The article, "Changes in Your Classroom: From the past to the Present to the Future" by Gail Burril, is in regards to math anxiety and how it guides the perception of what is, or should be, taking place in mathematics classrooms. The article leads us from the past to the present, and to the future of mathematics while at the same time acknowledging the importance of a coordinated curriculum and representation.

Twenty-five years ago, most students did not like the mathematics that they took and did not find it to be useful. For this reason most students did not take mathematics beyond the first or second year in high school.

In recent years, we have seen improvements. More students are taking three and four years of mathematics. At the university level the number of students taking remedial courses has dropped. Even with these signs of improvement, we still have more goals to reach. To continue changing the direction of mathematics some existing beliefs must be overcome. "In Algebra Unplugged, Jim Loats and Kenn Amdahl (1996) summarized some 'great lies in mathematics': (1) There is only one way to get the answer. (2) All problems can be used by a step-by-step method. (3) There is a mathematics gene. Some people have it, others do not. (4) Mathematics is hard - too hard for most people to learn. (6) Mathematics is mostly memorizing. (7) Only geniuses are capable of creating or understanding formulas and equations." Overcoming these beliefs is an important hurdle. Too often these beliefs are conveyed to and lived up to by children.

We need to re-examine what we should teach. The career options today's and tomorrow's students have are very different from those we had. In order to prepare students for the technological world we live in, we may need to change the content that we teach in mathematics as well as how we teach that content. We must build a curriculum that flows through pre-K-12 into one coherent whole. In the Proctor School District, we are attempting to adopt a new coordinated mathematics curriculum that will meet the needs of our students. We want to find a common knowledge base for students to have by a certain grade level and to avoid too much review and remediation.

Not only do we need to look at curriculum coordination, more attention needs to be placed on representation. Representing and understanding representation is the key to using technology effectively and organizing and processing information. We need to show students that there are different ways to address a problem. Often the problems students see in text books are similar and when they are confronted with a problem not in the text they struggle. "Too often we teach students to do, not to think." One of the things I hope that the Graduation Performance packages can do is show how concepts overlap and reinforce one another. These performance packages should draw from real life situations and help students assess how their strategies are working.

Improving mathematics education will continue to be challenging. The National Council of Teachers of Mathematics encourages a vision for a future where people do not live in fear of mathematics; where people use more mathematics in their daily lives; and where mathematics will continue to build on what we already know.

Burrill, Gail. "Changes in your Classroom: From the past to the Present to the Future." Mathematics Teacher Dec. 1998: 800-806.

-- Anonymous, January 19, 1999

Answers

THE IMPORTANT CHARCTERICSTICS ATHLETICS DEVELOP AND HOW THEY RELATE TO EDUCATION.

The information in the article, "Education--A Whole New Game," by Dr. Joel Kirsch lends additional support to our thesis topic that students involved in high school athletics do better academically than their peers who are not involved in high school athletics. According to the article there is currently a push to reform our educational system. The focus may be on standards, instruction and curriculum, vouchers, or charter schools. In each situation many people believe that participating in sports takes away from academic achievement. As a result, we are seeing a decrease in emphasis on sports in our schools. A loss in funding also coincides with the decreased emphasis on sports. With the information provided in this article, people may change some of their perceptions on the important characteristics athletics develop and better understand how these athletic characteristics can benefit education. The following concepts are developed through athletic participation, many of which could also be applied to educational settings. 1. Self-paced learning: Developing skills at their own pace, no matter their age, gender, ethnicity, or how hard they work. 2. Mastery-based learning: Working on skills continually, instead of moving from one thing to the next. Quality is valued over quantity! 3. Relevance: Spending countless hours on the basics because they are relevant. 4. Engagement: One must be actively engaged in the learning process or he/she simply will not improve his/her skill level. 5. Learning through coaching: Demonstration on how to do something, explaining why it should be done in a certain way, and then repeating it over and over until performed at a high standard. 6. Demonstration learning: Perform in front of others to demonstrate skills. 7. Team-oriented learning: Individuals seeing themselves as part of a larger cause, something that goes beyond themselves, they must experience a sense of place and belonging. 8. Character development: The quality and success of a team is directly related to the character of its players.

Many examples from athletics could be given for each and every one of those concepts. Those concepts are a large part of what makes athletics successful and a valued learning experience. Throughout the school day, one could surely provide instances where these concepts come out in education. However, to say the focus of a particular academic subject would be on those concepts would be unfounded. As an example, if a basketball coach were to spend two weeks on the techniques of shooting a free throw, go through all of the coaching sequences, and provide many opportunities for repetitions, would this coach experience success and then say that his team has covered this aspect of the game and not return to it any more during the season? Highly doubtful. This situation would never occur. Does it occur in the educational settings? The answer is yes. Often a teacher will cover a unit, say OK now that unit is completed, and move on without ever mentioning it again. At times this can be caused by the pressures of getting all materials covered before running out of time. Perhaps if more of these ideas were taken from athletics and incorporated into daily educational settings, we would see a rise in success rates with students. Kirsch, Dr. Joel, President of the American Sport Institute., "Education--A Whole New Game." Available: http://www.amersports.org/pers/kirsch.html (10, March 1999) Yahoo

-- Anonymous, April 05, 1999

#3 Professional Article

The article, "A Star to Guide Us," by Rick Norwood explains the history of the multiplication sign. The author, Rick Norwood, refers to the multiplication sign as having the worst luck of any mathematical symbol and goes on to say it has been a problem from the very beginning.

The symbols we use today in mathematics for addition, subtraction, and division were put into use around A.D. 1500. It was not until as early as A.D. 1000 that "5 times x" was written as 5x or 5(6), where parentheses are needed to avoid confusion with number 56. However, mathematicians thought that rather than multiplication being the "understood" operation that it should be addition, and 5x should mean 5 plus x. This assertion soon faded out. It was not until around 1574-1660 that William Oughtrid invented the times sign, x, but this symbol was and is too often mistaken for the unknown x. For this reason is 1646-1716 Gottfried Wilhelm Leibniz indicated a new sign for multiplication, the raised dot. Although the dot is raised it still leads to much confusion with the decimal. Even with all the confusion the three previous symbols are still in use today.

Modern mathematicians are doing away with two of the previous symbols and are using the understood sign or now the computer sign, *, the star. As a high school math teacher I too would like to see us eliminate the times sign and the raised dot. The star symbol seems most appropriate for all age levels and we are moving forward in the world technology. Most calculators show the multiplication symbol on the view screen as an star. The unknown method appears to be valid in upper level mathematics when students or mathematicians are trying eliminate too much writing and no one wants to do away with our elegant notation for writing polynomials. For example the unknown method for a polynomial would look like this, (3x2 + 2x + 5). The star method would look like this, (3 * x^2 + 2 * x + 5).

I agree with the author that it may be time to eliminate both the times sign and the raised dot. It would be great for math education if students could learn the star from the very beginning.

Norwood, Rick. "A Star to Guide Us." Mathematics Teacher FEB. 1999: 100-101.

-- Anonymous, April 07, 1999