Keywords: Technology, Teaching Strategies, Curriculum
Ref: Kerry1
Author(s): Huinker, DeAnn
Date: 2002
Title: Calculators as Learning Tools for Young Children?s
Explorations of Number
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: vol. 8, no. 6, 316-321
Reviewer: Kerry
Date of Review: 02.12.02
This is an article about the benefits of using calculators at a young age to stimulate understanding of number sense. This article consisted of information from two classes, one a kindergarten class and another a first grade class. By allowing children to ?explore? with the calculators, they were receiving a more concrete grasp on numerals, counting, number magnitude, and number relationships. These children were also exposed to negative numbers and multiples, which would not have been in their traditional curriculum. Another benefit to using calculators is that it motivates the students and captures their interest.
I have always been a little hesitant to allow children to use calculators. I was allowed to use calculators in each of my math classes, which I think caused me to become calculator dependent. I think it is important for these children to solve problems without calculators; however, the teachers in this article were using calculators as a learning tool to develop a foundation of number sense. Hence, I think that they were using calculators in a good way, but I would still be cautious to use this in my own classroom.
Keywords: Communication, Standards
Ref: Kerry2
Author(s): Pugalee, David K.
Date: 2001
Title: Using Communication to Develop Students' Mathematical
Literacy
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: 6, 5. 296-299
Reviewer: Kerry
Date of Review: 02.14.02
This article discusses the importance of communication in the classroom. According to the author, communication helps the students increase their self-confidence by developing their ability to express their reasonings through both oral and written interpretation. Communication skills are emphasized in the 2000 NCTM Standards documents and has several goals that the teacher should aim for such as using mathematical language, organizing their communication, and analyzing and evaluating the work of their peers. The NCTM stresses that a "balanced mathematics program requires communication."
I strongly agree with this article. I think it is very important to
emphasize proper listening and speaking skills, especially in a subject
such as math where it is often overlooked. I think that keeping math journals
are excellent ways of working towards this goal, as well as having students
explain their work to their peers.
Keywords: Teaching Strategies, Research
Ref: Kerry3
Author(s): Martinez, Joseph G. R.
Date: 2001
Title: Exploring, Inventing, and Discovering Matematics:
A Pedagogical Response to the TIMSS
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: v.7 no.2, 114-119
Reviewer: Kerry
Date of Review: 02.19.02
This article focused on the differences in instruction between different countries, mainly the United States and Japan. On the TIMSS test, scores of Japanese students exceeded those of the US by a great amount. There seemed to be a significant difference in the way time was used in the classroom in both settings. For example, in the US class is usually started with a warm-up followed by the main activity and seatwork, with the homework being done in class. In Japan, the main activity comes first followed by seatwork, then classwork where the students collaborate with their peers, then they have more seatwork and another time for classwork. The lessons for the Japanese students were also designed around exploring, inventing, and discovering concepts, rather than listen to a lecture for the majority of the class.
Although the classes for the Japanese lessons, on average, had a shorter
amount of time, it seemed to me as if the time was used more effectively.
I think that more classrooms should focus on discovery. By discovering
concepts on their own, I feel that they will be able to thoroughly understand
the reasoning behind them and be able to apply them to various situations.
Keywords: History, Connections
Ref: Kerry4
Author(s): Chauvot, Jennifer B.; Wilson, Patricia S.
Date: 2000
Title: Who? How? What? A Strategy for Using History to Teach
Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: vol. 93, no. 8, 642-645
Reviewer: Kerry
Date of Review: 02.21.02
This article posed the question of how to teach history in the math classroom and what the importance of doing so is. The authors pointed out that integrating mathematical history "sharpens problem-solving skills, lays a foundation for better understanding, helps students make mathematical connections, and highlights the interaction between mathematics and society" (642). The students should know where a concept came from, why, and how it connects to other things in the world such as world history, science, economics, art, communications, etc. It is very much an interdisciplinary field and by teaching students the history of mathematics, the teacher is helping them to see these connections and understand why mathematics is such an important subject.
I strongly agree with this article. I definitely think that history
should be an integral part of the units - especially in giving background
information. I would have liked them to talk more about the benefits of
multicultural history lessons. I think history is an excellent why to show
multiculturalism and promote understanding about different cultures.
Keywords: Teaching Strategies, Issues
Ref: Kerry5
Author(s): Feigenbaum, Ruth
Date: 2000
Title: Algebra for Students with Learning Disabilities
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: vol. 93, no. 4, 270-274
Reviewer: Kerry
Date of Review: 02.26.02
This article focused on students with learning disabilities, and modifications that can be made in the classroom to help them learn math. The author had focused on a successful community college algebra class for students with learning disabilities, but stated that "a similar environment, with teaching and learning strategies that are based on students needs, can lead to a successful experience in any mathematics class, at all levels, for motivated students with learning disabilities" (274). The problem seemed to stem from these students being discouraged to take math in high school, and then when they go to college and want to pursue an associate's degree, etc. they must complete an algebra class at the minimum. According to this article, "the problems encountered by a student with learning disabilities studying algebra are the same as the problems encountered by the average student; however, they are more pronounced" (271). This means that special attention must be given to these students. The teacher of this classroom had several strategies. One was to limit the class size to 20 so that she would have 1-1 time with all students. She also limits the classtime to an hour and she is constantly varying the activities. She also schedules an additional class period each week for testing so that the students can ask her questions and she can clarify the test for them. Another thing that proved useful was how she gave all of the students lecture notes since that is an important resource for them but only if it is accurate. Some other teaching strategies include treating algebra as a foreign language, focusing on english phrases, insisting on a one-step-at-a-time process and use of proper terminology, and using colored pencils to mark negatives, terms, and distribution.
I think that she was doing an excellent job focusing on the needs of
the students and coming up with effective and creative solutions. It was
important that the students were involved in the developing of these strategies,
and that she could easily modify a technique to help students with different
disabilities. This article definitely shows that with a little patience,
and the use of strategies that focus on students' strengths, math truly
is for all students.
Keywords: Teaching Strategies, Issues, Communication
Ref: Kerry6
Author(s): Flores, Alfinio; Perkins, Isabel
Date: 2002
Title: Mathematical Notations and Procedures of Recent Immigrant
Studies
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: vol. 7, no. 6, 346-351
Reviewer: Kerry
Date of Review: 02.28.02
This article discussed the issue of misunderstanding of mathematics to immigrant students. The problems arise due to different methods of representation in many different areas. One major problem was the numerical differences. Many immigrant students have difficulty distinguishing the number 1 with the number 7 in the United States. There are also differences in the way numbers are read, negative number notation, the use of commas, periods, and semicolons within numbers, and fraction notation. Immigrant students also find converting to the United States method of measurement confusing because linear metric measures are rarely used in other countries. A lot of teachers expect students to show work and this contradicts with how many immigrant students were taught in their home countries...places where the ability to do mental math rapidly was considered a great skill. Therefore, many of these students simply write down answers and then are accused of cheating. It also makes it difficult for the teachers to see where mistakes were made. Many immigrant students are also very hesitant to ask questions because they have been discouraged of this in the past. Therefore, it is necessary for teachers to understand different systems and point out notational differences before the beginning of each lesson. The authors pointed out 3 main recommedations - 1) "validate students' previous experiences both linguistically & mathematically," 2) "find common beginning points for students to start their experiences in the United States," and 3) "establish a sense of rapport in which both students and teachers are learners."
I really liked this article and thought it did a good job explaining
many of the differences that arise. There were a lot of things to consider,
and unfortunately it is a little different in every country and therefore
one could never know all of the different types of notations. I think that
having a basic understanding is always a really good thing though, and
if there is an immigrant student in your class, it would be a very good
idea to get some background information about their common notation. It
is just so important to be patient and encourage these students...it's
hard enough being in a new environment and even harder when everything
seems to be extremely confusing.
Keywords: Teaching Strategies, Curriculum, Standards
Ref: Kerry7
Author(s): Phillips, Elizabeth
Date: 1991
Title: Investigation 3: Exponential Decay (Decreasing Growth)
Patterns
Journal or Publisher: Curriculum & Evaluation Standards
for School Mathematics
Volume, Issue, Pages: Grades 5-8, Patterns & Functions
Reviewer: Kerry
Date of Review: 03.05.02
The "investigation" that I looked at was about exponential decay. The teacher would give the students a piece of 8.5" x 11" paper and then have the students continuously fold it in half, making sure to record the number of regions each time and the area of the smallest region. Then the class was to discuss what was happening. The second part involved the observation of temperature in a Styrofoam cup. The group members would record the temperature every 5 minutes. Then they were to graph the results.
I thought this was a very good experiment. It involved the students,
and had them come up with hypotheses about what would happen in the future.
It also included the communication standard well by the way the students
had to discuss in both groups and the class as a whole. I think it is also
a good idea to have the students take their own data and make their own
corresponding graphs. It taught the students to look for patterns, which
is a very important concept.
Keywords: Problem Solving, Teaching Strategies, Issues
Ref: Kerry8
Author(s): Knuth, Eric J.
Date: 2002
Title: Fostering Mathematical Curiosity
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: vol. 95, no. 2, 126-130
Reviewer: Kerry
Date of Review: 03.07.02
This article dealt with the component of problem-solving in learning mathematics. Two researchers, Brown & Walter, claim, "problem posing is almost always overlooked in discussions of the importance of problem solving in the curriculum" (126). They believe that problem posing is closely related to problem solving in two main ways. The first way is that both reconstruct a problem by posing new problems or relating the problem to a simpler one that they already know how to solve. Secondly, they suggested that "a person often does not fully understand or appreciate the significance of a problem's solution until he or she begins to generate and analyze a new set of related problems" (126). Using problem posing allows students to experience "making up mathematics rather than merely absorbing it" (126). By implementing problem posing into the curriculum, it creates a classroom environment that encourages, develops, and fosters mathematical curiousity. The teacher may start class by posing a problem as a warm-up and then after sharing some observations, the teacher might pose a new problem related to the first one. Teachers should also encourage students to pose new problems of their own and expand their thinking. It is often difficult for students to begin this process because many students lose their natural curiousity, especially in regards to mathematics, by the time they reach secondary school. Most of the students are used to mathematical experiences that are solution-driven and they are "rarely asked to formulate problems or to view a solution to a problem as a starting point in problem solving" (129), and therefore the process often stops as soon as they find a solution.
I think that encouraging students to think open-mindedly about mathematics
is a very important concept. In my opinion, we need more open-ended thinkers
because those are the ones that come up with solutions to hard-to-solve
problems because they can look at it from many different angles. I do think
that it will be difficult to implement, especially if it is one teacher
trying to do this when the students have been taught to think linearly
throughout all of their previous classes. Is it possible to regain this
sense of mathematical curiousity at a later age?
Keywords: Teaching Strategies, Problem Solving, Issues
Ref: Kerry9
Author(s): Rubenstein, Rheta N.
Date: 2001
Title: Mental Mathematics beyond the Middle School: Why?
What? How?
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: vol. 84, no. 6, 442-446
Reviewer: Kerry
Date of Review: 03.12.02
This article focuses on the importance of mental math. The author, Rheta Rubenstein, posed the question, "Why teach mental math?" One main reason for teaching mental math was because it is a very important skill to have in daily life - "it is useful for workers, consumers, and citizens" (442). According to Rubenstein, many of our daily tasks involve percents and proportions, which is part of the middle school curriculum but oftentimes is not mastered. Another important reason to study mental math was that it "facilitates learning many important structural topics" (442). Yet another reason was to prevent students from becoming calculator-dependent. The final reason she introduced was that mental math is a rewarding experience for students because they feel challenged. Implementing this is not as hard as it seems because every curriculum has mental-math objectives. For example, mental math can be applied in geometry to find basic areas, perimeters, identify equal & supplementary angles, etc. According to this article, objectives must be clearly specified at the beginning, and much time must be given to this. Another thing that should be done is to give the students frequent, but brief, in-class practice, such as a warm-up or closing activity. Suggestions of ways in which to formally assess the students is to have mental math quizzes or two-part examinations, where one part is mental math and the other calculator oriented.
I think that this is a good article that proves mental math is important
and should be implemented in lessons every day. It should be made a priority,
especially since more and more students are becoming calculator dependent,
which may hurt them in the long run.
Keywords: Assessment, Measurement, Standards
Ref: Kerry10
Author(s): Steele, 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: Kerry
Date of Review: 03.14.02
This article dealt with a unit on measurement and how to assess the work of the students along the way. Mrs. Grant started her 4-day lesson with forming cooperative groups of five, and letting the students measure a variety of objects using a long and short nonstandard tool (i.e. paper towel rolls, paper clips, straws, etc). Each pair of long and short nonstandard tools were related in some way, for example, one of the groups used a whole egg carton as their long tool and a single egg cup for the short. Mrs. Grant stated that the reason behind that was to have the students make associations between the short and long tools. She also had the students make estimates before they started, which was to help the students reflect on the meaning of measurement and develop conceptual knowledge of the procedures. After each group was finished, she lead a whole-class discussion. On the second day the students were given standard measuring tools, and were asked to take the same measurements as the previous day. This helped the students to make a connections. The 3rd day primarily focused on the solving of word problems that were similar to measurements the students had done the past 2 days. The last day was reserved for a formal assessment of each student. Every student worked individually to solve measurement problems. Most of Mrs. Grant's assessment techniques were informal, such as questioning answers, talking to students, etc. The article strongly suggested that teachers make an effort to view instruction and assessment as simultaneous acts.
I thought that this unit was very interesting. I think that the hands-on group activities really helped the students to thoroughly understand the concepts.
Keywords: Assessment, Teaching Strategies, Communication
Ref: Kerry11
Author(s): Albert, Lille R.; Mayotte, Gail; Sohn, Sheila Cutler
Date: 2002
Title: "Making Observations Interactive"
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 7, No. 7, 396-401
Reviewer: Kerry
Date of Review: 04.11.02
This article focused on a study of the role of interactive observational assessment. Interactive assessment is an approach to increase reasoning and understanding through the use of written dialogue, in which the teacher poses questions or writes comments and the student responds. The article states that the questions should do four things: provide insight to the problem, include a reference point relating to prior knowledge, encourage creative thinking, and encourage thinking beyond basic skills. Utilizing math journals in such a way allows students to reflect on their work, explain their thinking, and gain insights. The authors also provided the following suggestions for teachers: Maximize classroom space for easy movement Use a variety of problem-solving & critical thinking variations Write in every student's notebook Revisit students a second or even a third time to write comments in their notebooks Write brief, clear, and direct questions and comments Use this strategy in combination with other assessment techniques One of the largest benefits from this use of assessment is the way in which it is personal, and minimizes the involvement of other students. Thus, shy students, or those intimidated easily, feel more comfortable. Overall, interactive observational assessment provides individual guidance while allowing students to take risks, build writing/communication skills,and deepen their understanding of mathematical concepts.
I thought this was a good suggestion. I do think that it would be fairly difficult to write in all math journals once during one sitting, and even more difficult to reach each student a second or third time. I can see how this will work well in a small classroom, but also how it would be beneficial if implemented in a larger classroom. I think that it would definitely take some practice to come up with appropriate questions consistently!
Keywords: Teaching Strategies, Issues
Ref: Kerry12
Author(s): Petrella, Gerald
Date: 2001
Title: Subtracting Integers: An Affective Lesson
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: vol. 7, no. 3, 150-151
Reviewer: Kerry
Date of Review: 03.19.02
Oftentimes students have difficulty understanding mathematics because of the language that is used. The author of this article used parallelisms in everyday life to explain the operation of subtraction. He says, "our students are a valuable source of new instructional approaches. We need to keep listening to and observing our students both in and out of the classroom setting" (150). His idea for this lesson actually stemmed from a conversation between students he overheard in the hall. The lesson started unlike any other math lesson his students had known. It started with him describing an acquaintance of his that always appeared to be perky and cheerful, even during the worst of situations. He asked his students if they knew anyone like that, and most of them did. Then they were asked if they'd like these people more if they were "a little less positive?" Then they were asked to restate the idea in terms of negative thinking, and they came up with the idea that "to take away a little positive, we could add a little negative" (151). Then they did the same thing dealing with people that are too negative..."to take away a little negative, we could add a little positive" (151). They then summarized their findings into one sentence - "To take something that is positive or negative, add its opposite" (151). The final part of the lesson dealt with making the connection to integers.
I think that this lesson worked extremely well because it used familiar vocabulary and helped the students relate to something nonmathematical and then apply it to a mathematical procedure. It helped the students to see that math isn't just made up of a bunch of silly rules and formulas, and really helped the students see beyond the magnitude of the numbers.
Keywords: Teaching Strategies, Arithmetic,
Ref: Kerry12
Author(s): Azim, Diane
Date: 2002
Title: Understanding Multiplication as One Operation
Journal or Publisher: Mathematics Teaching in the Middle
School
Volume, Issue, Pages: Vol. 7, No. 8, 466-471
Reviewer: Kerry
Date of Review: 04.18.02
In this article, Diane Azim aims to provide numerous methods to help students understand multiplication. She suggests that many students view problems in very different ways. For example, some students "think about multiplication as taking one number (or quantity) of another number (or quantity)" (470) whereas others may see the situation as being one quantity that is acting on another. She discusses five different teaching techniques for understanding multiplication. The "Recipe Method" dealt with doubling, tripling, and halving recipes. The result of this real-world exploration activity was that students saw that multiplication increase, decreases, or preserves a certain amount of something determined by the size of the multiplier. The second was the "Multiplication Fulcrum Method." This was based off of a number line centered at 1. This allowed students to conceptualize the additive identity and the multiplicative identity. The "Photocopy Machine Method" also used a real-life situation, similar to that of the "Recipe Method." It demonstrates how a photocopy machine proportionally reduces, preserves, and enlarges something based on the size of the multiplier. The last two methods were developed by students of hers that still had difficulty with the other three methods. The "Frame Method" visually represented the situation, and the student could divide the framed whole into sections depending on the multiplier. The "'Number of a Number' Method" utilized the students ability to think in fractional quantities of other numbers. The student views multiplication "as one operation in which a given number is taken a designated number of times.
I thought this article was very informative. I thought that the first three methods were very good, especially in the sense that they used real-world examples. However, I thought the "Frame Method" was a little confusing. I can definitely see how a visual learner would benefit from this approach though. The "'Number of a Number' Method" made a lot of sense to me, and I believe that a lot of students do view multiplication in this way. Each of these methods certainly have great potential for helping students to understand that multiplication is indeed only one operation!
Keywords: Algebra, Teaching Strategies, Problem Solving
Ref: Kerry13
Author(s): Crocker, Deborah A.; Long, Betty B.
Date: 2002
Title: Rice + Technology = an Exponential Experience!
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 7, No. 7, 404-407
Reviewer: Kerry
Date of Review: 04.23.02
This article discussed the importance of integrating both literature and technology in the math classroom. One eighth-grade classroom that has successfully accomplished combining the three subjects was Phyllis Wisniewski’s class at Kings Creek Elementary School in Lenoir, North Carolina. They used the book One Grain of Rice, which is a story about a village girl named Rani in India. Basically, her village experiences a famine and the raja does not want to provide the people with rice. Rani picks up some rice that the servant had dropped and returned it to the raja. He offers her a reward and she asks for one grain of rice, double that the next day, and so on. Wisniewski’s class dealt with this in three steps. First, the students used a grid and actual grains of rice to model the amount of rice that would be received by Rani each day. They looked for a pattern, and filled in a corresponding chart. The second step was to determine the number of grains of rice Rani would have by Day 30, and express it in terms of the pattern they had found previously. The last step integrated technology through the use of TI-73 calculators. The students developed formulas and lists to enter in the calculators and then graphed the results. From this the students could see how much rice Rani would have on any given day based on the graph. The authors, Crocker and Long, gave 5 reasons why teachers should integrate literature and technology with math. Doing so helps children learn math concepts and skills, provide children with meaningful contexts to learn math, benefits the children’s use of math language and communication skills, helps students learn problem-solving, reasoning, and thinking, and also provides the students with positive attitudes regarding mathematics.
I thought this was an excellent interdisciplinary activity! The students started with a concrete idea and successfully moved to the abstract. The students were also very motivated and excited to find out how much rice Rani would receive! Letting the students explore and find the pattern themselves helped the students with their problem-solving skills, and made it a fun experience for them.
Keywords: Problem Solving, Geometry, Activities
Ref: Kerry17
Author(s): McClintock, Ruth M.
Date: 1997
Title: The Pyramid Question: A Problem-Solving Adventure
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 90, No. 4, 262-267
Reviewer: Kerry
Date of Review: 05.02.02
This article dealt with a three-day "problem-solving adventure" in which students explored and searched for the answer(s) to the open-ended question, "Does a connection exist between the perimeter of the pattern and the volume of the model?" (262). This activity could be applied to many different classroom levels, such as basic geometry, advanced geometry, precalculus, etc. One of the main objectives was to encourage students to continue to explore and question. The article suggested three ways to share this activity throughout the curriculum: 1) introduce the problem to geometry students and then ask the same question as they progress through a higher-level course, 2) invite different class levels to investigate the questions and to share insights and results, and 3) introduce the basic questions to precalculus level students as a whole and then have them work in small groups on extensions. The first day of this activity laid the foundation, and involved exploring integral triples with a sum of 36. Then students found the area for a particular triangle that was given to them, and asked whether it was acute, right, or obtuse. They then made conjectures. The second day was primarily discussion oriented, and helped students to think creatively and visualize changes that might occur relating to volume and linear measure. The last day was spent assembling models of their triangles, and students compared surface areas and volumes. The outcome of this largely time-invested activity was that students learned!!
This seemed like a very intricate project that required a lot of planning. It did appear to be a very worthwhile activity though, and there was definitely evidence that the students really understood the material!
Keywords: Teaching Strategies, Communication, Problem Solving
Ref: Kerry18
Author(s): King, Joann L.; Taylor, Lydotta M.
Date: 1997
Title: A Popcorn Project for All Students
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol. 90, No. 3, 194-196
Reviewer: Kerry
Date of Review: 05.07.02
Which brand of popcorn yields the greatest amount? That is exactly what the students from the combined transition prealgebra & honors precalculus class investigated! This was a two-week long project that compared the popping ratios of different brands of popcorn and found what size of box could hold the most popped corn. The students collected, organized, and analyzed data, communicated their findings in both written and oral forms, applied concept of percent, volume, mean, median, and mode to a real-life situation, and determined the maximum value of a cubic function using a graphing calculator. One of the objectives of the students was to improve self-esteem, motivation, and confidence. The idea for this activity came from one of the teacher’s students that misbehaved and was sent to an honors algebra class to work on his assignment. Besides the fact that he stopped goofing around, he observed the habits of the other students and responded to the stronger academic setting. Both classes taught the other class different concepts, for example, the transition math students gained confidence by teaching the precalculus students the difference between mean, median, and mode that they had forgotten. Through the use of both written and oral presentations, the students worked on their communication skills. After collecting data and analyzing it, the students created model boxes in order to find the maximum-sized popcorn box. This provided students with a visual representation of volume. Lastly, the students used graphing calculators to find the best values for their variables.
I thought this was an excellent way to combine classes. It didn’t hinder either level, and it benefited both sides greatly. The students had nothing but good things to say about this activity, so obviously they thought it was fun and enjoyed working on it. It was a great way to motivate students and strengthen communication skills!
Keywords: Problem Solving, Games, Probability
Ref: Kerry16
Author(s): Dilley, Clyde A.; Rucker, Walter E.
Date: 1974
Title: Math Card Games
Journal or Publisher: Creative Publications, Inc., CA
Volume, Issue, Pages:
Reviewer: Kerry
Date of Review: 04.30.02
According to the introduction, the book has two purposes: 1) to provide practice using mathematic concepts or skills, and 2) to provide an opportunity for children to develop higher level thought processes. Particular games in this book are created to "drill" the students on an understanding of a concept or skill. This provides children with a fun activity that strengthens their understanding. These games also help students develop probabilistic strategies. The instructions for teaching the games suggests that the teachers have a minimal role, and merely introduce the game to a group and let them figure out how to play, but step in if the students are not playing correctly. The authors also tell teachers to encourage students to invent their own card games, which expresses creativity. Most games only need 2 players, which definitely benefits smaller classroom sizes. Practically all games involve cards of some sort, hence the title "Math Card Games." These cards can easily be made from index cards, as stated on one of the first pages.
These games seem a bit elementary, but fun nonetheless. It might be time consuming to create the cards, and it might be possible to purchase various sets of cards that fit the descriptions. I liked how the games only required two to four people because that allows for greater involvement. It also makes game-playing easier when there are only a few students that have assignments complete, etc.
Keywords: Measurement, Geometry, Activities
Ref: Kerry15
Author(s): Berry III, Robert Q.; Wiggins, Joyce
Date: 2001
Title: Measurement in the Middle Grades
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 7, No. 3, 154-156
Reviewer: Kerry
Date of Review: 04.25.02
The authors, Berry and Wiggins, discuss the importance of the measurement standards in relationship to angle measurements. They began the article by listing possible careers that deal with angle measurements, which relates math to real-life situations. Problems arise in middle school with angle measurement due to the fact that students do not have a sense of angle size, they lack knowledge of angle attributes, and do not understand how to use protractors as measuring tools. Thus, the authors talked about a possible project for sixth graders in geometry dealing with the exploration of openness of angles and the use of protractors. Instead of simply teaching the students how to use a protractor, the students were asked to construct a protractor using nonstandard units of measure and create an angle model. The students then used their protractors to meaure constructed angles and to observe similarities between the standard protractor and the one they made. The students also measured the angles of various multi-sided polygons with their protractors as an extension of the activity. This project led to much discussion about protractors, degrees, why there are 2 sets of numbers on protractors, etc. The next day involved the students breaking into small groups to work on activities using Geometer's Sketchpad or Geometry Inventor. This helped the students understand the idea of benchmark angles and confirm their understanding of angle size. These activities combined helped the students to explore openness attributes of angles and develop appropriate protractor techniques.
This was a creative way to teach students about protractors. I think this would work well in both large and small classroom, especially for group work. I think that breaking the students into groups is a necessary aspect of this project for the sake of discussion. It would be cool if they wrote about their findings in a math journal!
Keywords: Connections, Probability, Standards
Ref: Kerry19
Author(s): Tarr, James E.
Date: 2002
Title: Providing Opportunities to Learn Probability Concepts
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: April 2002, 482-487
Reviewer: Kerry
Date of Review: 05.09.02
This article discusses the Data Analysis and Probability standard with respect to various grade levels. The author argues that this standard has a greater emphasis on data analysis than probability, especially for grades pre-K to 5. Although, the article states that “probability is sometimes regarded as the least intuitive branch of mathematics because people of all ages have difficulties developing correct intuitions about fundamental ideas in probability” (484), he suggests some activities to include probability in the elementary school curriculum. For example, the creation of “likelihood lines” represents the chance of various events occurring. He says that elementary school children should learn to distinguish events that are certain to happen and those that are impossible. He also say that they should have a understanding of sample space, and systematic ways to generate them. However, one drawback is that most students must have a certain amount of familiarity with fractions to work with probability concepts. Tarr views probability as being interconnected with several different mathematical areas such as the study of numbers (i.e. rational numbers), geometry (i.e. coordinate, area), and data analysis. This offers many opportunities to implement probability concepts in the curriculum without hindering the planned lessons.
I definitely agree with Tarr that probability is not emphasized in the earlier grades. In fact, I do not think I learned probability until I came to St. Olaf (well if I did it wasn’t apparent). I believe that if I would have learned probability concepts earlier on and been conditioned to think probabilistically I would not be so weak in that area now. Currently, it is very difficult for me to think in terms of chance and probability, and harder to apply those concepts to statistics and other areas of mathematics.
Keywords: Issues, Equity, Standards
Ref: Kerry20
Author(s): Gilbert, Melissa C.
Date: 2001
Title: Applying the Equity Principle
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 7, No. 1, pgs. 18-19, 36
Reviewer: Kerry
Date of Review: 05.14.02
Melissa Gilbert suggests numerous ways in which equity can be reached in the classroom. Calling on students randomly is on way in which to avoid inequity. One way to do this is to take Popsicle sticks and write the names of the students on them and then pick them at random so that each student has a chance and all students are called on once before they are chosen a second time. Another technique is to have the students form cooperative learning groups or participate in a jigsaw type activity, where each student becomes an “expert” in a certain area and then teaches his or her peers. Another suggestion for group activities is the utilization of team roles (i.e. recorder, resource monitor, captain). In general, teachers can reduce gender stereotypes by providing students with knowledge about women who have made achievement in math and science. Also, culture plays an important role in stereotypes formed and as a result, diverse students often become victims of inequity. One way to combat this is to understand the contexts of student’s lives and work to understand the educational experiences of their parents.
This article had excellent suggestions that I plan on implementing in my classroom! Hopefully inequity will not always be such a huge issue and each student will always be given equal opportunities to succeed. In striving toward equity, positive environments are definitely an important aspect!