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This article focuses on three main points: "what is mathematical thinking, what does it have to do with mathematical content, and can it be taught." Mathematical thinking according to this article is a series of operations that do not necessarily apply just to math, like the scientific method. There are four processes in mathematical thinking which are: specializing, conjecturing, generalizing, and convincing

In this article the authors talk about how students need an engaging work environment to work to their greatest ability, especially in the field of mathematics. It is often difficult to establish high-level tasks for students because these tasks often cause more uncertainty and stress for students since there is more risk involved. Also, provided in the article is a conceptual framework that is a framework for mathematical tasks. The purpose of this study was to show how classroom factors influenced student's engagement of mathematical tasks.

This article deals with uses of graphics calculators to help the understanding of mathematics, but takes a different approach. It addresses the issue that some scholars make concerning calculators, that calculators impede the understanding of mathematical concepts and only leads to incompetent students. This includes an in-depth analysis of the concepts a graphing calculator can help a student understand.

In this article the authors examine different self-concepts of 3000 students in England between the ages of 13 and 14 years. The subjects tested were English, science, and mathematics. The results were found to be similar to other test that had been done before. An interesting finding was that boys had significantly higher self-concept scores than girls, except for in English.

In this article Flower discusses the different processes that go into thinking and into writing. Also, she goes over the writing processes and the difference between writing to oneself or for different readers. There is also a case study that talks about a transformation. Flower makes several interesting points within the article that would be helpful in the comparison of mathematical and English thinking

Radford discusses in his article algebraic thinking and how students use signs with meanings in algebraic generalization of problems and also students' developing algebraic thinking. The author also examines different signs and their meanings then further discusses how these meanings affect students and their developing algebraic thinking. He also goes over different classroom discussions that took place regarding algebraic thinking. This article has many important points about the development of mathematical thinking but would not be excessively useful to analyze subject based thinking.

This article discusses the great impact that self-concepts have on students' grades and performance, mainly in English and mathematics. These authors found different results than have previously been found in tests; they found that "there were significant positive paths from math self-concepts to subsequent math outcomes but not to subsequent English outcomes." Also, they found that girls had higher English and math grades but lower math self-concepts then boys, these results differ from previous test which claimed that the gender difference was diminishing. These results were interesting due to their difference in regards to other tests conducted.

Rabb discusses how the No Child Left Behind Act has been underfunded leaving the teachers unqualified and underprepared to teach the necessary material for standardized testing. This is one of the reasons students have still received poor results in standardized test scores. Also, there has been such an emphasis on reading and mathematics that students are performing even worse in other subjects.

This article explains how graphing calculators can be used in calculus to benefit students, and also how graphing calculators are changing the way that calculus is being taught. One issue that sets this article apart from the other articles is its assessment of how students are required by most schools to purchase their own calculators. This article analyzes the effect this can have on how the class should be taught, and how calculators put students at advantages and disadvantages depending on how they are used, and how students with more computing power excelled or failed compared to those with the less powerful model of calculator.

About the importance of music education.