Keywords: Technology, Activities...
Ref: Katherine21
Author(s): Hollebrands, Karen Flanagan; Gosse, Paul
Date: 2003
Title: Technology Tips
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 96, Number 4, 292-298
Reviewer: Katherine
Date of Review: May 7, 2003
In the April edition of the Mathematics Teacher there is an article titled Technology Tips discussing an alternative view of functions examining parallel axes using the TI-83 Plus or Excel. First the article explains tips as how to map diagrams on the calculator. In order to perform the mappings on the calculator some programming is required. There are many positives of these activities on the calculator. The main advantages for students are they can quickly and easily switch between the algebraic, tabular, Cartesian graph, and mapping-diagram representations on one unit with little or no additional technical experience (293). Each activity examines one to one functions, contractions, and understanding codes. Students learn how specifically about mapping diagrams, range values and domains. One interesting point they investigate in the article is also looking at functions with restricted domains. The activities follow up with useful questions to spark inquiry in the class. This activity would be a nice resource for students working on student projects dealing with mappings of functions.
I thought this article was a bit confusing and might take a very patient group of students to learn this technique on the calculator. I did think, though, that the activity was useful and was a nice tool in order to visualize mappings, yet I think it would take a lot of time planning a lesson like this so every student truly understands what is going on while they use their calculators. I would hate to stand up at the front of the classroom and teach the kids how to use their calculators only for them not to understand what they are looking at. Before the lesson, I would also want to make sure every students had the program needed for this activity preloaded in their calculator or I would want a classroom set of calculators that already have this program. This is vital in order to save time in the classroom.
Keywords: Probability, Problem Solving...
Ref: Katherine22
Author(s): Kahan, Jeremy A.; Wyberg, Terry R.
Date: 2003
Title: Problem Solving Can Generate New Approaches to Mathematics: The Case of Probability
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 96, Number 5, 328-332
Reviewer: Katherine
Date of Review: May 7, 2003
Jeremy A. Kahan and Terry R. Wyberg discuss different approaches to mathematics specifically relating to probability. They use a problem based on a dilemma in the World Series. The predicament is that the Yankees and the Mets are playing a best-four-of-seven series, with the winning team to collect a 1,000,000 bonus. When the Yankees lead two games to one, an umpires’ strike causes the cancellation of the remainder of the games. If the Yankees and Mets are evenly matched and if the money will be divided in proportion to the teams’ probabilities of winning the series, how should the money be divided? (328)
Kahan and Wyberg discuss three approaches to solving the problem. The first is a simulation in which they use technology such as a box model take form the NCTM website. They both liked simulations because they believed it helped students build evidence, intuition, and insight, which they can use as a basis for further thinking, theory building and evaluating theory (328). The second approach is to solve the problem with a tree diagram. The third approach is generating functions in order to solve the problem. After Kahan and Wyberg present the approaches, they discuss how to solve the problems. They also discuss trouble spots students may encounter using a certain problem solving approach and they suggest an alternative approach to the problem.
After reflection Kahan and Wyberg believe that it is important to learn and understand each approach to solving the problem. They believe in Diene’s view that mathematics is the underlying structure that connects seemingly disparate representations. (331) In order for students to succeed in mathematics they should understand different mathematical models and that would help them find connections in mathematics. They follow up with other problems that are related to the World Series problem.
This is one of my favorite articles I have read all semester. I thought it was an interesting problem that would attract many students. I als
o appreciated that the authors presented three different approaches to the problem and not just one. Since not every student learns the same way it is important to have many approaches for solving a problem in order for each student to pick an approach that works best with their learning style.
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Keywords: Algebra, Activities...
Ref: Katherine23
Author(s): Hill, Careylyn
Date: 2002
Title: Print-Shop Cutting: Ratios in Algebra
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 95, Number 1, 260-263
Reviewer: Katherine
Date of Review: April 28, 2003
Careylyn Hill suggests an activity that helps students transfer skills that are learned in a textbook to real life dilemmas. Students need to pretend that they work in a print shop. There are three sheets that are handed out to each group of students. On Sheet 1 there are factual questions about the reading material that was assigned. On Sheet 2 there are three jobs students must complete which build off of sheet one. Through the activity students learn to deal with ratios and remainders in a non-traditional way (261). Furthermore, the activity encourages inquiry since students work with one another to solve the problems.
I liked this activity especially since I am currently planning a unit in Algebra dealing with ratios. I think Hill lies out the article very directly. I wish that she would've have discusses if her students enjoyed the activity and what each student learned. Overall I thought that the activity is one that I would like to use in my classroom. It doesn't require a lot of time or supplies. I also think it would be a good activity for a day that a substitute teacher comes to class.
Keywords: Activities......
Ref: Katherine20
Author(s): Weinberb, Suzanne Levin; Hammrich, Penny L.; Bruce, Matthew H.
Date: 2003
Title: The Giants Project
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Volume 8, Number 8, 406-413
Reviewer: Katherine
Date of Review: April 20, 2003
The Giants Problem focuses on proportional reasoning. It is an effort to help teachers more effectively teach proportion and its underlying concepts. There are four activities involved in the project. In the first activity students must record lengths between various points on the human body. They write ratios and describe the relationship between the largest and smallest lengths. In the second activity, students discover the connection between ratio and scale. They then explore ratios and corresponding lengths of a student and they figure out if they are equivalent. The third activity is where students examine equivalent measurements for individual students instead of exploring ratios between students or between a student and a figure. The last activity asks students to apply their knowledge they have learned for a giant person. The article comes with four very detailed worksheets for students to use in each different activity. The activities reinforce connections between ratio and scale.
This is an activity I would definitely use in my classroom. It is very interactive and reinforces many vital concepts when using proportional reasoning. I think the lesson encourages inquiry among students since it is interactive. It also helps the students develop a true understanding of relationships between variables. The worksheets are very sequential and help further students understanding of proportionality.
Throughout the article different teachers highlighted different concerns they encountered while using this activity. As a teacher I would look closely at these concerns and evaluate how I would address this in my classroom. Overall, teachers really enjoyed using this project. I thought this project was exciting and unique and most importantly helps students develop true understanding of proportional reasoning.
Keywords: Communications, Assessment, Teaching Strategies
Ref: Katherine17
Author(s): Bakal, Jacqueline
Date: 2003
Title: Sharing Teaching Ideas: The Oral Quiz
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 96, Number 4, 277
Reviewer: Katherine
Date of Review: April 16, 2003
This is a short but very effective idea for teachers in all subjects but this one speaks to math teachers. Jacqueline Bakal shares with readers her thoughts on the subject of oral quizzes. She shares a story about how she was teaching high school math at an all-girls Catholic high school. Bakal he always liked to give some form of assessment on Fridays because the students were always very "antsy" and talkative and she thought assessment was a good way to wrap up the work of the week (277). She had a lot of success with this kind of oral assessment and she differentiated the questions so that everyone in the class had a chance to succeed. She also thought that it was a nice way to review for a written test.
I enjoyed the reading because I was a product of the oral assessment in my tenth grade biology class. I thought it was a successful kind of assessment. I realize that in a large class it an often be hard to orally test everyone but I think a teacher can do it in a large class using Bakal as a resource. I also think that if a student can explain things orally it is a sign that they have truly mastered the concepts taught in class.
Keywords: Activities, Probability, Technology
Ref: Katherine18
Author(s): Hathaway, Dale K.
Date: 2003
Title: Birthday Lies
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 96, Number 4, 244-247
Reviewer: Katherine
Date of Review: April 23, 2003
Everyone who has taken a course in probability has heard of the birthday problem. Dale K. Hathaway notes that many teachers use it as a friendly wager with their students. He claims students love to try to one-up their teacher and this is a powerful motivator. Hathaway makes an interesting claim asking readers to question if their students have lied in order to win? If the students lie about their birthday will it give them stronger chances of winning? Hathaway uses these questions for a powerful lesson in probability. These questions could be posed to the classroom after the original birthday problem is posed. Hathaway first suggests a general approach to answering these questions. He carefully outlines his steps to attack the problem. He then introduces a slightly different approach through recursion. This technique is useful if teachers would like to use technology in their classroom by using a spreadsheet. In conclusion readers found that when students lie to avoid a match, any match of announced dates must mean an actual match of birthdays in the class, although the actual date that matches might be different from the announced date (247). Hathaway states that a teacher probably does not have to worry about students lying. Furthermore, this proves to be an intriguing investigation for students to discover.
I thought this was a great article. I find the birthday problem to be quite enjoyable. I think that this question also could be a great resource as an enrichment activity for those students are constantly questing to go above and beyond in the mathematics classroom. Hathaway describes the problem in the article in great detail. Furthermore, I really like that he has the option for technology in the classroom. I think activities can be a lot more interactive and exciting for students if they are used on the computer.
Keywords: Geometry, Activities, Measurement
Ref: Katherine19
Author(s): Touval, Ayana; Westreich, Galeet.
Date: 2003
Title: Teaching Sums of Angle Measures: A Kinesthetic Approach
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 96, Number 4, 230-233
Reviewer: Katherine
Date of Review: April 23, 2003
Ayana Touval and Galeet Westreich address a very unique and useful approach to demonstrating to a classroom the concept of angle measurement. Their activities stem from the kinematics teaching strategy (KTS) which is a new approach for stimulating kinesthetic intelligence (230). They claim that KTS is a unique way to help students understand math through body movement. They start with a warm-up explaining how to introduce students to angle measurement with their bodies. They then move on to four activities. The first activity is to find the sum of the measures of the exterior angles. The next activity is finding the sum of the measures of the interior angles. The third activity is finding the sum of the angles of a pentagon. The final activity is the sum of the measures of the interior vertex angles of a five-pointed star. Each ativity really engages each students and teaches them to work cooperatively with one another. Furthermore, the activites stimulate inquiry. Touval and Westreich claim that it motivated their class to find the proofs of their results.
I really enjoyed reading this article. I thought it had some great ideas and this lesson would work well in a geometry classroom. I thought though that before I initiate this lesson in a classroom I need to practice this with co-workers. The instructions of the activity were detailed and had diagrams, but this is a lesson I would not want to walk into a classroom and never have practiced it on someone before. I think there is a potential for it to go awry if the teacher is not well prepared.
Keywords: Discrete, Activities,
Ref: Katherine16
Author(s): Cuoco, Al; Goldenberg, E. Paul.
Date: 2003
Title: Delving Deeper: Match Making: Fitting Polynomials to Tables
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 96, Number 3, 178-181.
Reviewer: Katherine
Date of Review: April 13, 2003
Al Cuoco and E. Paul Goldenberg, coeditors of the brand new department in the Mathematics Teacher called Delving Deeper, provide readers with article about how teachers might help students find patterns in tables. It is a very direct article discussing ways to assist students to see the pattern in the table through the use of fitting polynomials into the table. (In their case it was a triangle.) The article gives many examples and is very straightforward. It also gives helpful hints on how to incorporate Pascal's triangle into the classroom. It helps show how you can relate Pascal's Triangle to combinations and tables. Furthermore, it also uses Newton's Difference Formula to aid students to see patterns in tables. It concludes nicely with a couple ideas on how to further this topic.
I thought this article was helpful for a day when a teacher might need a day off from complicated discovery lessons. Although, this was an investigation, it came across as a very direct lesson. There was no life application or problematic except dealing with the numbers and the data set in itself. I did like the idea of fitting a polynomial into a table in order for students to really understand patterns. I thought it was a very useful tactic. I think it is always important that students to truly understand what they are looking for and this polynomial method will help.
Keywords: Algebra, Activities, Teaching Strategies
Ref: Katherine14
Author(s): Lannin, John K.
Date: 2003
Title: Developing Algebraic Reasoning Through Generalizations
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Volume 8, Number 7, 342-348
Reviewer: Katherine
Date of Review: April 7, 2003
John K. Lannin very thoughtfully explains how students can develop their algebraic reasoning through generalization. He stresses how important it is for students to develop general rules and understanding for mathematical situations and that they should move away from memorizing algorithms for specific numeric situations (342). Furthermore, in order to help teachers help their students use generalizations he provides an example called the Cube Sticker problem. He outlines the problem and follows with different strategies students might use as they attack the problem. Such strategies are, counting, recursion, whole-object, contextual, guess and check, and rate-adjust. He links the strategies with algebra. Furthermore, he acknowledges certain mistakes that teachers or students may encounter as they face the problem. He follows that up with ways to correct these problems. He concludes the article nicely by continually looking at the positive aspects of generalizations. He states, "Generalizations encourage students to view variables as dynamic quantities that can be used to make sense of their environment." (348)
The reason I appreciated this article is because it seemed very well thought out. I also felt that the article does not just apply to middle school teachers. I think a really important aspect of this article was generalizations and not just in algebra. He just gave a specific example for algebra, but I think teachers of Geometry or even Calculus could walk away with a lot of good information in this article. I felt as if Lannin really knew what he was talking about. I liked that he recognizes all situations that could be experienced when facing the problem of the cube. What I liked most about the article was that it acknowledged the importance of understanding algebra not just memorizing how to attack a numerical situation.
Keywords: Measurement, Activities, Teaching Strategies
Ref: Katherine15
Author(s): Steeple, Diana F.
Date: 2002
Title: Assessment in Action: Mrs. Grant's Measurement Unit
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 7, No. 5, 266-272.
Reviewer: Katherine
Date of Review: April 9, 2003
Diana F. Steeple reports a very detailed approach on how a teacher, Mrs. Grant, planned a lesson on measurement. Mrs. Grant seems like a prize teacher. Steeple notes that she is constantly assessing her students in various ways, taking in account that everyone is a different kind of learner (266). The unit is based on understanding the concepts of measure, proportional reasoning, number sense and computation. Steeple then outlines four detailed linear measurement lesson plans for four days. Each lesson is based on constructivist theories. Each day has a discovery lesson planned. Steeple then discusses the importance and implications of different kinds of assessment throughout the unit. She feels that assessment and instruction go hand in hand. Most of her assessment is informal through listening to students' responses as they partake in the discovery activities.
I thought this was a very appropriate and an entertaining unit plan for middles school kids. I believe that it will keep the students engaged throughout the unit. What I most appreciated about the article was Mrs. Grant's theories. She reinforced my ideas that the most important part of a student's learning is to truly understand a concept. This is shown through Mrs. Grant's cooperative learning tasks that take place every day. I hope that I can reflect Mrs. Grant's teaching in high school through planning cooperative learning activities for the units I teach. Furthermore, Steeple had great comments regarding Mrs. Grant's theory on assessment. Mrs. Grant really stresses the importance of instruction and assessment. She felt as if they are simultaneous acts (272). I really believe this is important too. I think that teachers need to constantly be considering what kinds of assessments they need for various kinds of learners.
Keywords: Geometry, Activities,
Ref: Katherine13
Author(s): Moore, Sara Delano; Bintz, William P.
Date: 2003
Title: Teaching Geometry and Measurement through Literature
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Volume 8, Number 2, 78-83
Reviewer: Katherine
Date of Review: March 31, 2003
Sara Delano Moore and William P. Bintz wrote a captivating article about integrating literature with geometry. The article provided the reader with numerous resources and examples on how to connect literature with geometry. It noted the importance of literature and its potential to support mathematical thinking. They remind readers the importance of constructing a mathematical meaning from a book by considering the reader's background knowledge, the purpose for reading, and the social context in which the reading occurs (79). Moore and Bintz also provided two well thought out concept maps providing numerous examples of literature and their uses in the mathematics classroom. Furthermore, they not only provided readers with examples but also discussed several pieces of literature and why they were important in the mathematical classroom. They find books that are great for all math learners, not just one kind of learner.
This was my favorite article I've read so far. I think it is vital make note that mathematics is important not only for academics but for other aspects of life. I think it is even better to integrate other parts of students' academic and social lives into the mathematics curriculum. What better way to do this then by discussing literature through a mathematical perspective? I think it is important to constantly be looking for ways to look at all aspects of students' academic and social lives through a mathematical perspective so that every student no matter what ability will feel as if they are connected to and able to do math.
Keywords: Teaching Strategies, Curriculum
Ref: Katherine11
Author(s): Gerver, Robert K.; Sgroi, Richard J.
Date: 2003
Title: Creating and Using Guided-Discovery Lessons
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 96, Number 1, 6-10
Reviewer: Katherine
Date of Review: March 17, 2003
This article is a great resource for any teacher interested in discovery lessons. Gerver and Sgroi uniquely define a discovery lesson. They believe, guided-discovery lessons offer students an opportunity to become archaeologists on a mathematical dig," (6). Furthermore, they stress that it is not necessarily important for teachers to write their own discovery lesson. They suggest a couple of good resources to find discovery lessons. If a teacher wants to write their own guided-discovery lesson, they give eight specific tips. Finally, they remind teachers that reflection after each lesson is important to gauge the effectiveness of the lesson. Futhermore, they state that guided discovery is just one of the many successful teaching methods.
This article will be extremely useful for a teacher who expresses interest in writing their own discovery lesson, but does not know where to begin. I am an advocate for discovery lessons; hence, I’m positive I will return to this article when I am in need of guidance. Finally, I thought Gerver and Sgroi’s article was very clear and easy to understand.
Keywords: Curriculum
Ref: Katherine12
Author(s): Laser, James K.
Date: 2003
Title: CPMP Evaluation
Journal or Publisher: Core Plus Mathematics Project
Volume, Issue, Pages: http://www.wmich.edu/cpmp/evaluation.html
Reviewer: Katherine
Date of Review: March 19, 2003
I looked at the Core-Plus Mathematics website. The website is easy to access with very well organized prompts. I specifically looked at the evaluation of the Core-Plus Mathematics. I found that the curriculum is constantly being reevaluated. It states that because of Core-Plus Mathematics students succeed at higher levels then students without an integrated math curriculum. They succeed in the areas of quantitative thinking, student perceptions and attitudes, performance on college placement tests, and in college classes. Further down the page it has students and teachers comments. Every comment has nothing but positive remarks. It seems as if the curriculum is very rewarding for students and teachers. The top remark from students was that the curriculum is a lot more exciting than that of basic math curriculum. Overall, the website is very informational and easy to use.
I tutor at a school that uses Core-Plus Mathematics so I was extremely interested in this website. I liked the website because it really gave me a firm grasp as to what Core-Plus Mathematics curriculum is all about and where it came from. I did think it was extremely biased though. The statistics they used on students succeeding at higher rates than students with basic math curriculum was not totally legitimate because it was too small of sample size. In my opinion in order to get the most unbiased results you need to test nationwide. I do like the idea of Core-Plus Mathematics, although I admit that it is a challenging curriculum. It is nothing like the kind of curriculum I had in high school. I think though that it is important to show students that math is everywhere in life, not just in a formula.
Keywords: Teaching Strategies, Algebra, Activities
Ref: Katherine10
Author(s): Burke, Maurice; Erickson, David; Lott, Johnny W.; Obert, Mindy
Date: 2001
Title: Navigating through Algebra in Grades 9-12
Journal or Publisher: National Council of Teachers of Mathematics
Volume, Issue, Pages:
Reviewer: Katherine
Date of Review: 3-13-03
Navigating through Algebra in Grades 9-12 uses real world applications so students understand the algebraic elements such as a variable, operation, function, and relation. Each chapter is filled with real life applications that are extremely helpful because often students tend to wonder when does anyone use algebra outsides of the classroom. The activities are a good measure of students' understanding of the concepts. Also the book does an incredible job of incorporating technology throughout the chapters. It is important to realize that the use of technology in the activities really helps the student understand the concept rather then hindering their understanding; as some people argue that technology does. Furthermore, the book is well outlined. It has clear headings and objectives listed.
I really liked the books activities because almost all of them required technology. I think the activities seem enjoyable and almost exciting. I believe by using real-world activities, students will be much more engaged in their learning.
Keywords: Standards, Geometry,
Ref: Katherine9
Author(s): Coxford, Arthur F. Jr.
Date: 1991
Title: Geometry from Multiple Perspectives
Journal or Publisher: THe National Council of Teachers of Mathematics, Inc.
Volume, Issue, Pages: Addenda Series Grades 9-12
Reviewer: Katherine
Date of Review: March 10, 2003
Arthur F. Coxford, Jr. provides a useful resource for all teachers teaching Geometry. Coxford thoroughly investigates why geometry is important to look at from multiple perspectives. He touches on triangles, quadrilaterals, polygons, and solids. He then explores transformations, congruency, similarity and proofs. His chapters are very clear and in depth. The chapters point out the positives of looking at geometry from multiple perspectives. The book is filled with activity worksheets for each chapter. Although, with a little extra thought, teachers can easily transform these worksheets into a group discovery activity. The chapters are also filled with helpful hints labelled "Try This" or "Teaching Matters". "Try this" are usually some kind of discovery exercise that students can try. "Teaching Matters" address challenges that might come up during the lesson. These hints would be very helpful in planning a lesson. Furthermore, Coxford also fills the chapters with useful ways to approach assessment. This book really does a good job of looking at different ways to approach teaching geometry from multiple perspectives.
I would definitely use a book like this one. I am a big fan of activities as a way of discovery. This book if filled with different kinds of activities that address various kinds of geometry. I also think this book addresses multiple learning styles through the diverse kinds of activities suggested.
Keywords: Algebra, Technology, Activities
Ref: Katherine8
Author(s): Hall, Matthew
Date: 2003
Title: Calculator Cryptography
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 96, Number 3, 210-212
Reviewer: Katherine
Date of Review: March 5, 2003
Matthew Hall shares his unique idea of using connecting technology to real life applications. He found that an effective demonstration of this is teaching students the importance of algebra and the use of technology through the use of cryptography. Students first need prior knowledge of determinants. Each student then writes a message using a defined number scheme. Next students use their key matrix and use a calculator to multiply it with their message. Finally the students apply modulo 33 to their product. Their message is now in crypt language. To decrypt the message, students must invert their key matrix and multiply it with their message in the crypt language. Finally they again apply modulo 33 to return to their original matrix that can be decrypted using the original number scheme which is given.
I thought this was a nice activity to break the redundancy of what an algebra classroom has the potential to turning into. However, I did not understand the real life application to this activity. I do not know if I find it conceivable that the CIA to decrypt messages. uses this simple method. I thought it was more of a unique activity where students can discover the use of inversion of matrices.
Keywords: Geometry, Activities,
Ref: Katherine7
Author(s): Sharp, Janet M.; Heimer, Corrine
Date: 2002
Title: What Happens to Geometry on a Sphere?
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Volume 8, Number 4, 182-188
Reviewer: Katherine
Date of Review: March 3, 2003
Janet M. Sharp and Corrine Heimer explored the significance of connecting plane geometry with spherical geometry. The article successfully lays out an activity step by step allowing students to explore what happens to lines, segments, angles, and polygons on a sphere. The students have a sphere and a washable marker and they draw everything from rays, to perpendicular lines, to triangles on the sphere. They identify the relationship between lines and circles. Through the activity they discovered and understood what a great circle is. Furthermore, they experimented with drawing squares on a sphere and deducted that it is not possible. Also, the concepts in plane geometry are continually reinforced throughout the activity. Finally the students described in this article seemed very engaged in the activity.
I was quite intrigued with this article due to the high content of constructivism throughout the activity. I believed constructivism in math is a unique and exciting approach to teaching math. The students throughout this activity used their knowledge of planar geometry to make assumptions about spherical geometry. They went on to test their assumptions and they made conclusions. They learned a great deal of the relationship between spherical geometry and planar geometry. I believe this was a successful activity and students really understood the mathematical concepts instead of just memorizing terms. They were able to visualize everything. The activity seemed to be appropriate not only for middle school students but I believe teachers could use it in high school also.
Keywords: Activities, Probability, Puzzles
Ref: Katherine6
Author(s): Quinn, Anne Larson; Koca Jr., Robert M.; Weening, Frederick
Date: 1999
Title: Developing Mathematical Reasoning Using Attribute Games
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 92, Number 9, 768-775
Reviewer: Katherine
Date of Review: February 27, 2003
The article is a great example of constructivism in the mathematics classroom. Through the game of Set, students construct their mathematic reasoning. Through the game, they build on a variety of traditional mathematical topics, including the multiplication principle, combinations and permutations, divisibility, modular arithmetic, and mathematical proofs. (768) The article discusses different questions the teacher can use in class and the variety of different kind of student work that the activity entails. The game also encourages discourse among students. Finally, the authors poignantly discuss the benefits of the game. They state, “The game furnished an excellent context in which to promote problem solving and deductive reasoning in discrete mathematics, ideas that need to be emphasized in high school curriculum.” (775)
I really liked this article because the activity seemed to build on not only mathematical skills but also social skills. It posed numerous questions that requires and encourages discourse among students and teachers. I thought this game would be appropriate for an upper level enriched math class.
Keywords: Issues, Teaching Strategies
Ref: Katherine5
Author(s): Risher, Kathryn
Date: 2003
Title: Why Do So Many Students Perform So Poorly in Higher-Level
Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 96, Number 2, 102- 104
Reviewer: Katherine
Date of Review: February 24, 2003
This article is very intriguing because it is a reflection written by a teacher of higher-level mathematics. Kathryn Risher begins by expressing her frustrations about students performing poorly in higher-level mathematics. She then goes on to pinpoint many reasons why students might not perform to his or her potential. She says their bad grades and illogical thought process is a testament to the students' ever-changing emotions. She states, "Logical, orderly thought, and actions are contrary to their (the students) emotional way of thinking and acting." (102) Risher continues to talk about the importance of higher-level math courses. However, she thinks that educators are doing a disservice to the average student for allowing them to stay in a higher-level math class and not succeed. Risher believes average students should be in classes that are designed more for their type of learning style. She states, "We are performing a disservice to average students when we encourage them to take high level courses while simultaneously assuring their success." (102) Risher wraps up the article by expressing her passion for math and her strategies for teaching higher courses. She states, "...mathematics problems can be broken down into smaller, more manageable portions. One small bite at a time." (104)
I believe this article is important for teachers and futures teachers to read so
they can accurately reflect on what kind of teacher they want to be for the "average" students in
higher-level math classes. Is it really necessary to remove students from the classroom; if
they're just average? Maybe students would not perform as poorly if the teacher tried hard to
teach math for all; she would include activities for all types of learners.
Keywords: Activities
Ref: Katherine4
Author(s): Socha, Susan
Date: 2001
Title: Sharing Teaching Ideas: Less is Sometimes More
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 94, Number 6, 450-452
Reviewer: Katherine
Date of Review: February 18, 2003
Susan Socha's teaching idea reflects a perfect representation of constructivism in a classroom. Susan went to a teaching conference for mathematics and learned many ideas. Among those ideas, was the theory that sometimes "less is sometimes more." When she returned to her high school she decided to take this idea and run with it. Her class was studying exponential-decay functions and she read about an experiment using a water-filled bucket with a spigot at the bottom, releasing the water, measuring the depth of the water in the bucket, and graphing the depth against elapsed time. Altering the experiment a bit, with an idea of using pencils and a plastic bag of water, Socha came to class and explained the experiment to her class. She discussed possible problems of the experiment with her students and then she set them to work. She gave them no worksheets or written directions. The students were only given supplies and they had to direct where the experiment was headed. They were to formulate what kind of data they were looking for. After the experiments were finished students came together with their data and constructed scatterplots. They discussed further what they could do with this experiment mathematically. The experiment is an excellent representation of how less can sometimes be more and that constructivism along with being exciting, is also helpful to learners in the classroom.
I thought this experiment was very exciting and has the potential to really engage students.
Although I really believe that a teacher has to determine what kind of students he or she has and
how much direction is really needed. Socha noted that her class was a gifted and talented class.
I believe that the teacher needs to assess each type of learner in her class and then gauge what
kind of path is needed for his or her students.
Keywords: Standards
Ref: Katherine3
Author(s): Ward, Cherry D.
Date: 2001
Title: Under Construction: On Becoming a Constructivist in View of the
Standards
Journal or Publisher: Mathematics Teaching
Volume, Issue, Pages: Volume 94, Number 2, 94-97
Reviewer: Katherine
Date of Review: Feb. 17, 2003
The article investigates the importance the constructivist theory and how it fits in view of the National Standards. Immediately it touches on what the Standards are and why they are important. Readers learn briefly the history of the research done by the NCTM and the National Standards themselves. Furthermore, Ward discusses the importance for teachers to understand the Standards so they might implement them correctly in their classroom. Next, Ward explains what constructivism is and why it is important. She goes on to explain that constructivism promotes critical thinking. She highlights that communication and reiteration is key when teaching constructively. The teacher needs to always ask questions. The teacher needs to know how his or her students learn in order to properly teach. Ward then explains and gives an example of how constructed knowledge is retained successfully as opposed to direct instruction. Finally, Ward gives examples of activities to use in the classroom. Concluding, Ward summarizes the article and sends her readers away with the message that teachers must be an agent for change in the schools. In order to do this, she encourages teachers to take leadership positions in the community and in the schools.
I liked this article because it gave a great insight on using the constructivist theory in the classroom. Ward gave many good examples on why constructivism is so vital to the classroom. I was disappointed though with her discussion on the National Standards regarding constructivism. I felt like the article touched on the National Standards in the beginning, but I did not see exactly how the constructivist view intertwines with the constantly changing National Standards. My faith in the article was restored at the end when she encouraged teachers to advocate for change in the schools.
Keywords: Activities, Trigonometry,
Ref: Katherine1
Author(s): Peterson, Blake E.; Averbeck, Patrick; Baker, Lynanna
Date: 1998
Title: Sine Curves and Spaghetti
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Volume 91, Number 7
Reviewer: Katherine
Date of Review: February 10, 2003
Peterson, Averbeck, Baker created a unique activity to teach one of the most central ideas, which is the Sine Curve, in trigonometry through the use of spaghetti. This hands-on activity introduces the students to the standard trigonometric ratios of the sides of a right triangle. The activity is particularly helpful because it helps students understand the concepts through the use of concrete examples. The activity is simple yet very useful for making connections between triangle ratios and graphs of circular functions. Teachers can also build on this experiment by adding the concept of cosine. They attached an effective worksheet that goes hand in hand with the activity. It successfully helps students draw conclusions from their activity.
I thought this article was particularly interesting because it was an activity for all. This simple
activity can be furthered and expanded to reach the level of seniors in high school or it can be as
simple as an introduction to trigonometry course. I thought the authors statement, "If we are to
make mathematics accessible to all students, we need to develop activities that are appropriate
for all students." This is why I believed this activity could be very useful because it is
appropriate for all students. Furthermore, I believe it is essential to always make connections
with mathematical ideas through the use of activities.
Keywords: Communication, Planning, Issues
Ref: Katherine2
Author(s): Allsopp, David; Lovin, Louann; Green, Gerald; Savage-Davis,
Emma
Date: 2003
Title: Why Students with Special Needs Have Difficulty Learning
Mathematics and What Teachers Can Do to Help
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Volume 8, Number 6, 309-314
Reviewer: Katherine
Date of Review: February 15, 2003
The article immediately deals with how the NCTM advocates a "balanced approach of teaching both procedural and conceptual knowledge (NCTM 2000)" yet this is easier said than done for most teachers. The article than addresses different special needs that hinders students' potential for learning mathematics. They describe attention, cognitive-processing, memory and metacognitive disorders. Furthermore the article gives strategies on how teachers can adjust teaching styles so they have a balanced lesson both procedurally and conceptually. The article stresses that teachers must help students develop a deeper understanding for concepts. They do this through the example of a teacher named Ms. Dimarco. Furthermore, through the use of Ms. Dimarco, the article describes how to realize improvements in students. Finally the article draws conclusions. The authors state, "According to the spirit of the NCTM's Standards we need to begin instruction on our students' current levels of understanding before they will understand the mathematics we want them to learn." (313) Basically, it is important to address all learning styles in a classroom so every student recognizes their full potential in Mathematics class.
I thought this article was very thorough and there was a good example of Ms. Dimarco's
classroom and her student who has a metacognitive deficit. They give an example on how this
student can use different strategies for solving algebraic story problems. The example would be
useful in the classroom. Furthermore, I liked how they addressed different kinds of learning
disabilities and then strategies to help these children who have a LD. Although, I do not think
just reading this article will suffice when it comes to help promoting a classroom that is based on
balance both procedurally and conceptually. I think it is necessary to keep reading about
learning disabilities in order to address every students' learning style equally.