Keywords: Teaching Strategies, Problem Solving, Research
Ref: Young1
Author(s): Miller, Catherine M.
Date: 2000
Title: Student-Researched Problem Solving Strategies
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, Iss. 2, pg 136 (3)
Reviewer: Young
Date of Review: 3-21-00
This article dealt with problem solving techniques. What the teacher did was give the different problems and have the students give the problems to three different people to solve for them. The students were supposed to observe the person solving the problem and then ask questions on how the person solved the problem. The teacher then had the students hand in the notes to see what the students were observing. The next day in class the students had to present the problems that were solved for them and explain what different problem solving techniques were used in solving the problem. The students then compiled a list of the tactics used and made the list into a poster that they hung in the room. On each homework assignment the teacher has the students identify which problem solving technique they used to solve the problem. It promotes the students to show their work.
I think this assignment could be very useful to every kind of student. It
gets the students asking themselves how they could go about solving
different problems. It also allows the students to discover for
themselves different types of problem solving techniques.
Keywords: Algebra, Number Theory,
Ref: Young2
Author(s): Singh, Simon
Date: 1997
Title: Fermat's Enigma
Journal or Publisher: Doubleday
Volume, Issue, Pages: book, 315 pg.s
Reviewer: Young
Date of Review: 4-2-00
This book is great. If you want to know the history behind mathematics pick this book up and start reading. The author starts out by giving us the background of Pierre de Fermat and offers us insight on Fermat's Last Theorem. Fermat was an arrogant Frenchmen who challenged rival mathematicians for 350 years with the quote "I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain." The author then talks about the history of mathematics and the discoveries that mathematicians have made that made it possible for Andrew Wiles to solve this 350 year old problem. The book talks about how important proof is for a mathematician and that without proof nothing is for certain. Singh then goes into detail of what it was like for Andrew Wiles to spend seven years of his life proving the unprovable.
This book is really easy to read. I think that it is worth reading
especially if your going into math ed. This book provides us with the
history behind math and describes what tools that math provides. So if
you have a couple of days (the book is 315 pages), I strongly recommend
reading this book.
Keywords: Geometry, Algebra, Technology
Ref: Young3
Author(s): Iovinelli, Robert C.
Date: 2000
Title: Chaotic Behavior in the Classroom
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: vol. 93, No. 2, pg 148 (6)
Reviewer: Young
Date of Review: 4-2-00
This article dealt mainly with introducing chaos theory into the classroom. The article itself just went over the research that the students and teacher did. It was very boring to read. The students modeled equations usin there computers. They tried to find patterns. It was not very easy to read or very insightful. I thought it would be more interesting if the author wrote about how to impliment new material.
I don't think this article is worth your time reading. I just thought it
would be interesting because we learned about chaos and fractals in
geometry.
Keywords: Activities, Algebra, Teaching Strategies
Ref: Young4
Author(s): Winter, Mary Jean; Carlson, Ronald J.
Date: 2000
Title: Liquid Assets: Increasing Students Mathematical
Capital
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, No. 3, pg 172 (7)
Reviewer: Young
Date of Review: 4-2-00
This article illistrates a great activity you could use in your algebra classes. The lab was to take 6 sips of water and after each sip measure the amount of water taken with each sip and then plot your data point. The purpose of the lab was first to take meaningful data and analize it. After the students plotted their graphs they had to make equations that illustrated what their graph did. They had to find the y-intercept and slope using their data. This lab encouraged the students to work in groups. They had to learn how to work with each other in a productive manner. This lab also had an eliment of discovery learning to it. The students took their own data that they collected and came up with their own equations which can be very rewarding to students.
If teach algebra I will definitely consider using this lab activity. The
students learn more if their the ones that are guiding the class period.
It is nice to come up with different activities your students could do on
a regular basis. These kind of activities focus more on "what do I need
to use this (Algebra) for?" questions.
Keywords: Probability, Number Theory, Problem Solving
Ref: Young5
Author(s): Bay, Jennifer M.; Reys, Robert E.; Simms, Ken;
Taylor, P. Mark
Date: 2000
Title: Bingo Games: Turning Students Intuitions into
Investigations in Probability and Number Sense
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, No. 3, pg 200 (6)
Reviewer: Young
Date of Review: 4-3-00
This article first goes into the history of the game of bingo. The authors then tell what exactly bingo has to do with mathematics. Bingo has a lot of mental arithmetic, problem solving and geometry in it. The teachers would ask certain questions about the game of bingo, such as, "Is it easier to get all four corners rather than a postage stamp." The teachers would then listen to the children's comments and ask them to reason why one way would be easier to get bingo than the other. They would then help the students compute the probabilities of each method of getting bingo. Surprisingly to the authors the children's intuitions (reasoning) would generally be correct.
I think this would be an excellent way to introduce a lesson in
probability. I would have the students guess which way would be easier to
achieve bingo and at the end of the unit I would actually have them
compute the probabilities. Bingo relates something that children might be
interested in or at least heard of and puts it into the classroom
environment.
Keywords: Activities, Arithmetic,
Ref: Young6
Author(s): Thomas, Cynthia S.
Date: 2000
Title: 100 Activities for the 100th Day
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Vol. 6, No. 5, pg. 276 (5)
Reviewer: Young
Date of Review: 4-3-00
In this article the teacher came up with activities that you could do for the 100th day of school. She gave some examples, such as, having the students estimate how far down the road they would get if they lined up 100 students on their back. She then line up 25 students on the road and marked how far they got. After that she had the students change their estimations if they wanted to and finished the task. The student who was closest won a prize. For the next activity the teacher had the students see if they could eat 100 things (arranged prior to that day) for lunch and had them write down all they had eaten. The rest of the article gave a list of 100 things that you could do on the 100th day of school.
I think we could do these kinds of activities more on a regular basis.
These activities get the students actively involved and more interested in
what their doing. The hard part would be coming up with the activities
for the curiculum that you are teaching.
Keywords: Geometry, Teaching Strategies,
Ref: Young7
Author(s): Warkentin, Don R.
Date: 2000
Title: Finger Math in Geometry
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, No. 4, 266(3)
Reviewer: Young
Date of Review: 4-5-00
The NCTM says that we need to remove barriers that are language based. The author of this article agrees. He is all for the use of hand signals or gestures (mixed in with verbal directions)when it comes to teaching his students geometry. When introducing a new concept such as a right angle the teacher would explain to his students what a right angle was while holding one hand in the shape of a right angle. The hand signal serves as a mnemonic device to the students. Whenever the students think of a right angle they will think of the hand gesture (or vice-versa). Parents and students have responded very positively to this method of teaching
I think this is a wonderful way to get students to learn geometrical
concepts. You could also put your students into groups and see what types
of shapes they could come up with. Anything that stimulates learning
(hand signals) should be incorporated into the curriculum. Students could
also have a lot of fun working with hand signals.
Keywords: Games, ,
Ref: Young8
Author(s): Gaglione, Jeff
Date: 2000
Title: Relay Review
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, No. 4, 282(2)
Reviewer: Young
Date of Review: 4-5-00
This author starts off his article by stating that students need to see how mathematics plays in their everyday lives. He also believes that students need to enjoy math and they could do so in three ways: projects, group work, and review games. The game that most his students liked the most was a game called "Relay Review." You split the students up into teams of about 3-5 students and have each team line up in their designated rows. Then, place index cards (with problems on them) at the board directly in front of each team. Hand the first person in each team a baton. Start the game. The students with the batons then race up to the board and solve the problem from their designated pile. When correctly answering the problem the students at the board then pass the baton to the next person on their team. The author says this is a fun way to review for tests and the kids see how to do the math correctly while cooperating with other students.
Personally, I am all for review games. My teachers in high school always
came up with fun games to play to review for tests. Everyone in the class
participated and had fun. Review games are a great way to relieve tension
before an upcoming exam.
Keywords: Standards, ,
Ref: Young9
Author(s): NCTM
Date: 2000
Title: Shaping the Standards: "Higher Standards for Our
Students, Higher Standards for Ourselves"
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: vol. 6, No. 8, pg 498(2)
Reviewer: Young
Date of Review: 4-26-00
This article highlights the progress that the NCTM has made throughout the years. It goes on to tell us how much time and effort was put into creating the standards. The writers of the standards got feedback from a wide rand of audiences. The article then goes onto tell us about the electronic edition of the standards. We all can be proud of what the NCTM has accomplished.
The title of the article to me was very decieving. I thought the article
was going to tell about the high standards that we're setting for out
students, but it didn't. The article only reflected on the development of
the standards and that was it. It's not worth the effort to read--trust
me.
Keywords: Probability, ,
Ref: Young10
Author(s): Edwards, Thomas G.; Hensien, Sarah M.
Date: 2000
Title: Using Probability Experiments to Foster Discourse
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Vol. 6, No. 8, pg. 524(6)
Reviewer: Young
Date of Review: 4-26-00
The article starts off by saying that probability (informally) should be incorporated into the elementary classroom. The article then states that doing probability experiments is a good way to explore probablility because they are fun and they naturally peek the students interests. The experiments highlighted in this article are for fifth graders and they are as follows: (1.) Flip a coin 25 times, and record the results, (2.) Spin a spinner 25 times and record the results, and (3.) Toss a die 30 times and record the results. The goals of the experiments are for the students to construct a concept of equally likely events, assign a theoretical probability to events, and relate the theoretical probability of an event to the observed relative frequency of that event during the experiment. The article then tells what happens when the students do the experiments. The results I must say are very surprising. The kids catch on very quickly to what is being taught.
Using these types of methods to get the students to explore math is always
a great idea. This lesson was exactly like the one that the visiting
teacher gave in class. At first I didn't think that elementary students
would be able to grasp the concepts of equally likely events and what not.
I wonder if doing something like this would work in all classrooms. I
think this article is worth reading because it's exactly what we did in
class.
Keywords: Activities, ,
Ref: Young11
Author(s): Johnson, Carl
Date: 2000
Title: Human Coordinates and Floor Tiles
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, No. 1, pg 13 (1)
Reviewer: Young
Date of Review: 5-9-00
This article offers helpful suggestions one might use when teaching children how to graph. The way to set up the activity is to find a tile floor, take two long pieces of masking tape and make the x and y axes. One tile on the floor would serve as one unit on the graph. The teacher then takes four children and makes them into vertices on the graph in the shape of a square. The children that are watching could see that a square is made on the graph. The teacher then has the students (who are the vertices of the square) move about to simulate transformations, rotations and reflections. The author says this is a good way for the students to visualize how an object is transformed. Another suggestion the author made is to have the students choreograph a transformation dance and list what type of transformations they used.
I think this method would help students a lot. The students could see the
graph actually moving, instead of having to visualize the graph move on a
piece of paper. You could have the students do a project where they list
a bunch of transformations on paper and then model the transformations for
the class. I think transformations would be easier to grasp if the
students did see how something was transformed.
Keywords: History, ,
Ref: Young12
Author(s): Kelley, Loretta
Date: 2000
Title: Mathematical History Tour
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, No. 1, pg 14 (4)
Reviewer: Young
Date of Review: 5-9-00
The author stresses that the history behind math should be taught. The history needs to be taught by math teachers because the students are not going to learn about mathematical history in history class. The authors reasons that the history behind mathematics needs to be taught are: 1. It is good to put mathematics into a historical context (the students need to realize that math has a history), 2. It is good to recognize the cultures that contributed to the development of mathematics, and 3. Learning the history of mathematics might shed a light on what the students are learning. The author states that teaching the history behind math wouldn't be too hard. When teaching the Pythagorean Theorem one could give a brief biography about the life of Pythagoreus or the tell about the Pythagorean Brotherhood. You could also tell the students about the contributions of female mathematicians.
I do think that it is time for teachers to talk about the history behind
mathtematics because mathematics does indeed have a rich history. You
could write essay questions on tests about the history of mathematics. It
might be a good idea if you made a project out of it. For example, you
could have the students submit research papers on the history of
mathematics. The teacher could get the students to practice their writing
skills more by teaching history.
Keywords: Teaching Strategies, ,
Ref: Young13
Author(s): Magnu, Teresa
Date: 2000
Title: Will the Best Candidate Win?
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, No. 1, pg. 18 (8)
Reviewer: Young
Date of Review: 5-14-00
This article dealt with introducing voting theory into the middle school/high school setting. The author states that voting theory would be a good way to get the students to reason mathematically. The best part of the lesson is that it gets the children to think things out and create methods of voting. And there is no correct answer to the question "Which method of voting is the best?" This is a real world problem that the children get a chance to offer their opinions on. The author also states that when children are actively involved in lesson itself (teacher not just lecturing) they are more motivated to do work.
I agree with the author when she said that the more the children are
active the more pleasant the classroom is for you and the children. I
think this lesson would be intresting to try in a real classroom. I would
like to see how the children respond to the way the teacher is teaching
it. I tried this lesson for my micro-teaching and I must say that I
thought it went very well. Of course, the people I was teaching were
pretty bright. I do, however, think that high school children would be
able to understand this lesson. This lesson would be a nice change of
pace from the other math that the children are used to.
Keywords: Assessment, ,
Ref: Young14
Author(s): Liebars, Cathy S.
Date: 1999
Title: Journals and Portfolios: Alternative Assessment for
Preservice Teachers
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Vol. 6, No. 3, pg. 164(6)
Reviewer: Young
Date of Review: 5-14-00
The article states that since we are trying to assess children differently we should try to assess the preservice teachers differently as well. The article suggests that a couple of ways of doing this is for the preservice teachers to journal and have class portfolios. The reasons for doing these two things are that it gives preservice teachers a better understand of assessment after they have just assessed themselves through journaling and portfolios. The teacher of the class should assess the preservice teachers and let the preservice teachers assess themselves. The articles suggests that the assessment should be done with criteria. The journaling will allow the preservice teachers to do a significant amount of writing while the portfolios would allow the teachers to self assess their learning.
I just thought that this article was interesting because we are journaling
and doing a portfolio. I like journaling because it allows me to voice my
opinions in a non-aggresive way. As far as the portfolio goes I don't
know how much I like doing that. I realize that it's a good idea, but my
math professor really teaches every math class the same way. He doesn't
have to build interest because if we fail it doesn't have anything to do
with him. It's our fault. Where as, in high school a teacher needs to
motivate their students because some of them don't want to be there and a
teacher whose children are constently failing won't be teaching for
long.
Keywords: Communication, ,
Ref: Young15
Author(s): Covington, Judith
Date: 1999
Title: Bridging the Gap
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Vol. 6, No. 2, pg. 98(4)
Reviewer: Young
Date of Review: 5-14-00
This article just deals with the gap between college and elementary school mathematics. The article states that college professors need to have a better sense of knowledge of what the elementary school students are being taught and how their being taught. There are programs in which college professors can visit and observe an elementary school classroom for a day. Some of these programs are the Exxon K-3 Mathematics Organization and Project Next. Through these programs college math professors can gain insight into what and how future college math students are learning. A quote from the article says it best "Teachers at all levels need to view the big picture of mathematics."
I really agree with the point of this article. Some of the biggest
problems high school math students face when they get to college are the
transition from their high school math text to to their college math text
and the way in which college professors teach. I think that it would be
in the college professor's best interest if they learn how to teach
similarly to the ways in which high school teachers teach. As a tutor one
of the main things I help the students with is how to approach/read the
math text. Students aren't used to that type of reading and therefore
don't fair too well.
Keywords: Problem Solving, ,
Ref: Young16
Author(s): Kelly, Janet A.
Date: 1999
Title: Improving Problem Solving Through Drawing
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Vol. 6, No. 1, pg. 48 (4)
Reviewer: Young
Date of Review: 5-14-00
The article states that problem solving is one of the greatest challenges that studens face in mathematics. Students are used to systematic approaches to solving word problems which is fine. The only problem is when given related word problems the students had trouble solving them or couldn't solve them. This article found that the students had easier times solving problems when they could visualize the problem. The article also says that we need to teach teachers how to give the students problems where the students could draw pictures. So the author had six week seminar in which a bunch of elementary/middle school teachers solved problems using drawings. When the teachers got back from the seminar one of the problems the students were having was that they were having problems organizing their thought and transferring them into a drawing. What the teachers did was ease the their thoughts down in a form of a drawing. The advantage of having the students draw pictures with the word problems is that the teacher could actually see what the students are thinking.
In most of my math classes here the professors always state that if at
first you can't solve the problem draw a picture. Drawing pictures
usually helps me think through the problems especially in geometry and
calculus. I do believe that problem solving is a little easier when you
can visualize the problem in your head or on paper.
Keywords: Planning, ,
Ref: Young17
Author(s): Baroody, Arthur J.; Bartels, Bobbye H.
Date: 2000
Title: Using Concept Maps to Link Mathematical Ideas
Journal or Publisher: Mathematics Teaching in the Middle
School
Volume, Issue, Pages: Vol. 5, No. 9, pg.604 (6)
Reviewer: Young
Date of Review: 5-16-00
The article states that the NCTM is emphasizing making and assessing connections. Understanding can obtained by connecting to pieces of information. As the authors state, the degree of a student's understanding is determined by the number, accuracy, and strength of connections. What a concept map does is visually illustrate mathematical connections and describes them in writing. Concept maps can be used as tools for teachers to use in their everyday classroom. They can be used to transmit information about concepts to students or to help students construct an understanding of concepts. As the article states concept maps can achieve many things, such as, they can introduce new concepts and connect them, encourage active construction of concepts, foster metacognitive knowledge and autonomy, motivate conjecture making and testing, underscore personal interpretation, provide an world need for introducing and practicing algebraic notation.
After reading this article I think it would be a great idea for my future
students to make concept maps. Concept maps will challenge the students
to make the connections between concepts that we want them to make.
Keywords: Manipulatives, ,
Ref: Young18
Author(s): Lesser, Lawrence M.
Date: 2000
Title: Sum of Songs: Making Mathematics Less Monotne!
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, No.5, pg. 372(6)
Reviewer: Young
Date of Review: 5-17-00
The author states that the use of songs in the mathematical classroom can be fun and functional: they can supply motivation and mnemonics. And if you use lyrcis to popular songs it gets the kids even more interested. An example of a song is "American Pi". This song is very interesting and it recounts the history of pi. The famous chorus by Don McLean is replaced by: Fink, find the value of pi, starts 3 point 1 4 1 5 9. Good ol' boys gave it a try, but the decimal never dies, the decimal never dies... As you can see a high amount of creativity goes into making these songs. There are plenty more songs in the article just like this one and they are all interesting.
I think that kids would love to sing songs like these in school. The
songs would offer humor to the classroom if nothing else.
Keywords: Planning, ,
Ref: Young19
Author(s): Diaz, Donna
Date: 2000
Title: Classy Tips
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, No. 5, pg. 400 (1)
Reviewer: Young
Date of Review: 5-17-00
This article gives some good insight on parent teacher relationships. The author says that thinking as a parent rather than a teacher will make the parent more comfortable. We should let the parents know that we want to teach their children to become independent thinkers and learners. As teachers we should be willing to learn something from the parents to help our relationshis with the students. The parents will be in our corner if they believe that we are in the child's corner.
I think it is important to build a healthy relationship with parents.
With the parents help we could further the child's education. We are not
going to be at home with the children, the parents are and that is more
reason to get the parents on your side. The child is the important thing
and we should make every effort to help the child.
Keywords: Geometry, History,
Ref: Young20
Author(s): Natsoulas, Anthula
Date: 2000
Title: Group Symmetries Connect Art and History with
Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 93, No. 5
Reviewer: Young
Date of Review: 5-17-00
This article states that mathematical groups are often hard for childrent to understand. Symmetry in art (history) can be a good visual tool for children to learn symmetry. There are universal symmetries in all of art and they exist because of the underlying mathematical principles. For students the examples you show in class can provide a concrete visual image and notion of the mathematical unity that is definded in a mathematical group.
I think that showing art in math class would first obviously be a great way to integrate the two subjects and second get some kids interested in mathematics who weren't interested in the past. Showing symmetry by the way of art can be fun and interesting. Not all students would like to look at art, but it would be a nice change to the students who do like to look at art.