Great Ideas of Primary Mathematics

Rationale

Following the completion of the unit, students will have achieved a proficiency in concepts fundamental to mathematics and Science. This is of critical importance since statistics show that US students are falling significantly behind in math and science. The latest PISA (Program for International Student Assessment) results reported that Americans were receiving lower scores than schools in over half of the developed countries in the world. This implies that US students are not achieving a robust understanding of key principles of mathematics. Thus, many questions have to be answered to find a solution to this systemic problem. The immediate question of this unit, is how can students overcome the challenge of understanding scientific notation. The unit provides a solution to the question by providing strategies that reinforce the concepts of accuracy and order of magnitude. Essentially, this is the foundation of scientific notation. Understanding these concepts could help students deal with more complex, abstract concepts, such as Black Holes and The Big Bang Theory.

For my students in particular, much of the emphasis will be placed on understanding what scientific notation represents. My students struggle with this concept equally if not more so than other concepts in astronomy. Therefore, we will spend a significant amount of time on the topic.

The students in my class dress the same, talk the same and also come from similar backgrounds. They consist of kids from urban areas whose families generally do an adequate job of providing for their children. It is understandable to see how these characteristics can make my class seems as though it lacks diversity. On the surface it may appear that way, but when analyzing intellectual levels, the students in my class can range from a elementary to high school levels in math and reading. This requires diverse strategies when attempting to attain the objectives with the overall class. Thus, by focusing on the fundamentals and less complex concepts, I will give the students a higher chance for success. Successes, whether small or large, have proved to perform wonders for my students, giving them the confidence they need to excel in my class over the course of the year.

Astronomy is both fascinating and challenging to my students,. This is, in part, due to aforementioned relationship shared between math and science. Specifically, students seem to face most of their challenges when applying problem-solving skills. This could be due to their inexperience with the practice. According to some theorist, individuals construct their own knowledge bases, which is to say that human learning is largely a constructive process ². Therefore, without much relevant information to draw from students can become discouraged, inhibiting their growth as a learner. The constructive learning model implies that learners do not simply add new information to their "store of knowledge", but connect the new information to already established knowledge structures and construct new relationships among these structures ². These same theorists also attribute the recognition of patterns as an indicator of the ability to understand content. According to their research, it is likely that pattern recognition skill may involve episodic or imagistic memory representation built up through hours or years of extensive practices in the task domain ³. Because of this, I will implement the strategy of establishing procedures, which the students can use when problem solving with scientific notation. By consistently reviewing these procedures the students will cement concepts in their memory until it becomes second nature and they are able to apply the skills whenever necessary. This is similar to the model used in Japan where teachers are known to spend entire class period or more actively exploring and discussing the variety of approaches that might be taken to solve a particular problem. This supports the argument that depth in contrast to breadth, serves as a stronger method for instruction in the classroom.

As mentioned before my intentions for the unit are to enable students to break down barriers blocking their understanding of the fundamentals of scientific notation. A byproduct of this will be the student's ability to solve real-life problems by applying scientific notation concepts. Currently, my student's struggles seem to stem from their misunderstanding of the fundamentals of Mathematics. In addition, they become frustrated when the problem appears to be a challenge, i.e. word problems or algebraic type problems involving variables. I see these struggles accentuated when the students attempt to process scientific notation concepts in regard to Astronomy. Frustration is also evident when the problem resembles the type of standardized testing question they often see. Their struggles appear to stem from a lack of understanding that has manifested itself during their progression through each grade level. The type of thinking necessary to overcome these obstacles has been lost in time due to teacher's inability to connect fundamental ideas.

In particular, many of the strategies utilized in this unit are drawn from things the students experience in their everyday life. Temperature and currency are two examples that are sure to relate to the interest of the students. In fact, my students give more credence to currency then almost any other representation of success. Therefore, intertwining currency with scientific notation almost assuredly will allow the students to achieve some type of success. It also shouldn't be much of a stretch to expect the same results with distance, time, and size and its relation to light speed since these concepts are also a major part of a student's life. As the unit approaches it's conclusion the idea of estimation will be explicitly discussed so that the students may identify its practical uses and understand its application to scientific notation and accuracy. I also intend to compare aspects of computer science with scientific notation. This will intentionally be done towards the end of unit.