**Keywords:** Equity/Diversity,

**Ref: **Brooke1

**Author(s): **Berry, RQ III

** Date: **2005

**Title: ***Building an Infrastructure for Equity in Mathematics
Education *

**Journal or Publisher: **The High School Journal

**Volume, Issue, Pages: **88(4), p. 1-5

**Reviewer: **Brooke

**Date of Review: **02/15/06

**Summary: **Berry first discusses NCTM's influence on reform paying
particular attention to the equity of students who have been ignored by
mathematics education. He mentions the criticism of the NCTM for not thoroughly
addressing equity relating to race in books such as Principles and Standards
for School Mathematics. He believes it is absolutely necessary to create
infrastructure for equity in mathematics education similar to previous reforms
regarding assessment and curriculum. Berry believes that it is important to
understand the causes of common biases among teachers in order to start addressing
equity in mathematics education. His main point begins with discussing Calvin's
Story, which tells the experience of an African American middle school student
who performs very well on standardized tests in math but sometimes has a
difficult time sitting still in the classroom. Calvin's mother fears that
he may not be challenged enough in school and that his teachers are not openly
showing interest and care towards Calvin in order to help him be more productive.
Calvin is not recommended by his teachers to take a mathematics placement
test for an upper-level math class even though he meets all of the other
requirements. This particular class ends up having no African American students
in it, which is common among high-level math classes since non-Caucasian
students are sometimes faced with low expectations from teachers. Berry
argues that in order to address such inequalities, educators must first examine
the inequities in a broader sense. Educators must also understand how racial
inequalities in math classrooms may affect a students's success in the future.
Berry discusses several approaches to help teachers overcome their possible
biases in the classroom, such as support groups and informational panels.

**Personal Reaction:** I appreciated Berry's efforts to summarize
some of the NCTM's influence on reform, as well as discuss some of the issues
that NCTM has been criticized for. Calvin's Story was a great introduction
to one of the main issues that minority students may face in a mathematics
classroom. I am very glad that Berry discussed some of the ways in which
teachers can overcome their personal biases, or how teachers may even just
begin to identify what their internal biases are. I recommend this article
for all math teachers because I feel that it opens up your eyes to the daily
struggles that some students face in the classroom. It also fits well with
the NCTM's goal to address the Equity Principle.

**Keywords:** Problem Solving,

**Ref: **Brooke2

**Author(s): **Hart, L C

** Date: **1993

**Title: ***Some Factors That Impede or Enhance Performance in Mathematical
Problem Solving *

**Journal or Publisher: **Journal for Research in Mathematics Education

**Volume, Issue, Pages: **24(2) p. 167-171

**Reviewer: **Brooke

**Date of Review: **02/16/06

**Summary: **Hart discusses how research has looked at the problem-solving
skills of those who have high math abilities as a way to help those who
may be *average* or below-average math students. Others believe that
such skills might be hard to teach and apply with students who may struggle
in math. Hart discusses a study of twelve seventh-graders who are labelled
as having *average* math abilities. These students were put into groups
and videotaped working on a certain problem that includes information they
should be familiar with. After reviewing the tapes, four negative factors
were identified relating to problem solving and three positive factors were
found that helped students. After examining the study, Hart believes that
it is important for students to have experience with problem solving and
that group work aides students in deciding which steps to take in addressing
the problem.

**My Reaction: **I wish that Hart had gone into more detail of previous
thoughts on a students's ability to problem solve in math. While I am glad
that Hart provided a brief description of the study, I would have appreciated
more specific examples of what students did or did not do when it came to
solving the problem. I think that it would also help if she had provided
more helpful hints for teachers regarding how to improve their students's
problem solving abilities. I think group work is great, but I also think
that it is very important for students to be able to problem solve on their
own.

**Keywords:** Algebra, Teaching Strategies

**Ref: **Brooke3

**Author(s): **Steele, M. M and Steele, J. W.

** Date: **2003

**Title: ***Teaching Algebra to Students With Learning Disabilities
*

**Journal or Publisher: **Mathematics Teacher

**Volume, Issue, Pages: **96(9), p. 622-624

**Reviewer: **Brooke

**Date of Review: **02/22/06

Summary: Students with learning disabilities are often placed in a mainstream classroom that is not necessarily the least restrictive environment. The Steeles first explain what a learning disability is and how it affects students, particularly with Algebra. They bring attention to the fact that the typical ways in which a teacher may teach Algebra are not necessarily the best way to teach Algebra to a student who has a learning disability. One area where students with learning disabilities often struggle with is memorization. The Steeles point out that students with learning disabilities are definitely capable of learning Algebra, and that it just may take more time and patience. One way in which students will benefit is if the teacher provides one-on-one instruction and provides plenty of examples and practice problems. They also suggest having the students create a self-monitoring system to track their progress. Algebra teachers need to be well aware of how to help students with learning disabilities learn algebra.

My Reaction: I appreciated how this article outlines several of the different ways in which learning disabilities may affect students, especially related to mathematics and Algebra. I think often times we forget that sometimes a mainstream classroom is not the best for students. From my personal field experiences, I have noticed when students with learning disabilities get lost in the crowd because they are not receiving adequate attention. This is when I believe that math resource rooms are very important, even if a students uses them every once in a while. Since Algebra is so important to learning and is used all of the time, I think that teachers must learn different strategies for teaching it, especially for students with learning disabilities or another exceptionality. I wish that the article discussed more strategies for helping teachers teach Algebra to students with learning disabilities. Since there is not one single type of learning disability and not one single strategy that works for all students, I think that more information would have been helpful. I believe that this article would be beneficial for teachers because it would help them realize why a student who has a learning disability may be struggling in their Algebra class, and what they can do to help.

**Keywords:** Assessment, Geometry, Teaching Strategies

**Ref: **Brooke4

**Author(s): **Walmsley, A. L. E and Muniz J.

** Date: **2003

**Title: ***Cooperative Learning and Its Effects in a High School
Geometry Class *

**Journal or Publisher: **Mathematics Teacher

**Volume, Issue, Pages: **96(2), p. 112-116

**Reviewer: **Brooke

**Date of Review: **02/24/06

Summary: Walmsley and Muniz discuss common feelings that high school students have towards math, such as stress and boredom, as well as math-anxiety. They explore and discuss the benefits of cooperative learning as a tool to help students enjoy math and improve their overall success in math. They emphasize the importance of holding students accountable for their work and working together with other students as a team. They point out that a positive outcome of using cooperative learning is communication skills while working in a group. Walmsley and Muniz also make teachers aware of the difficulties they may have while attempting to use cooperative learning in their classroom such as one individual doing the majority of the work and a perceived loss of control by the teacher.

Walmsley and Muniz go on to discuss a study they did with two geometry classes where cooperative learning wasn't originally used often. During the second quarter, one class continued to use limited amounts of group work while the other focused primarily on cooperative learning, using extra-credit points for students to use as a reward of individual accountability. Comparing the grades of the first quarter with the second quarter, the cooperative learning group's grades increased by five points more than the other group. Walmsley and Muniz have concluded that cooperative learning positively adds to a classroom and benefits the overall math abilities of students. My Reaction: While I appreciated the description of cooperative learning, I wish that they authors had gone into more detail regarding the informal study that they conducted. There didn't seem to be that much of a connection between the initial explanations of cooperative learning and the study. I am glad that they explained some of the difficulties teachers might be faced with if they choose to use cooperative learning in their classroom. I recommend this article for future teachers because it describes some of the positive benefits that cooperative learning can play in a classroom and also discusses ways in which to help monitor the learning that is going on in the classroom.

**Keywords:** Activities, Number and Operation, Teaching Strategies

**Ref: **Brooke5

**Author(s): **Don Crossfield

** Date: **1997

**Title: ***(Naturally) Numbers Are Fun *

**Journal or Publisher: **Mathematics Teacher

**Volume, Issue, Pages: **90, p. 92-95

**Reviewer: **Brooke

**Date of Review: **03/01/06

Summary: Crossfield describes his experience of using number sequences in his classroom. He chooses to create banners with different number sequences to display in his classroom. Each number sequence was labelled with a color. He presents many questions that he asked in class and the different ways in which the students explored them. By using the sequences, he is able to introduce a variety of theorems and mathematical concepts such as the law of exponents and number theory. The students are able to examine the relation between the sequences. He is challenged because he does not know when to let the students keep exploring or when he should spoil the fun and explain famous theorems. Crossfield goes on to explain how the students greatly benefited from constantly exploring such sequences - they always have a visual guide in the classroom and are able to have clear examples that all students are familiar with.

: My Reaction: I think that the banners of sequences are a great idea, especially since he is able to relate the sequences to one another and keep building the lessons off of the banners. I thought that it was very interesting how he was challenged whether or not to reveal the theorems, etc. Sometimes I am faced with how far to lead the students on with the problems or how long to let them explore on their own. I can imagine how exciting the classroom must have been when they were discovering new ideas. I was very impressed with how the students were able to pick up on the different number sequences and how it became much easier for them to discuss the mathematical concepts.

I think it would have been interesting if he had included some comments from students regarding what they liked about the banners and how it has changed their way of approaching such types of problems. I appreciate how he let us know what actual sequences he used with the banners. I also like how he divided up the article by going over the different questions that can be asked about the sequences. I suggest this article because I feel that it provides new and exciting ways to introduce concepts into the classroom. After reading this, I am very interested in doing something similar to this with banners in my high school classrooms.

**Keywords:** Representations, Activities, Assessment

**Ref: **Brooke6

**Author(s): **Perry, J.A and Atkina, S. L.

** Date: **December 2002

**Title: ***It's Not Just Notation: Valuing Children's Representations
*

**Journal or Publisher: **Teaching Children Mathematics

**Volume, Issue, Pages: **9(4) p. 196

**Reviewer: **Brooke

**Date of Review: **03/06/06

Summary: Perry and Atkins discuss how it is important to investigate what students are thinking while they are learning, not just seeing if they are thinking exactly how we as teachers might. The NCTM, as well as Perry and Atkins, suggest looking at a studentï¿½s representations to understand how and what students are learning. In order to do so, teachers need to understand which types of problems will allow students to individually represent their thoughts. On explanation of this is when students were asked to u se a manipulative (Unifix cubes) and to then record their representations/findings in any way they choose. It turns out that students had all different types of response, and that having the students explain their reasoning greatly helped their teacher examine whether or not students were really understanding the mathematical ideas. These particular first graders ended up having very different explanations than what their teacher had planned on them having. The article continues to explain two other classroom representation lessons where students were asked to explain their reasoning. One example of a studentï¿½s misunderstanding of a mathematical concept is her definition of ï¿½two-thirdsï¿½: two separate pieces that equal one-third. Perry and Atkins discuss the importance of allowing students to work through a problem by using representations. They also stress student-teacher dialogue as a way of understanding what a child is really thinking about a math concept through their representations, rather than just assuming what they know.

My Reaction: I enjoyed this article because it emphasized how each student
does not think exactly the same as their peers. It also helped explain why
it is so important for teachers to have good communication with their students
in order to check for understanding and to see whether or not students are
truly able to grasp the mathematical concepts, or if they are just able
to produce an answer. I want my students to be able to explain their reasoning/representations
and justify their answers. This will help tell me that they are learning
what I would like them to learn. I felt that the article was written in an
informative way because it clearly went over what teachers discovered their
students were doing and gave real-life classroom examples. The pictures with
the different representations definitely helped me understand where the students
were successful or where they may have been struggling. I suggest this article
for all mathematics teachers, especially those who would like to focus on
elementary or middle school because it communicates to the reader that while
their student may seem like they understand the math, they really may not
understand why something is happening.

**Keywords:** Algebra, Activities,

**Ref: **Brooke7

**Author(s): **Devries, L.

** Date: **1996

**Title: ***Solving Equations: How Sweet It Is! *

**Journal or Publisher: **1996

**Volume, Issue, Pages: **

**Reviewer: **Brooke

**Date of Review: **03/08/06

I chose this lesson plan regarding solving equations with variables on both sides because I felt that it was very well organized. There are various aspects of this lesson plan that provide an outline for how I feel we as students and teachers should write our lesson plans. The objectives are clearly stated with what the students should be able to know and accomplish after the lesson. For example: "see the advantage of getting variables together first and keeping the variables positive." In addition, the important terms that students should be familiar with are given.

This lesson plan provides a lot of organizational details for the teacher, as well as someone who may be a substitute teacher. The materials are neatly described and step-by-step instruction for the entire lesson is provided with examples of problems that would be good to use. One aspect of this lesson plan which I thought was great is the creativity of solving equations with balance scales and candy. I think it will help involve all of the students and teach them a lot about successfully solving equations. There are also a lot of references to real-life situations such as sharing money and balancing a teeter totter. A video is suggested which is a great way to cater towards multiple intelligences and use different materials to teach a lesson.

As a teacher, I would feel very confident following and using lesson plans such as this one. It is very practical and useful for all different topics within mathematics.

**Keywords:** Problem Solving

**Ref: **Brooke8

**Author(s): **Schettino, Carmel

** Date: **2003

**Title: ***Transition to a Problem-Solving Curriculum *

**Journal or Publisher: **Mathematics Teacher

**Volume, Issue, Pages: **96(8), 534-537

**Reviewer: **Brooke

**Date of Review: **April 1st, 2006

Summary: Schettino begins by describing some of her student's reactions after finding out that they were going to be switching to a problem-solving curriculum. Students appeared frustrated because they were very used to being told what they are supposed to be learning and what they are supposed to do. They feared that the problem solving would be too difficult for them to understand what to do. She discusses the benefits of a problem-solving curriculum and emphasizes the importance of having students independently solve problems. The idea that problem solving allows students to gain a concrete knowledge regarding when to apply certain information and also relating the ideas to real life situations is also emphasized. She also covers some of the obstacles found when introducing a problem solving curriculum. One example is choosing the correct assessment and being sure to emphasize the use of writing to explain the thought process behind solving a problem. Schettino explains how she had students use journals as a way to record what they were doing and reflect on the problems. She also emphasizes the importance of a teacher's comfort level with the material because they will need to understand various ways to approach and solve the problems. Some of the disadvantages are also discussed, such as how the classroom can become chaotic if the teacher does not have control.

My Reaction: I felt that Schettino covers a lot of good material related
to using a problem solving curriculum. I appreciated how she covered both
the positive and negative aspects associated with problem solving and different
strategies she used for addressing these issues, such as the use of journals.
One thing that I wish was included is input from other teachers regarding
their experiences of using a problem solving curriculum. I think it helps
when you receive opinions and ideas from various sources. I really liked
her description of the homework she would assign because it gave me some
ideas for how to use problem solving in my classroom, even if I do not strictly
base the entire curriculum on problem solving. She suggested assigning 5-7
problems and having students reflect on each problem by writing about what
they discovered and how they went about solving them. I think that is a
very good idea because I am a huge supporter of having students always show
their work. This helps them remember the problem and helps me pinpoint where
they either went wrong or where they were successful. She also includes
an example of a specific homework problem, which helps the reader relate
better. I suggest this article because it provides a lot of information
regarding what to prepare for as a teacher introducing a problem solving
curriculum, as well as makes you aware of some of the obstacles you may
be presented with.

**Keywords:** Algebra, Equity/Diversity

**Ref: **Brooke9

**Author(s): **Feigenbaum, Ruth

** Date: **2000

**Title: ***Algebra for Students with Learning Disabilities *

**Journal or Publisher: **The Mathematics Teacher

**Volume, Issue, Pages: **93(4), 270-274

**Reviewer: **Brooke

**Date of Review: **April 1st, 2006

Summary: This article discuses the common problem of students with learning disabilities graduating from high school without having much exposure to algebra, even when more and more students with learning disabilities are going to college. Colleges such as Bergen Community College are now offering math courses designed especially for students with learning disabilities. It is known that students with learning disabilities can succeed in an algebra class, especially when extra attention is given to their learning styles and when topics are broken down into short groupings of time. In these classes, teachers provide students with detailed notes of the lecture and focus on maintaining a positive and safe learning environment. There is also a large emphasis on showing all work in step-by-step procedures.

My Reaction: While this article presents a lot of ideas regarding how to successfully teacher students with learning disabilities, I did not feel that many new ideas were given. The ideas for conducting the class seem to be exactly what should be done in ALL classrooms (using various activities, hands-on work, board work, etc). I think that this article is a good reminder for math teachers (especially algebra teachers) because it provides detailed examples of how to use various approaches in a classroom and how to successfully teach algebra. I wish that the author had given new ideas for teaching students with learning disabilities across all grade levels, not just college students.

**Keywords:** Curriculum, Algebra

**Ref: **Brooke10

**Author(s): **

** Date: **1996

**Title: ***Making Matrices Accessible to All: The Dutch Perspective
*

**Journal or Publisher: **Addenda Series: A Core Curriculum

**Volume, Issue, Pages: **17-27

**Reviewer: **Brooke

**Date of Review: **April 5th, 2006

Summary: This article compares the applications of matrices in a high school setting of both the United States and the Netherlands. The Dutch curriculum chooses to introduce matrices beginning in the ninth grade and continuing throughout all of high school, while the American system typically introduces matrices only in the 11th or 12th grade. Problem solving is emphasized as being a necessity in the classroom and is used by the Dutch at a very early stage in a student's education. Many of the problems introduced by the Dutch require students to take information for a certain problem and apply it to a matrix. Students are also required to interpret data presented in matrices. Throughout the article, sidenotes are provided explaining certain aspects of the lessons presented and additional information for teachers. Towards the end of the article, information is provided regarding assessment and tests. The use of matrices is emphasized, especially the real-life applications and importance of having students be able to interpret and create different matrices.

My Reaction: I thought that this chapter of the Addenda book was very
interesting because it addressed the subject of my unit (Matrices) in a way
which I never would have thought of. I thought it was a great idea to compare
the use of matrices in an American classroom and that of a Dutch classroom.
After reading the article, I have gained some new ideas of how to introduce
matrices into any type of high school mathematics class. I liked how different
examples of problems were provided because it allowed me to grasp an idea
of what students in the Netherlands are required to do. I think that the
Addenda books in general are very interesting because a lot of information
about neat topics are provided.

**Keywords:** Teaching Strategies, Algebra

**Ref: **Brooke11

**Author(s): **Choike, James R.

** Date: **2000

**Title: ***Teaching Strategies for "Algebra for All" *

**Journal or Publisher: **Mathematics Teacher

**Volume, Issue, Pages: **93(7), p/ 556-560

**Reviewer: **Brooke

**Date of Review: **April 7, 2006

Summary: Choike begins by discussing the importance of algebra in the
real world. He mentions how teachers are faced with teaching algebra to students
with a variety of different math backgrounds. He also addresses how to reach
all students, regardless of their previous math experiences. The first issue
discussed is how to decide what topics to cover since it is often difficult
for a teacher to get through the entire book. Choike suggests discussing
the big ideas in order for students to gain an understanding of what is important
regarding Algebra. He also emphasizes that teachers should rewrite problems
to use simple numbers (such as by eliminating decimals) initially introducing
students to the idea of writing algebraic equations. Teachers should always
encourage and support students asking questions, especially if they are asking
for clarifications, and help them feel more comfortable with math. Choike
emphasizes the importance of using various representations and relating these
representations to each other. He gives an idea for engaging students; relate
problems to things going on in the student's lives so that they become more
interested in what they are learning. My Reaction: I appreciated the thoughts
that Choike provides us relating to teaching Algebra. I think that some
of the topics he discussed were somewhat of a reminder of the key issues
we learned in our Education 330 classes. I feel that this article is important
for all teachers to read because it summarizes some of the basic tools that
will help teachers in the classroom. I thought his emphasis on relating
the problems to the students was very important because I would really like
to incorporate daily facts and experiences into the problems and math that
I choose to use in my classroom.

**Keywords:** Issues, Activities, Curriculum

**Ref: **Brooke12

**Author(s): **Bright, George; Freierson, Dargan Jr; Tarr, James E.;
Thomas, Cynthia

** Date: **2003

**Title: ***Navigating Through Probability in Grades 6-8 *

**Journal or Publisher: **Navigations Series

**Volume, Issue, Pages: **

**Reviewer: **Brooke

**Date of Review: **April 10th, 2006

Summary: This book provides some clear-cut examples of helpful activities for working with probability in the middle schools. Provided by NCTM, the Navigations Series is meant to help teachers adapt the various "Principles and Standards for School Mathematics" within their actual classroom setting. For each activity, the goal, materials needed, and a summary are provided. Within some of the margins, there are quotes and explanations from certain educators pertaining to the material. At the end of the book, there are various worksheets and handouts pertaining to the activities.

My Reaction: I was very impressed with this book. I feel that this series
would be a great resource for me because I would feel comfortable picking
up a book pertaining to the particular unit that I am doing and finding an
activity that fits right in with my objectives. I appreciated how each activity
is explained in somewhat of a lesson-plan form, listing the various objectives
and what teachers will need to do to successfully teach the activity. I
think it would be great if I could gain some knowledge on what these books
have to offer so that I know when to turn to them when I am in need of a helpful
activity. I liked the term "navigating" because I feel that it represents
what successful math teachers do; they help students discover the different
concepts and find real life problems that they can apply the math to. You
don't just give them the material, but instead you provide them with the tools
for success through their own self-discovery of math. I loved how there
were worksheets in the back of book for teachers to use as additional resources.

**Keywords:** Connections, Teaching Strategies

**Ref: **Brooke13

**Author(s): **Manouchehri, Azita and Douglas A. Lapp

** Date: **2003

**Title: ***Unveiling Student Understanding: The Role of Questioning
in Instruction *

**Journal or Publisher: **Mathematics Teacher

**Volume, Issue, Pages: **96(8), p. 562-566

**Reviewer: **Brooke

**Date of Review: **April 10th, 2006

Summary: The article begins with an example of a class period where a teacher is going over solving systems of linear equations. The teacher seems to ask yes/no questions that do not check for understanding or intrigue students. Manouchehri and Lapp list several positive aspects of the lesson, but focus mostly on the negative aspects such as how the "questions seemed to control the students' answers." The authors emphasize the importance of having the teacher ask questions that will get students thinking about the concepts they are learning, as well as openly discussing what they may be struggling with. In addition, there is emphasis on focusing on the depth of understanding by using open-form questions that emphasize content. The article ends by emphasizing the importance of having teachers think about the main objectives and ideas of each lesson prior to actually teaching it so that they can predict questions that students may ask, as well as create some good questions to actually ask students.

My Reaction: I liked how this article started off by giving an example of a lesson where the teacher didn't do a very good job of questioning their students. This allowed me to think about what the teacher did well and what they could improve on. It would have helped a lot if they had then provided an example of a lesson where there was good questioning. The article would be great for student teachers to read because it emphasizes the important parts of creating questions to ask students in order to check for understanding.

**Keywords:** Research , Equity,

**Ref: **Brooke14

**Author(s): **Crawford, C.

** Date: **2004

**Title: ***Race research "misrepresented" *

**Journal or Publisher: **NAS Online Forum - http://www.nas.org/forum_blogger/forum_archives/2004_02_08_nasof_arch.htm

**Volume, Issue, Pages: **

**Reviewer: **Brooke

**Date of Review: **04/17/06

Note: I used this source for the paper I wrote this summer for Exceptional Child. Summary: This forum discusses the issue of a "stereotype threat" that is sometimes present in schools. This is when minority students, in this case African American students, perform lower on tests when they feel that people are expecting them to do poorly. My Reaction: I found this source very interesting because it discussed how one explanation of the achievement gap between whites and blacks might be the "stereotype threat". This means if one is constantly threatened or told that because they are a minority they will not do as well, when they take the actual test, the will do worse than a group of whites. However, if there is no stereotype threat, the two racial groups will have basically the same scores. While the actual research for this reasoning is often debated, I feel that it could be one of the reasons that explain the psychology behind the achievement gap. I also feel that we need to continue to pursue finding out more about the possible causes for the achievement gap.

**Keywords:** Technology, ,

**Ref: **Brooke16

**Author(s): **Barrett, Gloria B

** Date: **1999

**Title: ***Investigating Distribution of Sample Means on the Graphing
Calculator *

**Journal or Publisher: **Mathematics Teacher

**Volume, Issue, Pages: **92(8), p.744-747

**Reviewer: **Brooke

**Date of Review: **April 26th, 2006

Summary: This article discusses options for selecting samples on the TI-83 calculator. In one example, one learns how to choose samples and then compute the mean. There is various information regarding what to enter into the calculator, as well as pictures displaying what the information would look like on the calculator. My Reaction: I was very confused while reading this article because I was not able to constantly track what was being said. Maybe if I had actually had a TI-83 calculator in front of me while reading the article I would have understand what was going on. I do not suggest this article unless you are in the process of covering very similar material in your classroom.

**Keywords:** Activities, Algebra
**Ref: **Brooke15
**Author(s): **Rubin-Forester, Allison
** Date: **
**Title: ***Get 'em Moving! Kinesthetic Lesson Ideas That Help ALL Students Learn
***Journal or Publisher: **
**Volume, Issue, Pages: **2006 MCTM Conference
**Reviewer: **Brooke
**Date of Review: **May 1st, 2006

Summary: This session provided great examples of how to get students moving around the classroom in order to learn different algebraic concepts. One topic that was emphasized was actually “showing” slope by having groups of students line up and form an x-y axis. Students are then given a certain slope to “act out” and ribbon is used to show the actual slope. You can also use this idea to physically show different equations, such as y=2. The speaker, Allison Rubin-Forester, emphasized the importance of hands-on learning, especially in a math class. She discussed how easy it is for students to get bored in class because they are expected to constantly sit still in their chairs. She provided us with many great examples as to how to create a more hands-on learning environment in out math classes.

My Reaction: I am so glad that I attended this session. The speaker provided me with really interesting information that seems so simple, but is actually difficult to brainstorm on your own. One of the most important points that I gathered was that it is very easy to distribute information to different groups and then have them work together in order to solve something related to math. For example, she handed out strips of overhead paper with a step of an actual proof of an equation. Once the strips are all passed out, students are to work together to figure out how to solve the actual equation. I plan on definitely using the tools that I learned here and applying them to my classroom. I can’t wait to try it out in my student teaching in the fall. I recommend this session for ANY math teacher because you receive very valuable information that will make learning for students much more fun.

**Keywords:** Activities, Geometry
**Ref: **Brooke17
**Author(s): **Lundquist, Janet
** Date: **MCTM Conference 2006
**Title: ***Origami Cube and Tetrahedron
***Journal or Publisher: **
**Volume, Issue, Pages: **LeCenter Public Schools
**Reviewer: **Brooke
**Date of Review: **May 2nd, 2006

Summary: Janet Lundquist from the LeCenter Public schools in LeCenter, MN, discussed various ways to incorporate origami into a geometry lesson. We learned how to create cubes and other shapes out of colorful origami paper. She went through the process, teaching us how to create the basic shape that is used throughout the particular unit where the shapes are from. She also discussed the common problems that students run into when trying to create these shapes, such as not folding the crease hard enough and quickly becoming frustrated with the project. Lundquist emphasized the importance of hands-on activities when teaching students geometry. She suggested doing this project and the end of the unit, or periodically throughout the year when there is an “off” day.
My Reaction: I am very glad that I went to this workshop because I realized how easy it is to use origami. I think that I would be able to teach the concepts to my students. Although the booklet listed this workshop for grades 6-8, I definitely believe that origami could be used throughout high school and even college-level math courses. A class is able to discuss various angles, similarity, symmetry, etc throughout the time of making the different shapes. One thing I was thinking about while attending this workshop is how students could easily become frustrated because they may not believe in themselves that they can actually do origami. I think that a teacher would have to be very supportive of the students without showing them exactly what needs to be done. Through discovery, students will eventually be able to make the shapes. I recommend this workshop because I learned some valuable origami skills. However, I feel that I could have taught myself origami had I been using an actual book that explained what to do.

**Keywords:** Research , Issues
**Ref: **Brooke18
**Author(s): **Cotter, Joan
** Date: **MCTM Conference 2006
**Title: ***Place Value: Some Innovative PRoven Techniques for Teaching
***Journal or Publisher: **
**Volume, Issue, Pages: **
**Reviewer: **Brooke
**Date of Review: **May 2nd, 2006

Summary: Joan Cotter discussed some of the common issues among today’s elementary school students pertaining to understanding place value. She raised the point that many students do not understand what they are counting and why when they say “1, 2, 3, 4, 5, 6….”. She compared the Japanese school structure with the American school structure, emphasizing the Japanese usage of mathematical language relating to the concept of quality. She suggested that we must teach our students what they are doing when they are counting, not simply teaching them to count from 1-10. One issue she pointed out what that typically American children learn to count up to 99, which is confusing because then they do not see the relationship between tens and one-hundred. She also suggested that we should do groupings in fives and tens, so that students are visually able to see a number.
My Reaction: While I feel that some of the information given in this session is very valuable, I also feel that she was basically preaching her research. I was not completely convinced that what she was discussing pertaining to place value made sense. At times I felt that her concept would confuse students more. She also seemed to severely criticize concepts that have been taught in the school for years, which is OK, but not in a way that I felt was completely appropriate. I think that this issue is important to pursuer throughout the next several years so that we are able to agree upon the best way to help our students understand place value.

**Keywords:** Activities, Geometry, History
**Ref: **Brooke19
**Author(s): **Neumann, Maureen D.
** Date: **Febrary 2005
**Title: ***Freedom Quilts: Mathematics on the Underground Railroad
***Journal or Publisher: **Teaching Children Mathematics
**Volume, Issue, Pages: **11(6), 316-321
**Reviewer: **Brooke
**Date of Review: **May 2nd, 2006

Summary: Neumann discusses the two books relating to the use of quilts during slavery that inspired this lesson (designed for late elementary/early middle school). The article describes the use of reading about slavery and the Underground Railroad and incorporating the geometrical and mathematical concepts behind making the quilts that were used to communicate with other slaves regarding escape routes etc... Neumann touches upon the various mathematical concepts that are seen in the quilts, such as patterns, symbols, geometry, proportion, and so on. One of the mathematical objectives is for students to understand that “A square has four right angles and four sides of equal length. Students then learn how different shapes are related to each other,” (p. 318). The article provides a detailed description of how to conduct the actual lesson and how to incorporate the various math connections.
My Reactions: I feel that this idea is very creative and is something that I most likely would not have come up with on my own. I like the idea of having lessons combine various subjects, such as math and history, so that students are able to relate real-life situations to mathematical concepts. This type of project would be great for elementary students because it allows them to have a hands-on experience relating to math. I appreciated the pictures that were included in the article because it gave me an idea of what the students were actually creating. One concern that I have is that as a teacher, I would have to be sure to know what the objectives are for the lesson and be sure to follow through in the teaching of those objectives. I feel that it would be fairly easy to lose the actual math when doing this lesson. I think a similar project could be done in a high-school geometry class, possibly incorporating the idea of using shapes and patterns to tell a story. I recommend this article, especially for those who are thinking about going into teaching elementary school or being a math specialist at an elementary school. This activity is a great idea.

**Keywords:** Puzzles, Activities, Manipulatives
**Ref: **Brooke20
**Author(s): **Shockey, Ted L., and David M. Bradley
** Date: **April 2006
**Title: ***An Engaging Puzzle to Explore Algebraic Generalizations
***Journal or Publisher: **Mathematics Teacher
**Volume, Issue, Pages: **99(8), 532-536
**Reviewer: **Brooke
**Date of Review: **May 2nd, 2006

Summary: This article relates to the “golf tee”, or otherwise known as the “Moving Bears” problem commonly seen in Discrete and Gateways classes here at St. Olaf. The authors discuss the reactions of various people, such as a current math teacher, a student teacher of mathematics, and a researcher in the field of mathematics, regarding how to solve this puzzle or create an equation/formula explaining how to solve. The article emphasizes teacher-student dialogue relating to solving this puzzle, particularly for determining whether or not there are fewer moves than originally thought. Although the various people tend to agree upon the basic concepts, the researcher ends up giving the most mathematical description of a formula. The authors emphasize how this information can be used in an actual math classroom, by increasing the use of mathematical language among our students. My Reaction: I liked how a common puzzle was used as the example because I was able to relate to how to actually solve. I thought it was interesting how they tried to incorporate various views on the problem, although I feel that the authors could have done a better job of elaborating on the ways in which the three people went about solving the problem and how they think that it should be taught to a class. I believe that it is very important for our students to gain a better understanding of mathematical language, and to feel more comfortable using it in a classroom. This article is interesting to read, but I don’t think it will be very helpful when it comes to teaching my own classroom.

**Keywords:** Puzzles, Activities, Manipulatives

**Ref: **Brooke20
**Author(s): **Shockey, Ted L., and David M. Bradley ** Date: **April 2006 **Title: ***An Engaging Puzzle to Explore Algebraic Generalizations
***Journal or Publisher: **Mathematics Teacher **Volume, Issue, Pages: **99(8), 532-536 **Reviewer: **Brooke **Date of Review: **May 2nd, 2006

Summary: This article relates to the "golf tee", or otherwise known as the "Moving Bears" problem commonly seen in Discrete and Gateways classes here at St. Olaf. The authors discuss the reactions of various people, such as a current math teacher, a student teacher of mathematics, and a researcher in the field of mathematics, regarding how to solve this puzzle or create an equation/formula explaining how to solve. The article emphasizes teacher-student dialogue relating to solving this puzzle, particularly for determining whether or not there are fewer moves than originally thought. Although the various people tend to agree upon the basic concepts, the researcher ends up giving the most mathematical description of a formula. The authors emphasize how this information can be used in an actual math classroom, by increasing the use of mathematical language among our students. My Reaction: I liked how a common puzzle was used as the example because I was able to relate to how to actually solve. I thought it was interesting how they tried to incorporate various views on the problem, although I feel that the authors could have done a better job of elaborating on the ways in which the three people went about solving the problem and how they think that it should be taught to a class. I believe that it is very important for our students to gain a better understanding of mathematical language, and to feel more comfortable using it in a classroom. This article is interesting to read, but I don't think it will be very helpful when it comes to teaching my own classroom.

**Keywords:** Teaching Strategies, Assessment, Activities

**Ref: **Brooke21
**Author(s): **Norwood, Karen S. and Glenda Carter ** Date: **November 1994 **Title: ***Journal Writing: An Insight Into Students' Understanding
***Journal or Publisher: **Emphasis on Assessment: Readings from NCTM's School-Based Journals **Volume, Issue, Pages: **81-83 **Reviewer: **Brooke **Date of Review: **May 3rd, 2006

Summary: Norwood and Carter discuss the approach they use in their fifth-grade math classroom regarding journal writing. They use journal writing at the beginning of each class period as a way to allow students to express their views of the day on math or to answer to questions posed to them relating to math. One example of this is the question: "How do you use fractions in your life?" The authors suggest creating a special journal for each individual student so that they take ownership and look forward to writing in their journal each day. They also emphasize how important this writing can be for evaluating a student's understanding of different math concepts by asking them questions related to the objectives of a previous lesson. Math journals can also be used for projects.

My Reaction: I like the idea of using writing in my math class because I feel that it is very important for mathematics teacher to emphasize the use of reading and writing. As reading and writing becomes more important throughout all educational curriculum, it is very important for me to feel comfortable incorporating writing into my lessons. Although this article discussed the use of writing within a 5th grade classroom, I feel that it is possible to use this across all of the different grade levels. This article presents the information in a very neat and organized manner because there are numbered bullets for the different approaches one can take in assigning journal writing. There are even student samples of what they wrote in their math journals pertaining to different topics within math. I recommend this article for all future math educators because I believe that reading and writing will become more and more important each year within the mathematics curriculum and we must begin to include this in our curriculum.