Keywords: Activities, Technology
Ref: Kim20
Author(s): Lanius, Cynthia
Date: 2002
Title: A Fractals Unit for Elementary and Middle School Students
Journal or Publisher: http://math.rice.edu/~lanius/frac/
Volume, Issue, Pages:
Reviewer: Kim
Date of Review: 4-29-03
Fractals, much loved by all involved in math. How do we teach these complex systems to our young students though without it just being a drawing task? These are the questions that gave rise to this website. With online materials, resources for teachers and many interactive activities for students to explore, this website gives a good background to fractals that can be understood at the middle grade levels.
This website would be very useful for the classroom. Either as a resource for teachers or as an activity for students to explore. It is more important every day that we help our students understand the resources available for them in the world. This website would be a good way to show them that what they’re learning in the classroom is out there too. The one thing to watch out for is the java fractal simulator because it has a tendency to crash computers, which wouldn’t be all that helpful during class since you’d have to sit and wait for the computer to start working again.
Keywords: Measurement, Connections
Ref: Kim19
Author(s): Koellner-Clark, Karen; Lesh, Richard
Date: 2003
Title: Whodunit? Exploring proportional reasoning through the footprint problem.
Journal or Publisher: School Science and Mathematics
Volume, Issue, Pages: v103, i2, p92(7)
Reviewer: Kim
Date of Review: 4-29-03
How big is a person that wears size 24 shoes? This is the problem posed to a group of students in an attempt to research their reasoning skills. This article outlines the phases of reasoning that children progress through. Then it goes on to look at a specific observation of a group of students. They were asked the question above and the article follows them through the reasoning that eventually leads to the conclusion that Shaq wears a size 24.
This was a useful article in showing the steps that students take to producing a solution. It shows their think processes and partially how questions can be framed to bring out the creativeness and deep thinking we like to see. The case study that they chose of the footprint problem brought out great responses from the students. After starting with a basic level idea of how to determine the person’s height they decided their first findings were inaccurate and dug deeper into the problem. As they developed their idea their measurement and think became more accurate, paying much more attention to detail. It would be interesting to see some of the other studies conducted.
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Keywords: Communications
Ref: Kim17
Author(s): Henriksen, Melvin
Date: 1982
Title: You Can and Should Get Your Students to Write in Sentences
Journal or Publisher: Using Writing to Teach Mathematics
Volume, Issue, Pages: # 16, 50-52
Reviewer: Kim
Date of Review: 4-21-03
This article outlines an effective method for getting students to communicate their ideas in math. This is an essential, yet still developing technique in math education. The process used by this professor is to not accept work not written in complete sentences and or paragraphs. This method gets students to really think about how they are reaching their answers rather than just giving them. It has come upon a great deal of opposition from the students but the professor keeps persisting and usually by the end of the term is seeing good results. Hopefully this method shows the students how valuable proper communication can be.
This article gave a good argument for the specific method used. There are specific examples of the types of assignments that were given and the expected responses to these questions. Each student was given the rules from the beginning and expected to know them without further prompting. The overlying theme from this was that the professor must stand strong against all opposition so that the point is made that their way is the only way. This may seem like a brash idea, especially at the college level. It is even more important to stand strong at that level because the professor must undo a train of thought that was set starting in kindergarten. For years we have seen math as merely symbols. Those symbols happen to represent and idea and communication is key to expressing those ideas. Activities like the ones described in this article should be started at a young age and continued in mathematics curriculum from then on.
Keywords: Probability, Discrete, Keyword 3, Optional...
Ref: Kim18
Author(s): Usnick, Virginia; McCarthy, Jane; Alexander, Shirley
Date: 2001
Title: Mrs. Whatsit "Socks" It to Probability.(Links to Literature)
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: v8, i4, p246(4)
Reviewer: Kim
Date of Review: 4-21-03
For the integrated math and literature course dealing with A Wrinkle in Time probability is key. The exercise described in this article has students dealing with probability and discrete counting systems through Mrs. Whatsit’s socks. Starting with the number of socks pulled out of a mixed drawer to make a pair, and moving up to the probability of such events. Young students can explore probability and discrete counting through a book they’re reading in Language Arts. These types of activities can be found in any number of correlating activities for Language Arts, History, Science, or other classes. It just takes the effort to find the connections.
I felt this was a very good, specific example of integration between literature and mathematics. It gave very specific examples but in a way that makes me wonder where else I could find similar ideas. The articles main emphasis is on the value of integration to show students real examples of mathematics at work. These types of activities can be used at any level and would be useful at all levels. In working with our fellow teachers we can integrate many of our lessons and make the learning experience richer and more fulfilling for our students.
Keywords: Algebra, Number and Operation,
Ref: Kim14
Author(s): Berkman, Robert M.
Date: 1998
Title: Exploring interplanetary algebra to understand earthly mathematics.
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: v5, n2, p78(6)
Reviewer: Kim
Date of Review: 4-10-03
Having students examine the counting systems of extraterrestrial beings can be pretty exciting. It can also be a very basic course in Algebra. The algebra is so hidden that even the students don’t believe it’s there, but to the experienced eye it is. After learning how to count in different base systems, through the example of a different number of digits on a hand, students are then asked to explain how they came up with their solutions and gradually build algebraic formulas. Conveniently this lesson is not as scary as some beginning algebra can seem to students, in fact they actually have fun.
This seems like a great activity. First to explore the aspects of a number system with base other than ten and then to develop basic algebra equations at such a young age. I would recommend this lesson to any level of student that could grasp the concept. High school students would even enjoy this activity. It gives a very real example of how to create equations and why they are useful. Honestly, who could resist numbers, algebra, and extraterrestrials?
Keywords: Measurement,
Ref: Kim15
Author(s): Burns, Marilyn
Date: 1990
Title: What's in a foot?
Journal or Publisher: Instructor
Volume, Issue, Pages: v104, n4, p28(2)
Reviewer: Kim
Date of Review: 4-10-03
This article describes a lesson used to show students the importance of understanding what units they are measuring in. Based off of the story of a king who is having a bed made for his queen. The king measures the queen using his feet and then becomes angry when the apprentice making the bed uses his own smaller feet. Students are given the problem of writing to the apprentice to help him out and to figure out what went wrong. Some expansions on this could be to measure objects in the room a similar way, or have students research where standard measure came from.
The queens bed activity is most useful for younger students. One could use the same exercise though at higher levels. In physics it is extremely important to understand that everything we use is approximated and relative to some standard. This type of activity could easily be used in a math class at the same time as a physics class to show this importance. Measurement is a skill that every person uses and so it is important for students to have a strong grasp on it. There are many other ways this activity could be used, it is a very convenient jumping off point.
Keywords: Number and Operation,
Ref: Kim16
Author(s): Moldavan, Carla C.
Date: 2001
Title: Culture in the Curriculum: Enriching Numeration and Number Operations
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: v8, i4, p238(6)
Reviewer: Kim
Date of Review: 4-10-03
This article contains a lesson in multicultural numbers. It expands on an activity of creating a new number system to exploring number bases and different cultures methods of working math. From Egyptian to Japanese this activity covers all of its bases. A teacher could take any piece of this activity and make a well balanced, culturally diverse lesson.
This article is extremely valuable. It is a great resource for any teacher seeking a lesson in mathematics of different cultures or just a good lesson in numbers. I would highly recommend it for any classroom as it could easily be adapted to any grade level.
Keywords: Geometry, History,
Ref: Kim13
Author(s): McCague, Hugh
Date: 2003
Title: A Mathematical Look at a Medieval Cathedral
Journal or Publisher: Math Horizons
Volume, Issue, Pages: April, 11-15 31
Reviewer: Kim
Date of Review: 4-3-03
Cathedrals are very mathematical structures. This article explores that math. It shows the ways that even with limited tools cultures were able to build mathematically complex structures. The article details the measurements and tools used by these cultures. The ratios were specifically important in Medieval Churches and are discussed in depth. In addition the article discusses the reasons religiously for these specific constructions. It is a very thorough article.
This would be a great article to use as a reference during a project. During a lesson studying floor plans or architecture this would be a good extension, preparation, or example for the lesson. It would also show students that this level of math can be done with simple tools and does not necessarily require complex formulas and the like. I would recommend it to any geometry teacher especially as a real life example of math in the world around us.
Keywords: Curriculum
Ref: Kim11
Author(s): Isaacs, Andrew; Wagreich Philip; Gartzman, Martin
Date: 1997
Title: The quest for integration: school mathematics and science.
Journal or Publisher: American Journal of Education
Volume, Issue, Pages: v106, n1, p179(28)
Reviewer: Kim
Date of Review: 3-17-03
This article examines the concept of integrated curricula through math and science. Mainly based on the TIMS system the article discuses the definition of integrated curriculum and the pros and cons of the system. Examples are given from studies using the TIMS and Math Trailblazers curriculum. All aspects are explored to give a very thorough report that allows the reader to make their own decisions.
This article gives all the information that a stranger to the idea of integrated curricula would need to form an opinion. It seems to be unbiased and gives a fair description of all sides to the matter. Everything is backed up with research down to the very definition of integrated curricula. The examples of TIMS and Math Trailblazers are explained carefully and include the different angles with which one can view them. This article brought up some very interesting ideas about the use of integrated curricula and would be useful to anyone considering using integrated curricula especially between math and science.
Keywords: Geometry, Technology,
Ref: Kim12
Author(s): Battista, Michael T.
Date: 2002
Title: Learning geometry in a dynamic computer environment
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: v8, i6, p333(7)
Reviewer: Kim
Date of Review: 3-19-03
This article discusses the use of technology to teach geometry. The main idea leans more towards using inquiry rather than direct instruction through technology. Through research examples of a class using The Shape Maker microworld the article shows the steps students take in developing their ideas and how technology can give them and inquiry based opportunity. While exploring parallelograms in this system the students are not given fact lists but are expected to build their own concepts of the parallelograms. Following the van Hiele Levels of thinking the article shows the progress that students thinking takes throughout the exercise. Overall the article gives a solid argument that technology exploration can be used to meet the NCTM standards.
I like the approach that this article took to explain the benefits of this specific program, The Shape Makers microworld. It would be more helpful if the article showed examples from multiple forms of technology. While a strong argument for use of technology it says nothing about how to pick good technology. With so many programs available today and the price of technology it would have been useful to have more examples. I would recommend this article to those that would like a positive argument for technology in inquiry learning and to those who would like to use The Shape Makers microworld in a unit or lesson.
Keywords: Algebra, Standards,
Ref: Kim9
Author(s): Burke, Maurice; Erickson, David; Lott, Johnny W.; Obert, Mindy
Date: 2001
Title: Navigating through Algebra in Grades 9-12
Journal or Publisher: National Council of Teachers of Mathematics
Volume, Issue, Pages:
Reviewer: Kim
Date of Review: 3-9-03
Navigating through Algebra in Grades 9-12 is a resource book to the Algebra segment of the Principles and Standards for School Mathematics. The topics covered in the book are Algebra-the Language of Process, Expanding the Notion of Variable, Expanding the Notion of Function Representation, Expanding Students’ Understanding of Algebraic Equivalence or Identity, and Expanding Students’ Understanding of Change. With each of these chapters there are examples and explanations of each. The book contains the resources to implement any of the sample exercises as does the accompanying CD Rom. The CD Rom also includes a copy of the book and software needed for graphing during the exercises. Between the book and CD Rom all materials needed to implement the sample exercises is accessible.
I like the idea of the Navigation book. As a teacher I would not find it as useful as it should be because there is not significantly quick access and reference. The exercises themselves would be very easy to use. One would have to spend careful time to read the book itself and understand its ideas. Most teachers I know would not have enough time during the school year get through this information compared to other more easily accessible resources.
Keywords: Number Theory, Standards,
Ref: Kim10
Author(s): Curcio, Frances R.; Bezuk, Nadine S.
Date: 1994
Title: Understanding Rational Numbers and Proportions
Journal or Publisher: National Council of Teachers of Mathematics
Volume, Issue, Pages:
Reviewer: Kim
Date of Review: 3-9-03
This book gives a series of lessons that will help to expand students’ knowledge on rational numbers and proportions. It gives step by step explanation of how to implement activities and why they are useful. All worksheets and specialized materials needed for the lessons are also included. The lessons pertain to three different concepts. Exploring and extending rational number concepts, applying rational number and proportion concepts, and making rational number connections with similarity. Overall it is a very useful collection of lessons and activities for the classroom.
This book is a quick easy reference and very easy to follow. The lessons can easily be adapted for different learning styles and all grade levels. All materials that are needed for the lesson are included in the book. The lessons also include real life problems so that the students might relater their math to the real world. I would recommend this book as a good resource for lessons on Rational numbers and proportions.
Keywords: Standards, Assessment,
Ref: Kim7
Author(s): Jehlen, Alain
Date: 2003
Title: High-Stakes Questions
Journal or Publisher: NEA Today
Volume, Issue, Pages: March 2003, 8-11
Reviewer: Kim
Date of Review: 3-3-03
This article pertains to the high-stakes testing and the validity of the results. It discusses studies that have been conducted that prove learning does not increase due to high-stakes testing. In many cases the students have not even made as much progress as students at non high-stakes schools. The article gives a very thorough background of schools that have been blue ribbon schools but are still ranked poorly through high-stakes testing. One of the issues discussed is that of teaching to the test. In some studies it was shown that schools that did better on high-stakes test actually did worse on other equivalent standardized tests in theory because they were being taught only how to take the one style of test. These ideas raise some fairly serious questions as to where these testing cycles are taking us.
I am consistently against high-stakes testing. I feel that high-stakes tests generalize schools too much and so put those that are different because of the community they are in, not because of their teaching, at a disadvantage and at risk. We have a nation that supports education for all, but are educations even close to equal in different areas? Not a chance, high-stakes tests don’t take these differences into consideration. I am a strong supporter of the ideas in this article and think that high-stakes tests are a ridiculous waste of our time. With the evidence presented in this article I feel even more strongly that we should focus less on high-stakes tests and more on what is really affecting our students scoring.
Keywords: Issues
Ref: Kim8
Author(s): Simpson, Michael D.
Date: 2003
Title: 'Thou Shalt Not...'
Journal or Publisher: NEA Today
Volume, Issue, Pages: March 2003, 17
Reviewer: Kim
Date of Review: 3-3-03
This article briefly and succinctly addresses the issue of religion in schools and its current debate. The article sights the most recent events, namely the posting of the Ten Commandments in schools. In every instance so far this has been deemed unconstitutional and the commandments have been ordered to be removed or never posted. The question remaining is what about “In God We Trust.” Does this phrase go against the constitution? Many are saying that it does not.
This an extremely prominent issue. What do we do in times of extreme patriotism in a culture that is guided greatly by specific religious beliefs? It seems to me that we lose sight during these times that there are other religious beliefs that these types of demonstrations go against. It seems to me that in a country based on religious freedom for all we should begin accepting all religions, not just those that are most popular. What will actually happen, we’ll have to wait and see, but according to this article and many others like it we won’t be seeing the Ten Commandments in schools any time soon.
Keywords: Games, Probability,
Ref: Kim6
Author(s): Brutlag, Dan
Date: 1994
Title: Choice and Chance in Life: The Game of "Skunk"
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: 1, 1, 28-33
Reviewer: Kim
Date of Review: 2-25-03
This article is an example of a probability and chance lesson. The game “Skunk” is used to help children explore taking risks in games involving probability and how to take the best risks. The game is played with dice and can be used as a full group activity or an individual activity. For every role not containing a 1 the player earns the number of points equal to the sum of the dice. The game is played in five rounds consisting of the S, K, U, N, and K rounds or “SKUNK”. A round is over when a one is rolled on either of the dice. If it is a single one then all points for that round are lost if you are still playing. If double ones appear then all points in that round and all previous rounds are lost. Of course the object of the game is to have the most points at the end of the second K round. The article discusses play of “Skunk” and options for teachers to use this game in their classroom. It also includes a sample worksheet of further thinking that can be used with the game.
“Skunk” could be a very useful activity
to teach probability. It can be used as an introduction for students to explore their own ideas,
as a follow up, to show what they already know, or both. This game also has a very broad age
range, it could be used for any grade level. One thing I would follow this activity up with in a
more advanced probability lesson would be dependent variables. Which types of games do
students know of where what was rolled before will change the outcome of the next roll? There
are many options for this type of further exploration with the game “Skunk”.
Keywords: Standards, Issues,
Ref: Kim5
Author(s): Minnesota Educator
Date: 2003
Title: New standards will focus on the basics
Journal or Publisher: Minnesota Educator
Volume, Issue, Pages: 5, 8, 3
Reviewer: Kim
Date of Review: 2-24-03
This article was an interview with the new Minnesota education commissioner, Ms. Cheri Pierson Yecke. The questions asked pertained to the new standards for Minnesota. One of the questions was, “Both you and the governor have talked about the need to replace the Profile of Learning with standards that focus on core curriculum. What do you define as ‘core curriculum?’ Does it include art, music, and other co-curricular activities?” The article offered little reflection about the interview, it consisted of merely the questions and the commissioners answers.
I thought that this was a very useful current article. The questions asked were
very pertinent to the present conflicts Minnesota educators are facing. The commissioner gave
very thorough answers that specifically outlined her plans for where things are going.
Commissioner Yecke also showed a great deal of faith that the teachers of Minnesota were
more than ready to face the challenges ahead. I think that it will still be a trying time for
educators. We face a world with a precarious balance between standards and the other stuff.
We must teach our students what they need to know for the tests, but not everything will be on
the test so we must also teach that information. Some teachers may be tempted to “teach to the
test”, as it’s called, which could cause great problems for the further development of skills
among our students. With a young optimistic mind it is easy to hope that we will get through it
all, but in reality one has to wonder if it’s really the best thing for our students.
Keywords: Assessment, Teaching Strategies,
Ref: Kim4
Author(s): Stenmark, Kerr; Beck, Pam; Asturias, Harold
Date: 1994
Title: A Room with More Than One View
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: 1, 1, 44-49
Reviewer: Kim
Date of Review: 2=19=03
This article is presented in the form of a play. It follows a group of teachers through their planning of implementing new assessment strategies. There are examples through their development of a problem and assessment for that problem. The article also presents the students thoughts and work throughout this process. The actual information about assessment is a little hard to get at but it is there.
I felt this article was a little too confusing to be really useful. It
seems that the content is talking about assessment through understanding rather than being able to
do the problem. I think this is extremely important and a very good point, it just could have been
presented better. I do like that they gave the outlook from teachers, students, parents, and
administrators during the article. Every time we implement important changes in our schools we
must look at all of these opinions to decide if the changes will really be beneficial. I think they
could have done a much more in depth article but it would have been much longer. It does help
that at least some people are attempting to make these changes in their schools and classrooms.
Keywords: Standards, Planning,
Ref: Kim3
Author(s): Clements, Douglas H.; Sarama, Julie; DiBiase, Ann-Marie
Date: 2002
Title: Preschool and Kindergarten Mathematics: a national conference
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: v8, i9, p510(5)
Reviewer: Kim
Date of Review: 2-16-03
This article discussed the difficulties of applying standards to preschool and kindergarten mathematics. At a national Conference on Standards for Preschool and Kindergarten Mathematics Education in May 2000, it was decided that standards should indeed be established for young children. The standards agreed upon have to do with Numbers and Operations, Algebra, Geometry, Data Analysis, and Measurement. In developing these standards two assumptions were made. “First, emphasis should be placed on standards for programs and for teaching. … second … knowledge of what young children can do and learn, as well as specific learning goals, is necessary for teachers to realize a vision of high-quality early childhood education.” Thus included with these curriculum standards will be information on what and how students should be able to perform. Each of the main topics was expanded on and will be published in a book soon. The meeting was concluded with these plans and marked as a success.
In my opinion this article is a very good advertisement for the book containing the standards decided on at the Conference on Standards for Preschool and Kindergarten Mathematics Education. I am happy that they have realized the need to start immediately with the standards if they expect them to be successful. It is obvious that if we are going to have standards at one level we must have them at all levels so that every student is prepared to continue their education at the higher level. I hope that this book is just the start in developing the future standards that will be the base of our students education.
Keywords: Geometry, History,
Ref: Kim1
Author(s): Swetz, Frank J.
Date: 1995
Title: The Volume of a Sphere: A Chinese Derivation
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 88, 2, 142-145
Reviewer: Kim
Date of Review: 2-10-03
This article discussed the original Chinese derivation of the volume of a sphere. It discussed the history of previous attempts made by Chinese mathematicians and the most accurate measure created. The article also delves into the idea that many different methods can be used to find a good measure and that without these attempts it was around one thousand years before a new mathematician came to the same conclusions. The history is very thorough and the explanation of methods tried is well diagramed. <P>I found this article to be very interesting. There was a very thorough history of the search to find the volume of spheres. I felt that the ideas of each mathematician and their tactics were presented very well. The visual representations helped to show the ideas and the formulas showed the steps very clearly. It seemed very important that they included the fact that other mathematicians were given credit for these early discoveries. It shows that even in the academic world the wrong people are given credit. It seems to me that this was a good article that has survived time fairly well and would not date itself to 1995 if read without that knowledge. I like that the article takes the time to build the background to the discovery and what other work had led up to that point. It seems that without the Nine Chapters on the Mathematical Art many discoveries would have taken much longer because each person would have started from the very beginning.
I would be tempted to use this article as a tool in the classroom to
show students that in mathematics there is not always just one way to look
at a problem. The history is also very interesting, it shows how the progress
of others can help lead to the break through of those in the future. Students
could learn a lot from the process of time and patience that it took to
derive the volume of a sphere.
Keywords: Connections, Teaching Strategies,
Ref: Kim2
Author(s): Roumasis, Charalampos
Date: 1995
Title: Concept Worksheet: An Important Tool for Learning
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 88, 2, 98-100
Reviewer: Kim
Date of Review: 2-12-03
This article discuses the use of Concept Worksheets. The Concept Worksheet includes Definition, Web of Attributes, Examples, and Nonexamples. The article explains the usefulness of each of these aspects and gives an example of a Concept Worksheet on parallelograms. The article also points out he benefits and downfalls of the Concept Worksheet. It’s a useful article, but a little out dated. The ideas it approaches have now been put to use in more efficient ways.
I liked this article. It seemed like an idea that would have helped out during the time period it was written in. Granted it was only seven years ago, but I feel that for the time period it was just the start of a good idea. Getting students to explore their own personal interpretations of concepts is very important. They understand ideas much better when they can put them into their own words. I think that the non examples could be done with more depth and a broader look at why they are non examples. It seemed to be a good article though with very strong arguments for using concept worksheets.