Keywords: Curriculum......
Ref: Liz1
Author(s): Martin, Tami S.; Hunt, Cheryl A.; Lannin, John; Leonard, William Jr.; Marshall, Gerald L.; Wares, Arsalan
Date: 2001
Title: How Reform Secondary Mathematics Textbooks Stack Up against NCTM's Principles and Standards
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 94, No. 7, pp. 540-589
Reviewer: Liz
Date of Review: February 14, 2005
This article addresses the need to align the curriculum with the NCTM Principle Standards. However, in 1989 there were no textbooks with material that would cover the standards. In 1990 NSF (National Science Foundation) made a $43 million investment to develop math projects that would follow the NCTM standards. This article discusses how well the NSF materials measure up against the NCTM Principle Standards. A high percentage of the NSF texts covered more problem solving, use of technology, connections to other subjects and a more in depth analysis. The NSF did have a lack of connections with traditional math and it might require the teacher to move between texts and possibly change their teaching perspective. In general, the NSF texts are worth examining but they must be done so with careful review before they are incorporated into the classroom.
Personally, I feel that if these NSF texts can get the students more interested in the material using problem solving and increased technology as well as cover the NCTM standards, then these texts may be something to look into using in the classroom. However, I also feel that it is important to include aspects of traditional math because traditional math is responsible for giving students the tools they need to problem solve. In high school, I took a three year Integrated Math Program which is similar to these NSF texts. However, the material was presented in a way that my classmates or myself found this class to not be useful. Our materials had good intentions of incorporating real world situations, but I believe that the teachers in the school should have been better prepared to present this material.
Keywords: Equity/Diversity......
Ref: Liz2
Author(s): Gilbert, Melissa C.
Date: 2001
Title: Applying the Equality Principle
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 7 No. 1 pp. 18-19, 36
Reviewer: Liz
Date of Review: 2-16-2005
This article discusses incorporating the equality principle into the classroom. This teacher gave several suggestions of ways to achieve gender equality as well as random volunteers, cooperative groups and providing examples from their every day lives. The teacher discussed the importance of resisting telling students the answer when they are struggling to find a solution. Rather, it is more helpful to ask them questions that will lead to their understanding. The teacher also tries to understand the home lives of her students so she knows if there are different circumstances that the students live with. She tries her best to get her students personally invested in the topics so they will internalize the information better.
This article was okay in detailing how to incorporate equality principle into the classroom. The teacher gave a few suggestions, but feel as though she left out how to deal with students that have different learning styles and learning abilities. She failed to mention that we need appropriate resources in order accommodate for these differences. I did enjoy that she felt that she needed to help the students personally connect to what they are learning as well as learn about their home situation. She failed to mention that we need to have high expectations for all students and not label students with low expectations to succeed.
Keywords: Probability, Teaching Strategies, Statistics
Ref: Liz3
Author(s): Lanier, Susan; Barrs, Sharon
Date: 2003
Title: Let's Play Plinko: A Lesson in Simulations and Experimental Probabilities
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 96, No. 9 pp. 626-633
Reviewer: Liz
Date of Review: 2-21-05
This article discusses use the game Plinko to show students how math can be used to model and predict real world situations. The teachers that used this game found it especially good topic because it involved competition and money, two things that high school students understand. Many different math concepts were also tied into the lesson. As well as math concepts, the students also had the hand on activities of constructing their own Plinko board. The class simulated a game of Plinko and discussed different strategies they would use each time. After many questions, the students finally asked what were their chanced of winning $10,000. This question leads the teacher to define terms as well as calculate the experimental and the theoretical probabilities. They also used a calculator simulation because they understood that the more trials they used, the better their answer would be.
Personally, I really enjoyed this activity because it is a fun, hand-on way to calculate and understand probabilities. The teacher said that the students really enjoyed both the Plinko and calculator simulations and really got them motivated to learn the probability behind these. Most importantly I think that this activity was fun for the students, proving to them that math can be fun!
P>Return to Index
Keywords: Algebra......
Ref: Liz4
Author(s): Thornton, Stephen J.
Date: 2001
Title: New Approaches to Algebra: Have We Missed the Point?
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 6 No. 7 pp. 388-392
Reviewer: Liz
Date of Review: 2-28-05
This article challenges viewing algebra as a formal structure, but rather as a study of patterns and relationships. According to the article we need to work on developing an understanding of variables, expressions and equations and less work on drill and practice. The three approaches to algebra suggested are patterns, symbolic and functions. But there are many who question if these representations will still help students develop sufficient reasoning. One reason to use alternative representations is that too often students are looking at too specific of a problem with the goal of obtaining a correct answer. We need to have students generalize what they are observing instead of learning a specific procedure. It is also helpful to encourage students to develop their own insight into patterns and relationships through explanation and comparison. We as teachers need to help students use their insights to examine fundamentals in algebra before we can help our students see the purpose in using algebra.
I enjoyed this article because it encourages using multiple representations in algebra. I also like using physical and hand-on activities to help students visualize what they are doing. I feel that this kind of analysis in algebra helps students to better see relations between different concepts as well as bring their insights into other areas of mathematics. However, I also sometimes fear what will happen if students do not make these connections? Would it have been better to use drill and practice? I think that when these alternative representations are explained well they can strongly benefit the student.
Keywords: Activities, Communication, Teaching Strategies
Ref: Liz5
Author(s): Martinie, Sherri
Date: 2003
Title: Families Ask: Cooperative Groups
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 9 No. 2 pp. 106-107
Reviewer: Liz
Date of Review: 2-28-05
This article discusses the importance of cooperative learning in the classroom. Some of the benefits include a positive effect on achievement, personal relationships as well as motivation and enthusiasm toward math. Studies have shown that working in groups helps students learn more and retain the information better. Students learn to work as a team and gain skills needed for their future working with others. Working together improves socials skills and also allows students to help each other. It has also been shown that students understanding increases when they have to explain to others and students can also explain math concepts in way that make sense to each other. Students are still held responsible for their individual learning and they build confidence and value in their own thinking.
I have always been a supporter of group work. I have personally witnessed students understand concepts better when they have to explain it to someone else. They must organize their thoughts and find a way to simply explain the concept. Working together in a group is something that everyone must learn to do at some point during their life. This allows students to not only learn their mathematics better but also practice their social skills interacting with another group. This is a real life situation that is applicable to all students. Cooperative or group work is definitely something that I will use in my own classroom.
Keywords: Problem Solving......
Ref: Liz6
Author(s): Bay-Williams, Jennifer A.; Meyer, Margaret R.
Date: 2005
Title: Why Not Just Tell Students How to Solve the Problem?
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 10, No. 7, pp. 340-341
Reviewer: Liz
Date of Review: March 7, 2005
Many parents believe that just telling their children the answer to the problem will help them to understand the problem. Instead, as teachers we are trying to ask questions that will guide their thinking about solving a problem without taking away the challenge of actually solving it. When this approach is used by teachers, students will often go home to tell their families that their teacher will not help them with their math questions. The teacher is trying to get the student to actually do the math. Teachers encourage their students to use their previous skills which will allow them to better understand the problem. The goal is to get students to use problem solving strategies that make sense to them. For some teachers, telling their students the answer may help them move through the material more quickly and the teacher feels that more material is being covered, but the students may not fully understand. Parents need to see the value in having their children develop mathematical skills rather than individual skills that have no connections. Teachers are trying to give math more useful meaning that they can use later in life and show that there is more than one way to solve a problem. When asking students the questions, they are more likely to remember how to do it later because they will use a strategy that makes sense to them.
I enjoyed this article because I believe that this is a valid complaint of many parents. Especially as more “integrated” math is introduced into the classroom, parents see that the math their children are learning is not what they learned in school. Math classes today are asking the students more questions and relying on them to use their previous skills and knowledge to solve problems. As a future teacher, I need to remember to continue to ask questions that will inspire mathematical thinking. This article would be a good hand out to pass out to parents that ask these questions about exactly what their children are learning.
Keywords: Representations, Problem Solving, Algebra
Ref: Liz7
Author(s): Preston, Ronald V.; Garner, Amanda S.
Date: 2003
Title: Representation as a Vehicle for Solving and Communication
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 9, No. 1, pp. 38-44
Reviewer: Liz
Date of Review: March 8, 2005
This article discussed a classroom were the students were challenged to use data to see which class party plan was the best. Students were given the freedom to choose any representation they wanted to use to solve the problem. Many students chose to use a table, written explanations, graphing calculator or graphs to represent the situation. The representations that they used are not only thought of a the process to get the answer but also the product. Representations allow use to share and communicate our results with others. At first the students were working on trying to find only one right answer. Most of them started by organizing a table based on a varying amount of people. Students quickly eliminated the idea of using drawings because the numbers they were using were too large. Most students first made tables, then made graphs from their tables and then formed equations from their graphs. As a class they discussed which option was better and they decided that the equations gave the best summary. There may be students that will choose their favorite or the one they are most comfortable with, which may not be the best representation. One way that they suggest getting around this is to introduce a lesson with the specific representation or tell students that they must have their final answer in a specific representation. This activity helps suggest the importance for using many different representations so that students can have many tools to solve a problem. I really enjoyed this activity. I think that having the students use their own method, eventually lead all of them to using an equation. I like the suggestion of telling students that their final answer must be written in a specific representation. I think that it is also a good idea for students to explore using many different representations until they get an answer that makes sense to them. This is a good way to have students use tables, graphs and equations to solve one problem. This would definitely be something that I would use in my classroom.
Keywords: Connections......
Ref: Liz8
Author(s): Farmer, Jeff D.; Neumann, Andrew M.
Date: 2004
Title: Patterns in Perfect Squares: An Activity for Exploring Mathematical Connections
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 98, No. 4, pp. 260-265
Reviewer: Liz
Date of Review: March 14, 2005
This article discusses a classroom activity where students are searching for an undetermined number of patterns using a set of integers and their squares. The goal of this activity is for students to represent patterns in different ways and find connections between them as well as other mathematical concepts. The students are given a list of integers from one to thirty as well as their squared values. Then they look for patterns and talk with other students about which patterns they found. Together the class shares patterns and discusses the similarities and differences between them. The students are asked to formulate their patterns in words to share with the class. This helps the students better understand connections. Student connect patterns both algebraically and geometric. An introduction to algebraic reasoning and proofs can be incorporated into this lesson as well. Connections are made between multiplication of fractions and binomials, sequences of numbers and differences between numbers. Students can also connect patterns with other kinds of patterns that have been found. This is also a good chance for the teacher to discuss patterns that do no repeat. It is also helpful to use this in a classroom where mathematical reasoning and communication are important. This activity and others like it also help build confidence that they can find connections and pattern on their own. Students also begin to see connections to many mathematical themes and areas of mathematics. I really enjoyed this activity between it makes the students search for patterns in something that seems ordinary. I like that the students have a chance to talk with one another as well as share their patterns with the class. Students begin to see new and difference patterns. The teachers that wrote this article said that they have used this with a variety of age groups and it works well in most classrooms. One of the teachers said that he has been using this activity for over 10 years and every time he teaches it someone finds a new pattern that has never been found before. I think this is a really cool way to begin looking for connections in math and with simple integer lists that we use constantly.
Keywords: Teaching Strategies, Management...
Ref: Liz9
Author(s):
Thurston, Cheryl Miller
Date: 1975
Title:
Junior High? Good Grief!
Journal or Publisher:
Today's Education
Volume, Issue, Pages: Sept.-Oct.
Reviewer: Liz
Date of Review: March 16, 2005
This teacher discusses all the things that she wished she would have learned about junior high during college. She believes that colleges need to spend more time preparing junior high teachers for what they can expect junior high to be like. Some of her suggestions include knowing when to play dumb. Teachers need to know what to ignore and what to take seriously. They must learn to develop a tolerance for unrelated comments as well as learning what to believe and take seriously. Teachers need to learn how to deal with flying objects because junior high students love to throw things in the classroom. Developing a thin skin to face the students is essential. Teachers need to learn to not take things personally when students make unkind comments. A big part of junior high is the relationships they have with one another. The teachers need to understand what it means to be going out and who is going out and who just broke up. Relationships are a big deal to junior high students. Junior high students also often have to giggles and find many things funny for no reason. This is something to remember and just to be aware. She says the most important things is for teachers to walk into their classroom assuming that no one is listening to them and they must learn to repeat things several times. In the conclusion of the article, she says that maybe college students should not learn this before they go out teaching. Also, there is nothing that one can do to prepare to teach junior high. She also fears that if the junior high bound teachers knew what it was going to be like, there would a shortage of junior high teachers. I enjoyed some aspects of this article. This teacher talks about things that definitely are issues within the classroom. However, since this article has been written, college students have had the opportunity to do more work in the classroom. The education classes now, especially at St. Olaf, do a better job discussing classroom management and behavior than in the past. There are some useful suggestions that she makes, but in the end she is right that there is nothing you can really do to prepare future teachers for jobs in the junior high.
Keywords: Number and Operation......
Ref: Liz10
Author(s): Bay-Williams, Jennifer M.; Martinie, Sherri L.
Date: 2003
Title: Thinking Rationally about Number and Operations in the Middle School
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 8 No. 6 pages 282-288
Reviewer: Liz
Date of Review: April 11, 2005
This article discusses rational numbers in the middle school classrooms. Classroom experiences with rational numbers should be "intriguing, with a level of challenge that invites speculation and hard work". Often when students are working with rational numbers they can compare fractions to decide which one is bigger, but they do not always have a sense of the value, such as fractions on number line. In an example using the game red light, green light and trying to decide which fractions were larger students used different approaches. Some students used benchmarks, such as zero, one half, and one. Other students used decimals and percents. It is important to be able to move to different forms but it is also important to know when to use certain forms. Students often pick up a calculator to compare, but we should try to help the students find the answer without the use of calculator. This gives student the opportunity to understand the meaning and effects of the rational number and be able to develop and analyze different ways to find the answer. For the benefit of the students it is also important to put problems in context because this is the key to understanding. Various contexts help students to develop algorithms to compare rational numbers using proportional reasoning. This article addressed some good points about using rational numbers in the middle school. Rational numbers are a big part of the curriculum in the middle school so it is important that teachers know the best ways to teach this concept to their students. This will be helpful in my future classroom because many students and even adults have a difficult time with rational numbers.
Keywords: Geometry......
Ref: Liz11
Author(s): Geddes, Dorothy
Date: 1992
Title: Geometry in the Middle Grades
Journal or Publisher: The National Council of Teachers, Inc.
Volume, Issue, Pages: pages 1-88
Reviewer: Liz
Date of Review: April 6, 2005
This book is a part of the Addenda Series put together by the National Council of Teachers of Mathematics and follows the Curriculum and Evaluation Standards for School Mathematics for grades 5-8. This book is broken down into four topics. First, Two and Three Dimensional Geometry Concepts, Relationships Among Properties of Shapes Including Angle Sums, Transformation Geometry and finally Enrichment Topics. Each topic has several different activities or lessons that are grouped together under a major theme and allow the students to discover material using different representations and activities. For each topic there is listed objectives and materials, full activity sheets, teaching notes, computer technology and evaluation notes. This book is not intended to be a textbook but rather to "provide teachers with ideas and materials to support to implementation of the Curriculum and Evaluation Standards". This should be not used at geometry curriculum but rather to give different approaches to some geometric topics as well as give some sample activities. I enjoyed the different topics because they included many different representations. The activities used a lot of pictures as well as asking many questions. Each activity had follow up questions at the end to use as an extension of thinking. The activities also asked the students to summarize the activity or put things into their own words. I like this reflection part because it forces students to think deeper about a subject when they must explain mathematics using words. I liked several of the activities in this book, but I enjoyed the activities in the other Navigations text better and I would use those before these.
Keywords: Geometry......
Ref: Liz12
Author(s): Pugalee, David K.; Frykholm, Jeffrey; Johnson, Art; Slovin, Hannah; Mallory, Carol; Preston, Ron
Date: 2002
Title: Navigating through Geometry in Grades 6-8
Journal or Publisher: The National Council of Teachers of Mathematics, Inc.
Volume, Issue, Pages: pages 1-127
Reviewer: Liz
Date of Review: April 4, 2005
This book is a part of the Navigations Series put together by the National Council of Teachers of Mathematics and follows the Principles and Standards for School Mathematics. On the inside cover of the book, the PSSM standards for grades 6-8 have been listed in a chart to use a reference for the teacher using this text. This book is broken down into four chapters. First, Characteristics and Properties of Shape, Coordinate Geometry and Other Representational Systems, Transformations and Symmetry and finally Visualization, Spatial Reasoning and Geometric Modeling. Each chapter had a section that discussed the important mathematical ideas found in the section as well as what the students might already know about these ideas. Each chapter was filled with various different lessons for the students to discover the material in the chapter using different representations and different kinds of activities. For each of these they listed the goal of the lesson, materials and equipment needed, an activity, ideas for discussion and then extensions on the lesson. The lessons followed a natural flow or progression into more complex ideas of geometry. One of the lessons of interest to me was called, Reasoning About the Pythagorean Theorem. This lesson had the students using area of squares to form triangles to discover about the Pythagorean Theorem. This activity was designed to help the students develop deep understanding of the relationships beyond just learning the formula. The lesson also provided students with "important experiences that extend their ability to analyze and use geometric knowledge to make conjectures" (28). I enjoyed reading the different lessons and seeing how the added to the big picture of understanding geometry. I enjoyed this book and I would consider using part of this in my future classroom.
Keywords: Geometry, Problem Solving...
Ref: Liz13
Author(s): Suh, Jennifer M.; Moyer, Patricia S.; Sterling, Donna R.
Date: 2003
Title: Junior Architects: Designing Your Dream Clubhouse Using Measurement and Geometry
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Volume 10, Issue 3, Page 170-180
Reviewer: Liz
Date of Review: April 11, 2005
This activity had students plan and construct a clubhouse using measurement and geometry. The activity encourages students to explore multiple approaches and problem solving. It was designed so that it was meaningful to the student and required them to develop their own solutions using mathematics as a tool. This activity is designed for grades 3-5 as a 2 week activity, but I believe that it could be used in the higher grades if more complex components were added.
The activity starts by reading stories to get students interested and begin looking at different geometric shapes. Then the teacher brought in an actual architect to show students how professionals work. Students worked together in team with a common clubhouse theme. The class discussed how to draw 3 dimensional objects on 2 dimensions as well as perimeter and area. After looking at examples of blueprints, the students created their own. When their plans were approved, they constructed 3 dimensional models using cardboard. The problems that arose during this process were actual problems the students had to work out on their own. They also had a component of decorating and they had to use a budget and compare costs. The final day of the project each group presented their clubhouse to the class as well as wrote a summary report about what they had learned.
I really enjoyed this activity and I would consider using something similar to this in my own classroom. The students have an opportunity to actually construct something and put their math skills to use. However, if I was teaching a unit on geometry I would want to have more geometry concepts and questions in the activity. I think that this can transferred to higher grade levels with more complex geometric questions.
**************
Keywords: Proof, Technology, Geometry
Ref: Liz14
Author(s): Scher, Daniel
Date: 2002
Title: Maximizing Triangle Area: An Interactive Inspired Proof
Journal or Publisher: ON-Math
Volume, Issue, Pages: Vol. 1 No. 1 pp. 1-5
Reviewer: Liz
Date of Review: April 20, 2005
This article discussed the role of technology in proofs as well as an active role in reasoning. A teacher told students that they needed to use calculus to find an exact solution for isosceles triangles and finding maximal area. However, a student found a simple way of moving a vertex around, while the base stays the same and looked at the altitudes of the vertex. Also, in a triangle where 3 segments meet in the middle the fact that they remain fixed in length when you move any vertex can be found by a technology representation. Then with three altitudes of a triangle, when one aligns the vertex with the altitude the others vertices will fall out of alignment. This occurs because each adjustment maximizes the altitude while keeping the base constant so dragging any vertex will shorten the altitude and decrease the area of the triangle. Technology can be a useful tool but you must be careful that the students can not find the numerical value before they find the geometric reasoning. In some programs, the numerical value can be found by the click of a button. It is still useful to find the numerical data as reassurance but be careful that the students see the reasoning behind it first. Technology should not be used as a substitute for a proof, but helps us to visualize proofs that would otherwise be difficult to understand,
I thought that this article would be helpful for teachers to find ways to help students visualize complex proofs such as why segments meet in the center of the triangle at the same point. I like the fact that they include a caution when using technology, that students see the reasoning before they go looking for an answer. This idea is also something to keep in mind for different lessons.
Keywords: Problem Solving, Games, Keyword 3, Optional...
Ref: Liz15
Author(s): Gardner, Martin
Date: 1956
Title: Mathematics, Magic and Mystery
Journal or Publisher: Dover Publications, Inc.
Volume, Issue, Pages: pp. 1-175
Reviewer: Liz
Date of Review: April 20, 2005
This book addresses problem solving in mathematics through magic. Martin Gardner says that mathematics magic "combines the beauty of mathematical structure with the entertainment value of a trick". The book offers many different magic tricks using cards, dice, dominoes, calendars, watches, dollar bills, matches, coins, checkerboards, handkerchiefs, rubber bands and magic with just pure numbers. These activities and tricks are fairly simple to perform, but have some complex mathematical ideas behind them. Most of the tricks provide some history behind the concept and the person that first showed this trick. Then they explain the trick and then how to perform the trick and the mathematics behind it. These activities could easily be used in a classroom to develop problem solving skills and discovering the mathematics behind how the tricks work. Especially the card trick or the dice problems can be repeated and picked apart to find how to mathematics works behind it.
I really enjoyed this book. I originally intended to read portions of the book for the review, but I was so interested that I read the whole book. I would definitely find ways to incorporate problem solving like this into my classroom. This gets the kids excited about mathematics in a new way and allows them perform exciting magic tricks while learning complex mathematics and problem solving skills.
Ref: Liz16
Author(s): Bridgman, George; Huang, Danrun
Date:
Title: Generating Prime Numbers Efficiently / How Honeybees Prove
Fibonacci Identities
Journal or Publisher: MAA Conference
Volume, Issue, Pages:
Reviewer: Liz
Date of Review: April 27, 2005
I attend two different sessions at the MAA Conference on April 23, 2005. The presenters were Dr. George Bridgman and Dr. Danrun Huang.
Dr. Bridgman spoke about "Generating Prime Numbers Efficiently". He presented two methods to generate these numbers and a third that generated less efficiently. After generating his numbers he looked for patterns called "Four Primes in a Decade". This means finding four prime numbers in a row within a decade of numbers. He had calculated the primes up to 2,100 and he was working on extending his research to 10,000 numbers.
Dr. Huang spoke about "How Honeybees Prove Fibonacci Identities". He used the idea of a honeybee honeycomb and how bees would walk to different combs to define Fibonacci identities. Some examples were the rule of walking and the rule of walking from 1 to n+2. He defined formulas that corresponded to the Fibonacci numbers.
I found both of these talks to be interesting. It was fun to get a short
"mini-lesson" discussing different ideas and research within mathematics. It
was also interesting because the two talks are similar to ideas that I am
currently learning about in my math classes. It was fun to expand on the
general concepts to something more complex. Even though I didn't understand
everything that was discussed, it was a good experience to hear the research of
different professors.
Keywords: Technology......
Ref: Liz17
Author(s): Hudnutt, Bethany Snyder; Panoff, Robert M.
Date: 2002
Title: ON Math
Journal or Publisher: NCTM
Volume, Issue, Pages: Vol. 1, No. 2, pp. 4-8
Reviewer: Liz
Date of Review: May 2, 2005
This article discusses using technology within the classroom. Many teachers don't use technology because they can teach the same topics without using a computer. The paper pencil techniques are what they are used to teaching and what will follow the curriculum. Often, large portions of time can be spent on just getting the program started or getting the students logged on the computer. Things can also go wrong easily. The benefits of using technology include doing time consuming things more rapidly. Computers should not replace arithmetic but it can simulate doing multiple representations without wasting class time to gather such data and probability. Students can also manipulate the parameters and functions to see the changes that occur quickly. There are some programs that have been developed to with the curriculum. Project Interactive is a program with both student and teacher resources that guides with the curriculum. Each activity has the what, how and why buttons to explain the activity. The activities are designed to cover multiple topics and can be used in many different ways to assist in following concepts in the curriculum.
I believe that using technology in the classroom is important. I also recognize many of the concerns that teachers may have with using technology especially large time commitments and possibly not having enough or proper equipment for the students. I understand that it can be difficult to find ways to incorporate technology into the lesson and the curriculum, but that it is also an essential element of the students learning.
Keywords: Equity/Diversity......
Ref: Liz18
Author(s): Berry, Robert Q. III
Date: 2004
Title: The Equity Principle through the Voices of African American Males
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 10 No. 2 pp. 100-103
Reviewer: Liz
Date of Review: May 9, 2005
The mother of an African American student stated that her child needed to feel that his teachers were interested and that they care about him in order for him to be productive in class. Both the student and the mother recognized that he could be rowdy in class, but that it was never extreme or out of control. This student was not recommend for an advanced math test and class even though he had good grades, his teacher thought that because he was not able to sit still in class that an advanced class would not be good for him. This teacher and a school counselor made assumptions that he would not pass and did not take into account his excellent past math performance. The school was focusing on the behavior rather than achievement. Studies have shown that African American males often have lowered expectations even though they do well academically. Three main element of the NCTM Equity Principle state: Equity requires high expectations and worthwhile opportunities for all, Equity requires accommodating difference to help everyone learn mathematics, and Equity requires resources and support for all classrooms and all students. It is the responsibility of teachers to communicate to their students with their interactions with the students. They need to help students believe that they can succeed. Teacher should also recognize that students that are having trouble need extra help and students with exceptionalities need opportunities to be challenged. In the case of many African American males, their teachers have lacked interest in their backgrounds and could not make accommodations for the diverse student population or did not have resources to provide support for all students.
I thought that this article brought up some important and valid points about equality in the classroom. It is important for all teachers to consciously incorporate ways of equality in the classroom. Often teachers make assumptions about students and label them before they have been given a chance to prove themselves.
Keywords: Algebra, Activities...
Ref: Liz19
Author(s): Rubin-Forester, Allison
Date: 2005
Title: Get 'em Moving!
Journal or Publisher: MCTM Conference 2005
Volume, Issue, Pages:
Reviewer: Liz
Date of Review: May 9, 2005
This MCTM session, “Get ‘em Moving!” was presented by Allison Rubin-Forester from the Minneapolis School District. Allison had numerous great ideas about getting student up and out of their chairs and moving around to stimulate brain activity. She told us all in the beginning that we did not need to furiously take notes because if we left our email address with her she would send us documents explaining all the activities. One activity was called, “Go East, Go West”. She would put a problem on the overhead, such at x^2=9 and tell students to get east if they thought the answer was 3, go west if the answer was 81 and go north if you thought it was something else. It was interesting to see that even a group of teachers was divided on the correct answer. She has also used this activity for order of operations and using different amounts as the different directions. One thing that she does before every class is go over the MCE or the most common errors. Often she can tell what her students will get wrong on the test so they talk about it in class as a review. She also does an activity that she calls “Knock, Knock”. She asks one of her students their hero. Then she has another student go out of the classroom and walk back in pretending to be that hero. They go around and shake hands with everyone, except the person who named them as their hero and then they leave. Then they talk about when you are distributing through parenthesis and that they have to “meet everyone”, otherwise you won’t be meeting your hero. She says that after she does this once, she can just knock twice on the board when someone makes that mistake and the student knows exactly what they need to fix. I thought this was really cool! She also has students use absolute value moods where students stand on large number lines made out of paper towels to represent the value. This is a good way for students to visualize exactly what is happening with absolute value. One more thing that she did was use a function box. This could be any area in the classroom, but make an input and output end and have students walk through the function box and change the number of people, and the class has to guess what the function is doing.
Overall, I really enjoyed this session. Allison had a lot of energy and great ideas to get students up and moving around. She have me some great ideas and I recently received an email from her with attachments of all the documents that explain her activities.
Keywords: Assessment, Manipulatives, Teaching Strategies
Ref: Liz20
Author(s): Gustafson, Jon
Date: 2005
Title: Giving Everyone a Chance to Answer
Journal or Publisher: MCTM Conference 2005
Volume, Issue, Pages:
Reviewer: Liz
Date of Review: May 9, 2005
The MCTM session “Giving Everyone a Chance to Answer” was presented by Jon Gustafson from the South Saint Paul Public Schools. This session discussed ways to get all students to be working on the answer and everyone a chance to get the answer. He had different worksheets with different markers or manipulatives so that each student could have their own. Then he would ask a question on the overhead and have the students mark on their worksheet the correct answer. While students were working on this, he walked around the classroom and he could easily do a quick check to make sure that everyone got the right answer. This way, the students that worked slower than other students still had a chance to answer the question. I also liked the idea of letting each students have a set of the materials so that they can figure out the answer right in front of them using visual and tangible representations. The worksheets included the topics: naming the whole numbers, naming decimals, tile metric conversion, divisibility number tiles, scientific notation, fraction cards and adding and subtracting integers. Most of the worksheets had a number line included on them. We were given a set of colored number tiles that we could place over the number line to represent our answer. For another activity, we were given a large graph with grids on it. Then we were given a list of coordinate points where we put markers. When we were done, the points spelled words, such as “yes” and “hi”.
Overall, I thought that Jon had some great ideas to use in the classroom. This is a good way to informally assess all the students in a quick amount of time as well as giving each student a chance to figure out the answer. The only question that I have after this session was what the teacher should do when a student does not understand what they are doing. Should the teacher stop and help that one student? Should the teacher stop and review for the whole class? Should the teacher talk to the student after class or during work time? I enjoyed this session and this will definitely be something that I will incorporate into my classroom.