Marit's Article Reviews, 2006

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Keywords: Research , Teaching Strategies
Ref: Marit1
Author(s): NCTM Research Committee
Date: 2006
Title: The Challenge of Linking Research and Practice
Journal or Publisher: Journal for Research in Mathematics Education
Volume, Issue, Pages: Vol 37, No 2, 76-86
Reviewer: Marit
Date of Review: February 16th, 2006

The article is designed to take the initial step linking important research to teachers, so that they are well informed and understanding of the implications actions taken in the classroom. The researchers see many problems with traditional practices and their goals are to translate research results into practical advice so that teachers can implement the advice into classroom practice. The goal of this team of researchers is to consolidate research and identify the key problems/questions in mathematical teaching today, so that they know what to research. The article discusses how the need to link research to practice is greater now than ever before. Researchers recognize that their research will not provide a magical cure for the ailments math classrooms experience today, rather that by making the research accessible to teachers, some of the ailments will be cured through osmosis (ie teachers will give strategies a try, and realize what works and what doesn't and make small alterations here and there). Teachers are encouraged to design and carry out their own studies, because researchers recognize that they are truly the ones that know and understand what works as a whole. This article was kind of pointless to read. I know that there is a challenge to link research to practice; I didn't need to read 11 pages about why it's hard and the specifics of it. I was expecting to read more about specifics for teachers, not how NCTM is addressing the challenge. I will not use this article again.

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Keywords: Probability, Problem Solving, Research
Ref: Marit2
Author(s): Rube, Laurie
Date: 2006
Title: "Good things Always Come in Threes: Three Cards, Three Prisoners, and Three Doors"
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 99, No 6, pages 401-405
Date of Review: February 17, 2006

"Good Things Always Come in Threes: Three Cards, Three Prisoners and Three Doors". The main idea of this article is to connect research to teaching. Laurie Rube discusses three different probability problems all based on a similar problem solving strategy, as seen through the famous Monty Hall problem. The main idea to solving these problems is to keep in mind that they are counterintuitive conditional probability puzzles. Initially the results of the study were based on how adults made mistakes in figuring out the problems. However, the latter part of the article focuses on what High School and Middle Schoolers did to solve the problems and their reasoning. It was interesting, like the adults, very few of the school aged students got the problems right. However, the children got them wrong for a much wider variety of reasons and with a more assorted system of results. Laurie Rube suggests that the implications of this research for instruction are vast. Teachers should conduct more simulations during their lessons, if going over a problem like the card one teachers should have cards there so that students can touch and hold three cards while they wrestle with the solution. Additionally, teachers should discuss the structure of the problems that they work with students. If students were able to recognize these sorts of problems as "conditional probability" questions, they are likely to have a much better idea of how to solve them. I found this article to be extremely helpful, because conditional probability problems are fun! Students love doing them and thinking about them, they are a great addition to any classroom, and the article developed specific explanations for how to approach these problems so that they make more sense for everyone! This is an article that every high school or middle school teacher should read!

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Keywords: Algebra, Arithmetic, Technology
Ref: Marit3
Author(s): Wade, William
Date: 2006
Title: "Sound off! A Dialogue Between Calculator and Algebra"
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 99, No 6, Feb 2006, 391-393
Reviewer: Marit
Date of Review: Feb. 17, 2006

The format of this article is more of a creative essay. William Wade wrote it as a dialog between a calculator and algebra, the two characters of the conversation. The dialog was great! The two discussed back and forth how to solve problems. The calculator was a bit cocky, and always thought that he could figure out the answer and work with big numbers and graphs much easier than algebra could, but somehow algebra always outsmarted calculator. In the end calculator suggests a problem that algebra can solve, but instead just works down to one simple calculation and then asks calculator to help. The bottom line is a bit obvious, that together they can work well, but it's a great message and one that I think we all need to be reminded of once in a while. I think any teacher could use this as an attention getter if his/her class is getting lazy and using the calculator too often and not thinking about problems anymore. You could also distribute the three parts to students in your class for a "math play", one to someone as calculator, someone as algebra and someone as the narrator. Or a teacher might use this as a fun little "story time" reading on the first day of school.

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Keywords: Manipulatives, Problem Solving, Teaching Strategies
Ref: Marit4
Author(s): Freer Weiss, Dana
Date: 2005
Title: "Keeping it Real: The Rationale for using Manipulatives in the Middle Grades"
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 11, 5, pg. 238-42
Reviewer: Marit
Date of Review: February 26, 2006

Dana Freer Weiss began the article by discussing the different learning theories that have developed over the years. Essentially, she explained, right now psychologists and educational researchers alike agree that constructivism is the best way for students to learn. The author then described why manipulatives fit into that learning theory. As in constructivism, manipulatives, or learning tools, allow students to have a concrete experience, which is what they need to understand the material, the best. They are also another way for students to symbolize abstract ideas. Currently, it is rare to see manipulatives used in middle and high school classrooms. As Dana Freer Weiss writes, many teachers believe that students are just to old to be "playing". Still other teachers are unsure how to incorporate them into upper level math. But Freer Weiss is an advocate, and she gave many more reasons as to why teachers should use concrete examples for students of all ages. Read her article and find out why! If nothing else, she explains, manipulatives help appeal to students as diverse learners, and they may be a way for some students to discover math. The last bit of her article is particularly poignant for teachers who plan to start using learning tools, here she warns teachers of the possible fallbacks and of certain things they should be aware of. The article was a well-rounded experience. Dana Freer Weiss followed up on her own advice, by writing the article in a way that gave teachers concrete examples of how and why to use manipulatives.

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Keywords: Connections, Representations, Communication
Ref: Marit5
Author(s): Helpern, Cara, Helpern, Pamela
Date: 2006
Title: Using Creative Writting and Literature in Mathematics Classes
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 11, 5, pg 226-230
Reviewer: Marit
Date of Review: February 26, 2006

The authors of this article set forth several goals that they wish to accomplish through incorporating literature in their classrooms. For example, they wish to use stories to introduce math concepts and help students learn and remember vocabulary, as a form of assessment/ to assess their understanding, to help students learn to enjoy math, to integrate math, to teach them that math is an important part of daily life, and to help students recognize the importance of language. While reading their goals I thought to myself, "Well, I like these goals, but if I were their students I would think that this is totally busy work- I would just rather do the math and not spend two extra hours writing about it! The math is not serious- it's cartoons! And this is not an art class! No one is going to learn anything new!". Well, as I read on I continued to feel that way, until I realized: teachers need to take risks, and that really good things can come out of them. For instance: one of their students made a connection to a real life serious event that they were all experiencing, war. Another student made a deeper philosophical connection to math, and still another to a deeper mathematical idea. All of the students learned the importance of pictures, if pictures were wrong the math was confusing. According to the authors, from this project many of them seemed to recognize that math contains history and culture. I also realized: that by tacking some additional requirements onto their original assignment, I really could use creative writing in my math classroom and make it meaningful for at least a good portion of my students. For example, I could require that they relate math to the real world in a serious way, or I could ask students to attempt to make a deeper mathematical connection than something our textbook offered, or a connection to something else in the "real world". Though this article was interesting, it only dealt with the idea of integrating creative writing in to a math classroom. What about other form! s of lit ouch literature?

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Keywords: Teaching Strategies, Representations, Connections
Ref: Marit6
Author(s): Bransford, John, Brown, Ann, Cocking, Rodney
Date: 1999
Title: How People Learn: Brain, Mind, Experience and School
Journal or Publisher: National Academy of Sciences
Volume, Issue, Pages: Chapter 2, How Experts Differ from Novices
Reviewer: Marit
Date of Review: March 5th 2006

In chapter two of John Bransford's book he discusses how experts differ from novices. Bransford writes, "People who have developed expertise in particular areas are, by definition, able to think effectively about problems in those areas". He goes on to explain that expertise effects learning greatly. Students that are considered experts in a certain topic or content area have a knowledge base that leads them to notice different things then students that are novices in that same area. Moreover, Bransford explains, that experts "organize, represent, and interpret information in their environment" in a completely different manner. Experts in math might recognize a pattern immediately that other students may never see without assistance or prompting. This is a really important concept for us, as teachers to recognize. Since experts organize their thinking around ideas that are indicated as important by our instruction, it is vital that curriculum cover the important math in a cohesive manner. Building on the idea of curriculum, Bransford ultimately explains, that conditionalized knowledge is the best way for students to gain a true understanding of the material. Thus, students need to work with concrete representations to develop their understanding of ideas. As a result students will better understand abstract concepts and be able to apply them to other ones that evolve as a result. Conditionalized knowledge is the key to helping students organize and retrieve knowledge in a meaningful way. As teachers this implies a lot, I highly recommend that you read this chapter and mull over the implications for yourself!

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Keywords: Algebra, Measurement, Connections
Ref: Marit7
Author(s): Rich, Jane
Date: May, 1994
Title: Measuring the Earth
Journal or Publisher: This lesson was the result of the work of many teachers at the Columbia Education Center's Summer Workshop
Volume, Issue, Pages: http://eduref.org/Virtual/Lessons/Mathematics/Geometry/GEO0004.html
Reviewer: Marit
Date of Review: March 5th 2006

I really like this algebra lesson because it also asks students to use their science skills. Not only does it just use algebra, but also geometry, critical thinking and problem solving skills are required. Students contact another school either directly above or below theirs (preferably in another state) and at the agreed upon time, they measure an object and it's shadow. They use their results combined with the other classes to solve the ultimate problem, to measure the earth. They also are asked to calculate percent error and determine whether their answer is legitimate. The teacher who wrote this lesson plan, Jane Rich, suggests doing this as an ongoing project throughout the term. "Measuring the Earth" is always something that you can come back to and grow on as the year goes on and as students want to know more. This lesson is the type of lesson that students will actually remember and probably learn more during than the whole year put together. Best of all, this is the type of lesson that students will really have fun participating in!

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Keywords: Discrete, Probability,
Ref: Marit8
Author(s): Burrill, Gail, Franklin, Christine, Godbold, Landy, Young, Linda
Date: 2003
Title: Navigating through Data Analysis in Grades 9-12
Journal or Publisher: NCTM
Volume, Issue, Pages: Chapter 2, pages 29-35
Reviewer: Marit
Date of Review: April 5

The activities in this chapter invite students to explore questions they might have about probability through an experiment that involves categorical variables. The experiment itself is really interesting, "Discrimination or Not?", asks students to create the most accurate model of an experiment possible. There are 35 files that they will look into and they need to decide what variations to consider. The chapter teaches students, by investigation, how to simulate a situation and analyze the simulation results. I think this is a great guide for how a teacher might set up an experiment. Moreover, this idea is one that takes students beyond the book and into the realm of personal interest and motivation.

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Keywords: Statistics
Ref: Marit9
Author(s): Burrill, Gail, Burrill, John, Coffield, Pamela, Gretchen, Davis, Lange, Jan de, Resnick, Diann, Murray, Siegel
Date: 1992
Title: Addenda Series grades 9-12, Data Analysis and Statistics
Journal or Publisher: National Council of Teaching Mathematics
Volume, Issue, Pages: Statistics in the Curriculum, pages 1-10
Reviewer: Marit
Date of Review: April 10, 2006

Chapter One proposes ways to integrate statistics into an already overloaded classroom, without compromising the "real mathematics". What I read is really helpful because it shows teachers tangible ways to institute a standard; something that the majority of teachers often view as merely something to check off that they taught. The addenda series shows the motivation for making statistics a standard. Teachers can see why statistical analysis really is important, and may even learn, through the addenda series, to view Data Collection and Statistical Analysis as "real math". I also really appreciate the comments that are made in the margins of each page. There is a "Teaching Matters" and a "Try this" and an "assessment matters" section on almost every page that gives specific pointers. The layout of the booklet is impressive and functional; I would use this in my classroom.

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Keywords: Teaching Strategies, Communication, Planning
Ref: Marit10
Author(s): Daniels, Harvey, Zemelman, Steven
Date: 2004
Title: Subjects Matter; Every Teacher's Guide to Content-Area Reading
Journal or Publisher: Heinemann Publishing
Volume, Issue, Pages: Chapter 5, "Tools for thinking: Reading strategies Across the Curriculum", pg 99-138
Reviewer: Marit
Date of Review: April 12, 2006

This chapter elaborates on the idea of student questioning that we have been discussing in class. Student questioning is often something overlooked, even by good teachers. But Daniels and Zemelman emphasize the importance of students proposing questions of their own in order to demonstrate engaged learning. They explain why kids need more engaging real-world reading in order to learn school subjects, and then develop definitive mental work strategies that students should do to make sense of such rich material. Questioning is at the top of their list, and they develop it in this chapter through specific mental strategies that readers should use, instructional strategies that teachers should use, and whole-class or individual student activities. Most of the strategies also activate a number of other mental tactics, besides questioning, that good readers use to understand a text. The emphasis of this chapter is on how to make understanding of something a student is reading, but I think these strategies could easily be employed in other classroom learning situations. I think every teacher should read this.

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Keywords: Equity/Diversity, ,
Ref: Marit11
Author(s): Gutstein, Eric, Peterson, Bob
Date: 2005
Title: Rethinking Mathematics; Teaching Social Justice by the Numbers
Journal or Publisher: Rethinking Schools
Volume, Issue, Pages: 179 pages
Reviewer: Marit
Date of Review: April 17th, 2006

The concept of "rethinking mathematics; teaching social justice by the numbers" is an exciting one for me, and one that I hope to continue to learn more about. Sadly though, it's one that very few have written on. I was excited to receive this book as a Christmas present, but even more so to discover the innovative ideas it's content presents. The eighteen chapters of this book range in style, from essays and poems, to personal stories and suggested activities and discussion questions. This book will be something that I use to incorporate social justice into my classroom. (I've always hoped to do that, but never really believed that it could actually be apart of a math class). If there's one lesson I learned from this book it's that teaching math isn't neutral! We can use math as a tool for understanding the changing world around us and for connecting students backgrounds with a classroom subject (math).

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Keywords: Activities, Problem Solving, Teaching Strategies
Ref: Marit12
Author(s): Presenter: Terry Wyberg and Tracy Bibelnicks
Date:
Title:
Journal or Publisher:
Volume, Issue, Pages:
Reviewer: Marit
Date of Review: April 24, 2006

Friday nights on CBS the primetime television show "Numb3ers" errs. Numb3rs is a drama about an FBI agent who hires a mathematician to solve crimes based on real life. The show depicts how math is used to solve these problems, and does it in the "primetime" way. So, as the speakers, Terry Wyberg and Tracy Bibelnicks, pointed out the content is somewhat sensitive. Unfortunately, most teachers would not be able to actually show the show in their classrooms, but the math that goes along with it is very valuable stuff. I think it's math that I will definitely use at some point. I found that you can legally download the show, which would be wonderful, because then you could introduce the mathematical content and them make the showing of the actual show optional during that week. The official "Numb3rs" website has activities sheets to teach the mathematical content, along with teachers guides. The speakers also pointed out that each episode is specified to a certain grade level in math (see website) and that there is mathematical history also included in each episode (something that most teachers don't find time to include). I'm really excited about this show because it makes math seem like it is useful and authentic- which ultimately is our goal as teachers. I think "Numb3rs" could be a great teaching tool if used correctly.

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Keywords: Technology, Probability, Management
Ref: Marit13
Author(s): The Speaker was Lisa Conzemius from Detroit Lakes Senior High- Detroit Lakes, MN
Date: 2006
Title: "Savings and Payments- How does it work?"
Journal or Publisher:
Volume, Issue, Pages:
Reviewer: Marit
Date of Review: April 26th, 2006

Lisa spoke of a project that she did with her pre-calculus students. She used excel to simulate retirement savings, house savings, and credit card payments. It was interesting, because even she admitted to not being an expert at working with excel. Sometimes things didn't go as planned as she was presenting the project she ran with her students- but that was realistic. Most of us aren't excel experts- that is why we were there- and most likely even if you are something won't go as planned. But Lisa practiced what she preached and just got up there and gave it her best, and ultimately the power of a spread sheet came across loud and clear. This exercise would work well in a unit on exponential functions, or just generally anywhere as a break from the normal textbook. Many other mathematical concepts could be tied in. Lisa illustrated step by step procedures and reasoning for demonstrating different ages to save and various interest rates. These are simulations that her students found to be exceptionally valuable and applicable. I agree, right after the conference was over I went back and ran the excel spreadsheet for house payments- this is most certainly authentic math. The technology of excel, in this case, allowed a teacher to adhere to the goals of the new standards and make interdisciplinary connections. I will use this in my classroom.

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Keywords: Connections, Representations, Standards
Ref: Marit14
Author(s): Bright, Christine
Date: 2006
Title: "Arts and Math Connect"
Journal or Publisher: MCTM conference
Volume, Issue, Pages: St. Francis School District- St. Francis, MN
Reviewer: Marit
Date of Review: April 26th, 2006

Christine Bright began speaking, at the MCTM conference in Duluth on how "Arts and Math Connect" by telling a story. In her theatrical voice she spoke of a student and his master. The student helped a butterfly come out of it's cocoon, but when it emerged as a butterfly it couldn't fly. The student was upset and asked his master what he had done wrong. The master replied that he had helped it too much. Ms. Bright compared this story to standard based education emphasizing the importance of allowing students to construct meaning. Christine Bright continued by encouraging educators to share math as a passion and to support students who take risks by establishing a safe environment first. She continued by speaking more generally to good education practices. Though very meaningful, this part of her talk should not have been so extensive because teachers were there for connecting math to art ideas. Bright's advise to engage more of student's senses while doing math is valuable. This way, she explained, more students may be reached. Students also benefit from sensory stimulation further because it allows them to relate to each other on a higher level through discovery. Some of the best examples she gave for connecting the arts were geared towards middle and elementary classrooms, but I believe that they could be applied to the upper grades. Examples include: math plays, stories, whole body representation of abstract concepts, and art projects using geometric shapes and patterns.


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Keywords: Assessment.
Ref: Marit15
Author(s): Garnett, Cynthia
Date: February 1992
Title: Teaching- Do not Disturb? A Concerned Parent's View of Testing
Journal or Publisher: NCTM
Volume, Issue, Pages: Arithmetic Teacher, February, 35-37
Reviewer: Marit
Date of Review: May 1, 2006

This article discusses assessment from the perspective of a concerned mother. The writer is mother of a seven and five year old and she discusses the educational stereotypes her daughters have come to believe in as seen through their play and story writing. It is interesting to read that even children that young know that spring time is test time, and that all teaching and learning stops while students are tested. The writer goes on to suggest that maybe we should reconsider stopping learning for assessment. After all, what have we really learned from basic skills testing? I can see her point, but the article frustrated me because though skills testing is not perfect, it has to be done in some way. Hopefully someday we will find the way that works for everyone… but I guess that day is a long ways off.

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Keywords: Assessment, Keyword 2, Optional..., Keyword 3, Optional...
Ref: Marit16
Author(s): Manon, Jon Rahn
Date: 1995
Title: The Mathematics Test: A New Role for an Old Friend
Journal or Publisher: NCTM
Volume, Issue, Pages: Mathematics Teacher, February 1995, 38-41
Reviewer: Marit
Date of Review: May 1, 2006

Jon Rahn Manon discusses the use of testing in the math classroom; he offers other assessment options as well as test making strategies for the traditional test. He suggests that teachers consider more seriously why they test while considering the NCTM assessment standards. One point that he made that will really stick with me is that, “All too often we save our most creative questions for the test”. And all too often our students are just overwhelmed and then walk away frustrated and without a clear understanding. If we were to bring some of those really creative questions up in class, we could still evaluate student progress, but it would be more fun for the students and they could work cooperatively and come to a conclusion. Also, when we are using a standard test as a form of assessment it should be designed to be a sense-maker for students. It should be reachable but challenging so students feel like they are achieving. This article really made me reconsider how assessment will work in my classroom.

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Keywords: Teaching Strategies

Ref: Marit17
Author(s): editors: Kilpatrick, Jeremy, Swafford, Jane
Date:
2002 Title: "Helping Children Learn Mathematics"
Journal or Publisher: National Research Council
Volume, Issue, Pages:
1-42
Reviewer:
Marit
Date of Review:
May 7th 2006

Helping Children Learn Mathematics is an interesting read, and good summary of the application of the NCTM standards. The major goal of the book is to establish the future outlook of what math should be for school children and then to suggest strategies we all can take to raise the children of today to this new outlook. I especially appreciate the section on what it means to be mathematically proficient. All too often we think students are proficient when they can compute fluently, but we forget that students should "understand math", "be able to apply concepts to solve problems", "reason logically" and to see how "sensible, useful and doable" math can be. Not only does this text recognize that these are aspects of demonstrating proficiency, but it goes on to suggest ways to achieve proficiency in all students.

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Keywords: Teaching Strategies,
Ref: Marit18
Author(s): Mathematically Correct
Date: 2006(?)
Title: http://www.mathematicallycorrect.com/
Journal or Publisher:
Volume, Issue, Pages:
Reviewer: Marit
Date of Review: May 11, 2006

I wanted to look into the “Mathematically Correct” site more, because the “traditional” side of mathematics often gets a bad reputation. I read on in hopes to see “the other side of things”. I was disappointed to find many of the links to be extremely biased; most of the links were from either New York or California. In the opening paragraph the authors suggest that applied or “fuzzy” math is not as rigorous as traditional math. I can appreciate the traditional side of the so-called math wars, but am disappointed to see to what extent this website goes to make its point. It is so exceedingly extreme that I fear little can come of what is learned from this website. Little meaningful math can be achieved through extremes of both sides, and this website just furthers the stereotypes. I read the first article link on the site, “Save our Children from Mediocre Math”. The article is two paragraphs long and in short states that “EveryDay Math” texts do not uphold California state standards, and should not be taught. Maybe their claim is true, but little or no evidence is offered to support “EveryDay Math”’s offence. The organization and quality of “Mathematically Correct” is very minimal; the traditional side of the math wars is a valid side and should be presented much more professionally.




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Keywords: Equity/Diversity, Teaching Strategies, Keyword 3, Optional...
Ref: Marit19
Author(s): Gilbert, Cuevas; Driscoll, Mark
Date: 1996
Title: Reaching All Students with Mathematics
Journal or Publisher: NCTM
Volume, Issue, Pages: 1-264
Reviewer: Marit
Date of Review: May 19, 2006

The main belief that the “Reaching All Students with Mathematics” centers around is that “all students can learn a significant core of high-quality mathematics” (vii). The book is comprised of a range of stories that address this issue. Some of the accounts of efforts made to “reach” all students are really quite revolutionary; I was amazed by the overall success rate of these stories to reach students of minority groups. Several of the essays include student reactions to the teacher efforts. Though I have only read two of the teachers account, I plan to read the rest this summer. This is a quality read that it seems all teachers would value. I think the first hand accounts make “Reaching All Students with Mathematics” all the more powerful. We as the reader get to better understand another teacher’s attempt through his/her mistakes and triumphs.

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Keywords: Standards
Ref: Marit20
Author(s): O'Shea, Mark
Date: 2005
Title: From Standards to Success
Journal or Publisher: Association for Supervision and Curriculum Development
Volume, Issue, Pages: 1-158
Reviewer: Marit
Date of Review: May 19, 2006

This book aims to provide “explicit directions to teachers and administrators that, if followed, will lead to standards achievement” (ix). Mark O’Shea takes the ever present problem of making AYP, and boils it down to a simple “for dummies” book. As I read and glanced through most of the chapters I realized that many schools do need something like this to show them the way. Topics covered include: communicating the need for curriculum reform, scheduling collaborative planning time, supervising and sustaining the planning cycle, ect. I guess something like this probably won’t help me too much next year, but there are several chapters that I would recommend reading: “Expectations for Standards-Based Lesson Plans” and “Curriculum Guide Focused on Standards Achievement”.

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