Keywords: Proof, Standards...
Ref: Nate1
Author(s): Knuth, Eric
Date: 2002
Title: Proof as a Tool for Learning Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 95, No. 7 pp. 486-490
Reviewer: Nate
Date of Review: 02-14-2005
This article brings up many points about proof. The first is that it is central to mathematics, but is not taught enough to represent that centrality. It also states that the NCTM standards are changing this, but that more remains to be done. Defining truth as "a demonstration of the truth of something," Knuth also argues that secondary students will actually understand math better if proofs are more prevalent. He continues to give examples of different ways to prove something using language and methods accessible to different age groups. These alternate forms of a proof allow it to enter the classroom without being overly daunting to the students.
This article brought up many good points. I think proof is a beautiful thing, and central to mathematics, just as Knuth does. However, I am one of the many that despised it in ninth grade Geometry. It was the first, and last time I saw it before college. I completely agree that my apprehension occurred because of a lack of experience with proof, and I think Eric's solutions should be implemented, and the subject considered more.
Keywords: Equity/Diversity......
Ref: Nate2
Author(s): Gilbert, Melissa C.
Date: 2001
Title: Applying the Equity Principle
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 7, No. 1 pp. 18-19,36
Reviewer: Nate
Date of Review: 02-16-2005
In the article, Milissa Gilbert does a good job of presenting a brief introduction to a problem of equity, and a couple good activities that can help solve that problem. She recognizes the main problem that students can contribute, and thus learn unequally in the classroom. She suggest a variety of learning tasks, instead of just teacher "question and response". Group work, in which each person is required to know the subject matter is a key idea. Also, an intriguing suggestion is one of having each group become the expert in something, and then form new groups with one member from each of the previous groups. Then, they each have something they need to teach to the others, and also have to learn from the others. Another key idea is reinforcing that each student is learning for themselves, with less emphasis on right and wrong, and more on discovery. Then each student is a discoverer.
This article laid out some pretty good solutions to equity problems. It didn't address where these came from, but the variety of activities and strategies outlines would be a very valuable tool. Some of these activities create other problems than equity, such as placing the level of understanding of an entire group on one expert. Equity is most certainly something that needs to be combatted, but we must realize that battling that problem can create weaknesses in other areas, in order to prevent those weaknesses from harming the lesson.
Return to IndexKeywords: Probability, Activities...
Ref: Nate3
Author(s): Barrs, Sharon; Lanier, Susie
Date: 2004
Title: Let's Play Plinko: A Lesson in Simulations and
Experimental Probabilities
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 96, No. 9, pg 626-629
Reviewer: Nate
Date of Review: 02/21/05
No one who has watching the Price is Right can deny getting excited when they hear the word "Plinko". Plinko is one of the games the show features, and it involves dropping chips into a pegged board so that the chip hits the pegs and comes to rest at the bottom. It's an exciting game to play, especially when you actually have the possibility of winning the 10 grand in the middle spot. It gives in depth instructions on how to build the Plinko board, and how to play the game, as well as how to arrange it as a class activity. Also included were questions that their students asked after playing that were exactly the sort of probabilistic ideas they wanted to raise.
This article had some good suggestions for class, and I know I was excited to play the game. The calculator program can also simulate much faster than in real life, if you'd like to perform a large amount of trials without actually dropping the chips, which would be very useful for a more advanced classroom. We could also watch the calculators' results approaching the theoretical expectancies. And, the kids can play Plinko on their calculators after, reinforcing their discoveries every time they play. Fun homework. It's not quite the new car, but it's something.
Keywords: Teaching Strategies, Measurement,
...
Ref: Nate4
Author(s): Beckman, Charlene; Thompson, Denisse; Austin,
Richard
Date: 2004
Title: Exploring Proportional Reasoning Through Movies and
Literature
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 9, No. 5, pg 257-262
Reviewer: Nate
Date of Review: 02/21/05
This article was very eye-catching. It was asthetically pleasing, and what could be more interesting than using movies to teach? It gives numerous examples of recent movies in which proportions were used to make people or objects look a different size than they really are. Harry Potter had Hagrid the giant. Lord of the Rings had the short hobbits, and seven foot tall Gandolf. The Perfect Storm had enormous waves. All of this was done by making the set a different size. The article was mostly a synopsis of these movies, and the actual ficticious sizes of the people and objects. It also included numerous sample problems with the proportions computed to be used in a classroom. After these problems, the article stated the purpose: to motivate students of mathematics. Just as I was interested in this article, so math students will be more interested in the problems knowing that they are working with some "real life" numbers from their favorite entertainment.
This article was quite long for the subject it posed. It was very helpful with the synopses and sample problems, practically giving the entire lesson. This implies that they did the work and a teacher doing this lesson would do practically nothing. I felt a little bored reading the article because of this, but obviously if I were teaching middle school math currently, the specifics would intrigue me more.
Return to IndexKeywords: Algebra
Ref: Nate5
Author(s): Martinez, Joseph G. R.
Date: 2001
Title: Thinking and Writing Mathematically: "Achilles and
the Tortise" as an Algebraic Word Problem
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 94, No. 4, pg 248-252
Reviewer: Nate
Date of Review: 02-28-2005
Achilles and the Tortoise is a classic problem. Not only does it have the fictional appeal of Greek gods, it is also a great paradox, and can introduce the subject of limits at a very young age. The author of this article presents studies that have stated that students, even able to perform the mathematics behind word problems will have trouble translating them into the mathematical form in order to complete them. He says that word problems need to be more prevalent in math classes. He uses this intriguing example as a word problem that can be completed, using several mathematical tools that are available at many different ages. He gives an example of the movie I.Q. in which this problem is presented, and this could be used as a discussion starter as well. The problem is a useful one at all levels.
Word problems bring in the everyday application that is necessary in math. Just performing arithmetic algorithms does not work on the many sides of math, like communication, or connect the students with a situation in which math is useful to solve something. This is the main reason why people don't like math, they think it is so abstract, something so distinct from everyday life that it could never be useful. Using word problems, especially word problems of this fun level, and with Martinez's great techniques, this could be an outstanding class time for beginning to end this disparity.
Keywords: Communications, Teaching Strategies...
Ref: Nate6
Author(s): Ross, John
Date: 1995
Title: Students Explaining Solutions in Student-Directed Groups
Journal or Publisher: School Science and Mathematics
Volume, Issue, Pages: Vol 95, No. 8, pg 411-416
Reviewer: Nate
Date of Review: 02-28-2005
This article summarizes an in-depth study on the results of cooperative learning in a math classroom. It also pulled together results of other significant studies and looked at the benefit and cost of student cooperative learning. The students were placed in groups, and asked to complete word problems that used the mathematical tools that had already been taught to them. The students were in 6th grade, and were supposed to build upon their problem solving skills, as well as their communication skills, being able to explain their answer to their group, in order that a "more preferred", not "right" answer be decided upon. This was meant to accentuate the possibility of more than one answer. Ms. Scott, the teacher, circulated and monitored group discussion, interceding to tell the students to explain how they got the answer so that everyone could understand. She did not tell them if their answer was wrong, but pointed out inconsistencies in their argument if they had one.
This article was great for analyzing the proposed, and continued change of how math is taught. This new kind of classroom reeks of constructivism, with the teacher's role reduced and student's knowledge increased. Additionally, their classroom has gone from an individualist view to a group-learning environment, more typical of the "real world". I especially enjoyed it, because it highlighted the problems with teaching math (or anything else) this way, and showed the appearance of them in Ms. Scott's classroom. One main issue was that students lost the belief that their teacher always held the answer, and was smarted than them. This and the fact that answers were witheld lead to a more uncertain classroom environment. I have felt this uncertainty myself in these type of classrooms. From this strategy arises less confidence in the subject, although more is learned in communcation, and problem solving skills instead of algorithmic thought. This is good for math, but I think Ms. Scott needs to somehow portray that there IS one known answer, and she knows it, but that the students need to discover it for themselves. The whole point of the group work is that they can explain the problem, not just yell out the answer. Another interesting result was that the strong students still dominated the group, even when the task of leadership was given to a quieter or person with less mathematics ability. An environment of tutorship was instilled, and this is a good thing, but still shows students if they are "better" or "worse" at the problem by more directly placing them with someone who can find the answer faster.
The results of group work are not surprising. Better communication skills, and a new view of math. But a danger comes along, and because it's a known danger, as a teacher whenever group work is done, I need to circulate and insure that students are attempting to explain their answers well to the group members. Also, constructivism is great, but the students still need to know I'm smarter than them in order that they have faith in the subject of math and its power.
Keywords: Representations, Keyword 2,
Optional......
Ref:
Nate7
Author(s): Rubenstein, Rheta; Thompson,
Denisse
Date: 2001
Title: Learning
Mathematical Symbolism: Challenges and Instructional Strategies
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 94, No. 4, pg. 265-271
Reviewer: Nate
Date of Review: 3-7-2005
One of the main reasons people consider math to be so highly abstract is the fact that it uses a completely different language. Symbols have their meanings, and they will not be visited in any other type of classroom, and that sets math apart, being different from everything else. The difficulties students have with understanding and writing these symbols is a major roadblock on their path to learning the material. Also, mathematical symbols need to be understood for their abstract meaning, and thus need to be vocalized not only in the conventional way, but possibly in a few others in order to completely define and understand
This article brings up some great points. I know one of the only causes of frustrations for me over the years of math has been so much new notation, and having the symbolism overwhelm me. I had to translate each part into "regular" language before continuing, and this was tough for large groups of symbols. If the recommendations of this article are taken, I think students would become less discouraged by the symbolism, which I would venture to say is one of the main cited reasons for a dislike of mathematics.
Keywords: Connections, Teaching Strategies...
Ref: Nate8
Author(s): Fernandez, Maria
Date: 1999
Title: Making Music with Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 2, pg. 90-96
Reviewer: Nate
Date of Review: 3-7-2005
This article highlights some activities children can complete while making music. They use pop bottles and water in order to create certain pitches by blowing into them. Varying the volume of water in the bottle changes the pitch, according to certain amounts. Using special hardware, they can graph the function on their calculators. They can then see which pitch it is, and then make certain ones for a song they had set out to make in the beginning.
Mathematics and music are closely related. From Pythagoras to the present, the oscillation of the air molecules have been observed to be in certain relations to the pitch, and this can show them that something that everybody loves in some form uses an application of mathematics. This is a large example of physics as well, which draws in another subject. Unfortunately, this would be a difficult thing to do without a good deal of equipment to measure the sound. Slight modifications, and a tuner could do the trick as well, with a follow-up with the mathematical properties of a sound wave.
Keywords: Algebra, Assessment...
Ref: Nate9
Author(s): Kenney, Patricia; Zawojewski, Judith; Silver, Edward
Date: 1998
Title:
Journal or Publisher:
Volume, Issue, Pages:
Reviewer: Nate
Date of Review:
Keywords: Algebra, Assessment...
Ref: Nate10
Author(s): Kenney, Patricia; Zawojewski, Judith; Silver, Edward
Date: 1998
Title: Marcy's Dot Pattern
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 3, No. 7, pg 474-477
Reviewer: Nate
Date of Review: 03-15-2005
Marcy's Dot Pattern is a widely used assessment problem in which one starts with 2 dots, side by side, and then goes to the next step by adding a row and column to have 6 dots, 3 across and 2 tall. This same process continues ad finitum. The problem is to figure for Marcy how many dots are in the 20th step without performing every one. Most of the students completed the problem by realizing that the dot arrays are n by n+1 where n is the step. They simply plugged in 20, and got their answer. The grading on a NAEP exam was done in a strict rubric, asking not only if the answer was correct, but if the student explained it well enough to have someone on the outside understand their process.
This is a great problem, in that it uses algebra where the longhand way would be very tedious, as the answer is 420 dots. I sure wouldn't want to draw that many. Also, it discusses many different solution techniques, as well as some grading information, which would make it an easy, and well-researched problem to include in an algebra exam.
Keywords: Number and Operation, Teaching Strategies, Representations
Ref: Nate11
Author(s): Lo, Jane-Jane; Watanabe, Tad; Cai, Jinfa
Date: 2004
Title: Developing Ratio Concepts: An Asian Perspective
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 9, No. 7, pg 363-367
Reviewer: Nate
Date of Review: 03-15-2005
This article present an excellent idea for looking at completely new ways to teach middle schoolers ratios. It is a main subject of study for students that age, and it remains a difficult task, to learn, and thus, to teach. The main difference in introduction is that 1:3 and 1/3 are thought of in two separate ways, which is unlike American textbooks.The 1:3 ratio is thought of as a "multiplicative relationship between two queantities", whereas 1/3 is called the value of the ratio. Presenting ratios in this way seems to limit confusion, saying that there are a couple different ways of representing ratios. In addition, other main studies were done in the ratios of sports scores, and in making sure units were equal when performing ratio problems.
In order to teach a difficult subject better, it's important to look at a number of different teaching strategies in order to find the best one(s), but also in order to be able to explain things as many ways as possible if a student still is confused. This article does a great job of representing a fresh viewpoint to the subject of how to teach ratios, and I think it's a great alternative viewpoint that can be mentioned if needed. It's important to keep a large arsenal, and more articles like this would do a great job of stocking it.
Keywords: Geometry, Activities...
Ref: Nate12
Author(s): Lege, Steve
Date: 1999
Title: Why Not Three Dimensions?
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 92, No. 7, 560-563
Reviewer: Nate
Date of Review: 04-06-05
This article discusses the authors frustrations in student's difficulties when encountering more than 2 dimensional ideas. He decided that the difficulties were due to the fact that standard curricula do not deal with the idea of a third dimension until it is necessary to already visualize it, such as in Calculus. Lege describes three different activities that are to be done in three separate grades, and thus give the students a continued background in this difficult area. They include making three dimensional ellipses, quadratic surfaces, and solids of revolution.
The most difficult subjects for me in Calculus were those of calculating volume. I loved the idea of extending it into another dimension, but my inability to visualize what we would have when rotating about some axis hampered mine, and everybody else's ability to progress. Multivariable calculus continued this trend, with it being very intriguing, but still slightly foreign. My professor did a good job of representing these figures on a two dimensional chalkboard, but I'm sure my brain would have appreciated it if I actually saw a three-dimensional object. I think this is a big area that I'd need to supplement in about once a year, as Lege suggested.
Keywords: Proof, Curriculum, Geometry
Ref: Nate13
Author(s): Cox, Rhonda
Date: 2004
Title: Using Conjectures to Teach Students the Role of Proof
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 97 No. 1 pg. 48-52
Reviewer: Nate
Date of Review: 04-11-2005
Proof is one of most difficult subjects facing students today, and it is one that they despise most. This suggests that proof is being taught in a way that is not best. Rhonda Cox devises an entirely new unit based on geometric proof. She replaces the normal unit on quadrilaterals with this one, and uses constructivist ideas in order that the students might come up with their own ideas to prove. Amazingly enough (or logically enough), most of the time the students come up with all the main theorems that were in the book about quadrilaterals, despite the fact that she temporarily confiscates the textbooks during this unit. Also, along the way if a concept needs to be concretized, such as a line joining the midpoints of two opposite sides, she just asks them to name their concept (it's normally coined a "midsegment"). This new unit produces a much more positive outlook on proof in the students' minds. Not only that, but their ability to process proof techniques is heightened; by the middle of the unit they are able to write proofs that have 20-30 steps. Even advanced mathematics students have difficulty with anything this involved. Also, the ability to search for things they think are provable about a defined object, while defining new terms along the way, is a huge part of what "real life" mathematicians do. All of these advantages result in Rhonda's recommendation of her unit.
Proof is a difficult subject, but one that lies at the heart of mathematics' true nature. This newer way of looking at proofs results in a much better outcome: the students understanding what proofs are and how to complete them. Due the the logical progression of math, the students also build for themselves the main theorems that are important classically to whatever subject they are studying. This sounds like a great idea for any teacher, especially of Geometry. Anything's worth a try if students come out of it saying, "Proof isn't as bad as I thought!".
Keywords: Algebra, Standards...
Ref: Nate9
Author(s): Burke, Maurice; Ericson, David; Lott, Johnny; Obert, Mindy
Date: 2001
Title: Navigating through Algebra in Grades 9-12
Journal or Publisher: NCTM
Volume, Issue, Pages:
Reviewer: Nate
Date of Review: 04-05-05
This book, presumedly because it is published by the National Council of Teachers of Mathematics, gives some in depth ideas for following the standards and principles of the NCTM. It illustrates its points by having sample problems, including how to teach them, and some samples of student's thinking. This is very helpful information, as it is real, and helps us understand how children think, and thus how we should teach.
This seems like a pretty neato thing. It dispels some myths, and shows us how to do things according to the standards. I think the standards and principles can become so disconnected from teaching, even if we read them and think we understand them. But if we read things like this, we can be refocused on those principles and standards. The included goals of each lesson help us to see the small, daily picture while keeping in mind the larger one.
Keywords: Games, Gifted , Problem Solving
Ref: Nate14
Author(s): Cheryyak, Yuri; Rose, Robert
Date: 1995
Title: The Chicken from Minsk
Journal or Publisher: BasicBooks
Volume, Issue, Pages:
Reviewer: Nate
Date of Review: 04/20/05
This is a great book of brainteasers. Despite the fact I was stumped by the first one (and most of them that I looked at), the puzzles were fun. They used logic, as well as mathematical ideas to solve. The upside down hints are a classic in these sorts of things, but with some of the more obvious puzzles, the hints in this book were mostly for comic relief. Of course, there are numerous puns, which add to the evidence that this book belongs in a mathematics classroom. The solutions in the back are thorough, and understandable.
This would be a great book to pull extra credit problems from, as well as to give to keep gifted students busy while you're teaching the rest of the class. The problems are presented in an attractive and goofy form, so a high school student would be likely to find these enjoyable, even if the solutions are fairly complex math in some cases. The authors of the book intended it to be this way, and since some of the problems stumped students at MIT, I suppose I won't feel bad about being confused.
Keywords: Equity/Diversity, Keyword 2, Optional..., Keyword 3, Optional...
Ref: Nate15
Author(s): Trentacosta, Janet; Kenney, Margaret
Date: 1997
Title: Multicultural and Gender Equity in the Mathematics Classroom
Journal or Publisher: National Council of Teachers of Mathematics
Volume, Issue, Pages:
Reviewer: Nate
Date of Review: 04/25/2005
This book is a very pertinent publication consisting of twenty-eight essays written by a number of different people that address cultural and gender issues in math class. We have all seen data that support that men have dominated mathematics in the past, but unlike most other disciplines, things have not evened out recently. It has been proven that, usually unintentionally, girls are discouraged in math classroom by many different factors. These include curriculum and teachers attitudes, to name a few important ones. Of course, it is hugely important to the discipline and to those individuals that everyone have a chance to contribute, and so this collection of essays responds to the problem with a number of discussions and solutions.
The essays are divided into five subjects, including 1) issues and perspectives, 2) classroom cultures, 3) curriculum, instruction, and assessment, 4) professional development, and 5) future directions. The essays cover the problems that have been outlined as well as educating the readers about the issues. As any educator should agree, making people aware of the problem is a great first step to solving it in and of itself. With such terms as "ethnomathematics, microiniquity, and feminist pedagogy", it is a great educational piece. Additionally, a number of solutions are offered. For the articles relating to gender inequity, they said that including each of the students personally in their assessment and other interaction is first and foremost. Also, steps to more broadly foundationalize math will also help. Some examples are including other subjects in the classroom, such as keeping a journal, and writing problems that include a broad range of subjects.
It seems as though the thing to combat equity issues are the same things that we need to do to keep each child involved. We need to make sure everyone is engaged, and keep them that way. Showing care with not only actions, but the assessment and curriculum will go a long way toward closing the gap.
Keywords: Games, Puzzles, Planning
Ref: Nate17
Author(s): Sobel, Max; Maletsky, Evan
Date: 1990
Title: Teaching Mathematics: A Sourcebook
Journal or Publisher: Prentice Hall
Volume, Issue, Pages:
Reviewer: Nate
Date of Review: 05-05-2005
This book looks like a lot of fun. It it packed full of problems that are good for supplmenting textbooks with. The problems are arranged by subject in chapters, and seem to be designed in order to expand the student's ideas of each of the subjects. The chapters include: opening and closing problems/tricks, algebra, geometry, statistics, iteration and fractals, and quite a bit more. I think this would be a great problem supplementer for any textbook. It allows the teacher to bring in some creative things that will peak students' interests and possibly even amaze them. One example is a "think of number" and then the number they end up with will all be the same. The book suggests writing this number on the back of your hand with soap, and then burning their number and using the ashes to make the end number appear after you have completed the operations. This mathmagic will amaze anybody in middle school, and allow for a discussion on algebra to occur. I would suggest this book to anyone looking for a way to put some extra excitement into the classroom.
Keywords: Technology, Number and Operation...
Ref: Nate17
Author(s): Calvert, Lynn
Date: 1999
Title: A Dependence on Technology and Algorithms of a Lack of
Number Sense?
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Vo. 6, I. 1, pg. 6-7
Reviewer: Nate
Date of Review: 04/27/2005
Calculator dependence seems to be one of the biggest complaints amount math teachers and other opinionated people. They seem to think that since they learned how to compute everything by hand, those younger would benefit from it as well. Calvert says that the problems with understanding have nothing to do with a calculator being present or not, and everything to do with the fact that we are not allowing students multiple ways of solving a problem. She says that we need to teach students to come up with creative number sense ideas that allow them to compute simple arithmetic tasks more quickly. For example, 6x4 can also be thought of as 5x4+4 or 3x4 doubled. These allow children to solve the problem without recalling the answer from memorization or writing it down with a set algorithm. Another example would be figuring the cost on 11 toys at 78 cents each. A good way to do this is to add the cost of 10 and the cost of 1.
This article brings up some good points. I don't think calculators are bad, or that kids need to learn algorithms to compute these problems. My elderly neighbor across the street likes to visit with me while I'm outside, and has been repeatedly appalled when I cannot compute square roots unless they are whole number solutions without a guess and check method. I think we need to look at problems in a number of ways, and discern what mathematical concepts are more important than computational algorithms. I think teaching these concepts will allow for more creative methods to be used.
i do think the author downplays the role of a calculator though. Possibly she didn't have time to develop this, but without the initial teaching of what multiplication is, students can't understand the symbol well enough to come up with different ways of looking at a problem. If they have always just plugged it into a calculator, it's likely that they will never bother to understand the concepts well enough to differentiate in their computation. In order to teach many of these subjects, calculators need to be hidden until a basis of knowledge is present, for multiplication and taking the square root alike.
Keywords: Proof, Problem Solving...
Ref: Nate18
Author(s):
Date: 2005
Title: Proof: Finally a Logical Approach
Journal or Publisher:
Volume, Issue, Pages:
Reviewer: Nate
Date of Review: 05-03-2005
This talk was about some new ideas for ways to go about teaching proof. Proof is one of the most difficult ideas, normally forced upon students in Geometry. It needs to be more slowly introduced, gradually with the small ideas before an all-out two-column proof is demanded.
Games were included, one with guessing a number the teacher was thinking of. The students can use proof by contradiction, and analytical thinking of many different pieces of information in order to arrive at the answer. Another activity was making pizza, arranging the different things that needed to be done. The students have to think of what needs to be done first, establishing the idea of assumptions, and what we can derive from these assumptions.
Proofs were by far my least favorite part of math up to college, and it's because they were thrown on me. Now, proofs are one of the most fascinating and exciting parts of math to me. Now that I understand the ideas, it is very envigorating. If we teach kids proof slowly, I think many of them can gain the appreciation much earlier than I did.
Keywords: Gifted, Connections...
Ref: Nate19
Author(s): Ed Zaccaro
Date: 2005
Title:
Journal or Publisher:
Volume, Issue, Pages:
Reviewer: Nate
Date of Review: 05-03-2005
Ed Zaccaro was the most entertaining speaker I saw at the MCTM conference. He had great stories, quips, and never skipped a beat, even when being asked questions from those observing. His talks that I attended were a talk on teaching gifted children, and a second one on the ten things future mathematicians must know. His points were well taken, and had great support to back them up. His quizzical mind carried tons of random data, and he showcased it in his talks.
Even though the talks were great, a lot of the information was less than useful. Many of the points are some of the most important things we need to convey in mathematics. One of his most interesting points was that statistics can be made more interesting by asking students to take data, and make it appear as though it says the opposite of what it does say. This helps students to become highly analytic when it comes to the statistics used everyday in the news. Another one is that the solutions to many problems are counterintuitive. This would be great to remember in math classes to make sure that students can back up their answer and are really thinking about what is happening.
I think his ten points were great life ideas, and I might post them around my room in order to point them out when I need to. They will also be useful for disagreements in class that have nothing to do with mathematics, and everything to do with the students' lives and feelings.
Keywords: Technology, Representations...
Ref: Nate20
Author(s): Wyberg, Terry; Wygant, Sue
Date: 2005
Title: Realize the Power of a Spreadsheet
Journal or Publisher:
Volume, Issue, Pages:
Reviewer: Nate
Date of Review: 05-03-2005
This session was conducted by Sue Wygant from Burnsville High, and Terry Wyberg from the U of M. The ability to conceptualize algebraic concepts is difficult, as many conic sections' properties can only be realized when various algorithms act on them in order to get vital data. Latus Rectum, vertices, and foci are only a couple of the terms that confuse algebra students. These terms and algorithms rarely leave students with a sense of accomplishment, or any intuitional understanding about what they learned all year. A new way of representing these ideas is necessary, but many of the computer programs are excessively expensive. The solution is using an extremely common program to do the easier of the graph work: Microsoft Excel.