealgebra strategies. We watched a video with young students working with different strategies such as solving word problems and coming up with their own language in order to understand the math problem at hand. Prealgebra strategies can be helpful for very young students because they are being introduced to reasoning skills early on and have more opportunities to practice them before they encounter more complex math problems.

While I was watching the video on prealgebra strategies I found myself thinking back on my days in elementary school math classrooms and my feelings towards math. When I think back on the things that I learned during math class I can remember solving word problems that were similar to the word problems in the video. I can remember solving word problems from 1st grade on up to 11th grade. Each year the problems became harder and harder. In 1st grade we would solve word problems using small numbers such as adding 3 and 2 to make 5. Once I reached the upper elementary grades word problems involved adding three digit numbers or more and multiplication and division. By the time I reached high school the word problems were very complex and involved various formulas and procedures. As I moved through the grades math became more of a struggle for me until I grew to hate math. I am realizing now that everything that I had learned was simply a continuation on everything that I had previously learned. In my mind I was learning something new every year. As a 1st grade I never realized that I was actually doing a form of algebra and as an 11th grader I never realized that the algebra that I was learning was something that I had experience with already. As I thought about my experience more my mind drifted to something that the class had discussed before and that is having a coherent curriculum. Many times my teachers would use different names for the same things or alter steps in solving the same problem. This was beyond confusing for me. I think my relationship with math would have been very different if my teachers based their lessons off of a coherent curriculum.

Should we be using prealgebra strategies in elementary classrooms? I believe that we should. Prealgebra strategies enhance a student’s ability to reason and use their logic skills. If they are able to develop those skills starting from an early age and be stronger problem solvers later, why shouldn’t they be used? If students are able to write and solve their own word problems they can be more confident when they come across a word problem that they didn’t create. Teaching these strategies early on can help create more confident math students and more confident math students means less negative relationships with math.

I found an interesting website for word problems. This website generates word problems based on the season. If your classroom wanted Spring time word problems, simply click on the Spring link under the appropraite grade level and it will generate problems for you.

A Coherent Curriculum- Math 1512

During this first week of class we read an article called “A Coherent Curriculum: The Case of Mathematics”. This article really made me think about curriculum that is being used and what I could do as a teacher. The article opened up with a great analogy:

“Consider the agricultural prospects of two countries: In Country A, the nation takes the best that’s known about growing crops and translates it into clear, coherent, manageable guidelines for farming. These guidelines are distributed to all farmers in the country. Further, Country A makes available to all farmers up-to-date tools (tractors, balers, harvesters, etc.) and training on how to use these tools that allow them to implement the wisdom contained in the guidelines. Just as in any other country, some farmers have inherently greener thumbs than other; they find ways to surpass the guidelines and cultivate extra-rich cops. But the broad availability of the guidelines and tools puts a floor beneath farming quality. As a result, the gap between the most and least-effective farmers is not very great, and the average quality of farming is quite good. Moreover, the average quality slowly increases as the knowledge of the best farmers is incorporated into the guidelines. In Country B, the situation is very different. States, and sometimes towns, assemble a list of everybody’s favorite ideas about farming. The list is available to any farmer who seeks it out, but it’s up to the individual farmers to develop their own guidelines based on the list. The ideas are interesting, but there are too many ideas to make use of, no indications of which ideas are the best, and no pointers on which ideas fit together with other ideas. Plus, using the ideas requires tools-and training about how to use the tools. Few farmers have ready access to either. The result: A few particularly skilled farmers in Country B figure out how to farm productively. They are mainly the farmers in more affluent areas-they have been able to attend great local agricultural schools and can afford the tools suggested by their training. A few additional farmers-those with a special knack-do fine anyway, despite their lack of training and use of poor tools. But most of Country B’s farms aren’t particularly efficient, certainly not in comparison with Country A’s. In Country B, the gap between the most-and least-effective farms is huge, and the productivity of the average farm is far less than its Country A counterpart.”

When I applied this same analogy to teaching it makes a lot of sense. Why wouldn’t we have some sort of guidelines for everyone to use when it comes to what to teach? There is tons of information out there available to teachers and at times it can make it very overwhelming. Now bring in a new teacher. They may have the necessary knowledge they need to teach students, but how do they sift through all of that information to bring together effective lessons. Having a unified curriculum for everyone throughout the country would be very beneficial. It gives teacher the push in the right direction when it comes to planning and all students have been given the same learning opportunities. The thing to remember is that having a coherent curriculum isn’t taking away a teacher’s freedom to teach how they would like. An individual teacher can still pick and choose what activities they use in their classroom.

As a new teacher, I am not going to have a lot of say when it comes to curriculum choices across the district, state, or country. I am sure that there are many current teachers out there right now who feel the same way. The question that comes to mind is what can I do when I first step into my own classroom? One of the solutions that can to my mind is working within the school to create our own coherent curriculum. Not only can I work with my own team of teachers but I can work with the other teams of teacher that make up the other grades in the school. If we can all create our own coherent curriculum, at least at the school level our students will be taught consistently.

I came across an interesting article. Timothy D. Kanold, Ph.D. discusses a coherent curriculum. He is the Superintendent of Adlai E. Stevenson High School District 125 Lincolnshire, Illinois. Stevenson is the only high school in the state to receive four Blue Ribbon Awards for Excellence in Education from the U.S. Department of Education. He must have a good idea of how to implement a coherent curriculum and it is obviously working well. Check out the article by clicking here.