Keywords: Discrete, Problem Solving, Keyword 3, Optional...
Ref: Jami17
Author(s): Drexel University
Date: 2003
Title: http://mathforum.org/discrete/discrete.software.html
Journal or Publisher: The Math Forum
Volume, Issue, Pages:
Reviewer: Jami
Date of Review: 5/5/03
Summary: This article is about several internet resources regarding discrete mathematics. These activities and resources range from different age levels, from kindergarten through grade twelve. It includes class materials, as well as many lesson plans to help teachers plan different activities for their students. A few of the lessons that are included at this site are "Combinatorics Topics for grade 12-8," "How many different paths," "How many different ways can a team win a seven game series," and many others. Each lesson is clearly detailed, and has clear objectives, procedures, summaries, and reactions. In addition, each lesson shows ways of evaluating each activity, and at what level they are appropriate.
Reaction: I really think this is a valuable article. It gives many excellent resources for a teacher who is going to teach a unit or a class on discrete math. I like how detailed each lesson is. A teacher could literally print off this lesson and be able to teach it directly. Since discrete math can be very difficult for many students to understand, I think that these lessons make the material clear and simple enough for elementary students to be able to understand. As the grade levels go up, the activities become more extensive and more complex. These activities will improve students' problem solving skills, and allow them to think at a more complex and different level.
Keywords: Algebra, Activities, Problem Solving
Ref: Jami18
Author(s): Mr. E
Date: 2003
Title: http://www.visi.com/~dethier/activities.htm
Journal or Publisher: Internet
Volume, Issue, Pages: all
Reviewer: Jami
Date of Review: 5/5/03
Summary: This article is about a teacher who has made a very extensive web site, containing many of his mathematics activities that he found useful in his classroom. Most of them had to do with his algebra unit. His activities had a very wide range of ideas. Some of the main topics in which he divided them into are: TI-83 Graphing, Calculator, Macintosh Graphing Calculator, Algebra Tiles, Real-World Applications, Spreadsheets Problem Solving, and resources. Each of these sub-headings has different activities for the students to do regarding these topics. The one that I looked at a great deal was the one dealing with problem solving. There was an excellent dominoes activity, that allow students to gain a better perspective of space and how you can fill it the most effectively.
Reaction: I really thought this was a valuable web site. You can obviously tell that this teacher has been around for a long time, and has done a superb job of keeping his valuable material and preparing it on a web site for other teachers to use. I also thought that the way he used technology to show different aspects of algebra was very effective. Each activity was very well prepared, and clear to read and comprehend. Also, I like the way this teacher organized each lesson or activity into different sections, and the fact that they are appropriate for many different grade levels, depending on how deep into the problem you want to go. Overall, this was an excellent article, and I will definitely look back at this in the future.
Keywords: Select one..., Activities, Communication
Ref: Jami19
Author(s): Alper, Lynne; Fendel, Dan; Fraser, Sherry; Resek, Diane
Date: 1998
Title: Solve It
Journal or Publisher: Interactive Mathematics Program
Volume, Issue, Pages: pp. 161-166
Reviewer: Jami
Date of Review: 5/5/03
Summary: This activity from the Interactive Mathematics Program book Solve It! takes place about two-thirds through the unit, in a high school algebra mathematics classroom. The activity is called Scrambling equations, and it is designed to show equation solving as an "uncomplicating" process and to reinforce the notion of equivalent equations. Each student will take a simpl equation, such as x=5, and write a series of more complex equations in which each is equivalent to the preceding one. When all students are ready, they will be paired up within their groups that they will be working on to check that their work is correct. Then, each example should be written on a separate sheet of paper, with the original equation writton on one side of the paper and the final, "scrambled" equation written on the reverse side. Each group will then trade its sets of examples with another group, with the sides showing the final equations face up. Either as a whole or in pairs, groups can then work backwards to retrace the steps for each of the other group's scrambled equations until they come up with the same original equations. These can simply be put on the overhead, which are the four methods that students can use to scramble their original equations: 1. They can add the same integer to both sides of the equal sign. 2. They can subtract the same integer from both sides of the equal sign. 3. They can multiply both sides of the equal signs by a nonzero integer. 4. They can divide both sides of the equal sign by a nonzero integer. Then, the students can divide themselves in groups, and the substitute can just moniter them to be sure they stay on task. Reaction: I really like this activity. It's a great way to get students out of their desks, and doing a fun activity that they will actually gain some valuable knowledge doing. The way it is set up, students are able to work together with different people from the classroom, and use each other's information to work on scrambling different equations. Overall, this is an excellent activity that I would strongly like to look back at in the future.
Keywords: Puzzles, Connections, Keyword 3, Optional...
Ref: Jami20
Author(s): Dr. Math
Date: 2003
Title: Ask Dr. Math-Middle School Archive
Journal or Publisher: The Math Forum
Volume, Issue, Pages: http://mathforum.org/library/drmath/view/56727.html
Reviewer: Jami
Date of Review: 5/8/03
Summary: This article is about a teacher who has created an excellent resource for both teachers and students. I referred to the middle school section, but there are references and activities for each grade level, as well as for college and beyond. One of the puzzles that I thought was very interesting was the one about if you are given a day, month, and year, is there a formula you can use to find the day of the week? It goes through different students writing back and forth to Dr. Math, and different possible ways of going about solving it. The results for this particular puzzle were: Here is a standard method suitable for mental computation: (1) Take the last two digits of the year. (2) Divide by 4, discarding any fraction. (3) Add the day of the month. (4) Add the month's key value: JFM AMJ JAS OND: 144 025 036 146 (5) Subtract 1 for January or February of a leap year. (6) For a Gregorian date, add 0 for 1900's, 6 for 2000's, 4 for 1700's, 2 for 1800's; for other years, add or subtract multiples of 400. (7) For a Julian date, add 1 for 1700's, and 1 for every additional century you go back. (8) Add the last two digits of the year. (9) Divide by 7 and take the remainder. Now 1 is Sunday, the first day of the week, 2 is Monday, and so on. There are many other problems that I found very interesting as well.
Reaction: I really enjoyed this website. It's an excellent way for students to see how problems are solved, as well as an great resource for teachers to find challenging problems for students to solve. I like the complexity of the solutions, and how clear the teacher is at giving feedback. As the grade levels increase, the level of difficulty in the problems strongly get harder, which is to be expected. Also, you can click on different subjects within mathematics, depending where you may be in your curriculum. Overall, this is an excellent website, and I will definitely refer back to it in the future!
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Keywords: Proof, Teaching Strategies
Ref: Jami16
Author(s): Galbraith, Peter
Date: 1995
Title: Mathematics as Reasoning
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: vol. 88 no. 5 pg. 412-417
Reviewer: Jami
Date of Review: 4/23/03
Summary: This article was about how the Curriculum and Evaluation Standards for School Mathematics defines a role for reasoning in school mathematics is so much different from the norm of the recent practices, and that until very recently, the study of mathematical reasoning was mostly contained in geometry class. The study also pointed out that the approach that was used in geometry was often very rigid, and it conveyed the impression that the style of the response was more important than its mathematical quality. The article went on to explain that many times, teachers struggle at teaching proofs, and do what they can to avoid it. The main focus for the students is for them to use a line of reasoning that is clear and compelling to others. Near the end of the article, it gives advice for possible teaching implications, that could be found valuable to teachers in such a situation. Reaction: I enjoyed this article. Thinking back to when I was in high school, I hated proofs. I did anything I could to avoid them. Looking back, I think that the main reason I did not like them is because my teachers did not do a quality job of teaching us how exactly to do proofs. They would just put a proof on the board, and expect us to be able to do them on our own. I think it is a good idea for the curriculum to begin teaching proofs before geometry, so that students have a good idea of the concept of what a proof is before they have to jump to the more complex ideas. I also like the fact that the article gives teaching implications. That way if a teacher may be struggling with teaching proofs to their students, they will be able to use this to their advantage. Also, for future teachers, it will better prepare them for the situation they may be in at some time.
Keywords: Algebra, Activities, Curriculum
Ref: Jami14
Author(s): Fendel, Dan; Resek, Diane
Date: 1998
Title: Solve It!
Journal or Publisher: Interactive Mathematics Program
Volume, Issue, Pages: Key Curriculum Press
Reviewer: Jami
Date of Review: 4/13/03
Summary: This book is a teachers guide to an interactive curriculum that is appropriate for a high school mathematics class, and it is the second year of a four year program. This unit goes through 33 days of activities, explaining each day with the goals of the day, and different homework assignments. At the beginning of each day, there is an outline, explaining exactly what the teacher needs to be sure that he/she is fully prepared. It also addresses different questions that the teacher can ask to the students, to be sure the students understand the material correctly. The idea of solve it introduces some of the important ideas from algebra that are useful in a wide variety of situations, and the students will be revisiting contexts and concepts from the units from the first year of the program to see how the ideas from algebra can be applied.
Reaction: I think this book is excellent. Instead of reading the equivalent information from a standard textbook, this curriculum gives students an opportunity to understand the same information by seeing real-life examples. Also, the different problems of the week, as well as homework assignments are very good problems that will make the students think. Also, the way the problems are asked, parents can also be active in their students' learning, because some of them can be very thoughtful. Overall, I think that the IMP series are very good integrated curriculum, and are an excellent way of getting rid of standard textbooks, while still enabling students with the information necessary to get what they need out of the basic math standards.
Keywords: Measurement, Activities,
Ref: Jami15
Author(s): Christine Sweger-Miller
Date: 2003
Title: Does it measure up?
Journal or Publisher: The Artsedge: Teaching Materials
Volume, Issue, Pages: http://artsedge.kennedy-center.org/teaching_materials/curricula/curriculum.cfm?curriculum_id=149&mode=full
Reviewer: Jami
Date of Review: 4/15/03
Summary: This article was about an excellent activity for second grade students learning the basics of exact measurement. The activity is designed for a 50-minute class period, and was used at the Thomas Pullen Arts Magnet School in Landover Maryland. What the students will do in this activity is to follow directions to draw a picture. The way they are assessed is by how accurate their drawing is. The students will then be asked to measure each part of their drawing again, and as each part is measured again, students should write a sentence to describe the length or height of that part of the picture. Then, the students will be told to be sure that the particular part in the picutre that they are measuring is described, and to write down the measurement and use the word centimeter in each sentence. Their work will also be assessed by their grammatically in their sentence structure. Reaction: I thought this would be an excellent activity for elementary school students who are just learning how to measure different things. I like the way the students are able to do the drawing. It gives them a hands-on idea of how to draw the pictures, follow directions, and measure what they drew. Also, the students are given a chance to work in groups, which is a good strategy for students at such a young age to develop. One thing I'm not sure of is how well second grade students are at deveping strong sentences, and being graded on it. I've always thought that math should deal with learning math, and English can be dealt with in English class. Other than that, I thought this was a great article, and if I decided to teach elementary math, I'd consider using it!
Keywords: Algebra, Activities, Problem Solving
Ref: Jami13
Author(s): Alper, Lynne; Fendel, Dan; Fraser, Sherry; Resek, Diane
Date: 1997
Title: The Overland Trail-Teachers Guide
Journal or Publisher: Interactive Mathematics Program
Volume, Issue, Pages: p. 44-52
Reviewer: Jami
Date of Review: 4/2/03
Summary: This teacher's guide is the first of a four year program, based in the Interactive Mathematics Program. Focusing on pages 44-52 of this textbook, it is about how shoelaces are on of the small items that are sometimes forgotten when thinking about what to take on a journey. The assignment will consider how much of this commodity will be needed, assuming that the shoes the family is bringing already has laces in them to begin with, and they need to bring an extra pair for each pair of shoes and boots. The students are given information about how many pairs of shoes and boots the adult men, adult women, and children need to bring, and how long each shoelace is. The students are then asked questions about how many inches of shoelace are needed for the men, women, children, and then for the family altogether, assuming there are two men, two women, and two children. When figuring that out, they are then asked to discover how they came up with their last answer, and decide how they could substitute variables in for the family members, and come up with an expression. This lesson is an introductory to variable lesson. The second activity followed these ideas, except they were given different information, and had to put information together using averages, and find out how many inches they had altogether by using the same ideas. Reaction: I thought these two activities were excellent. They are a great way to begin a unit on variables, because the students are actually discovering how to find the variables by using information they already know, and working together to solve problems. I like the way that these activities use an actual situation, because then the students can feel like it is their actual family taking this journey, and then they will be more interested in what they are doing. I also like how the students don't know right away that they are learning how to use variables. They are solving problems, and then using that information to figure out how to substitute variables. Overall, I thought this book was excellent, and I would recommend it strongly.
Keywords: Geometry, Activities
Ref: Jami12
Author(s): Alejandre, Suzanne
Date: 2003
Title: Dominoes Activity
Journal or Publisher: The Math Forum
Volume, Issue, Pages: http://mathforum.org/alejandre/frisbie/student.poly.html
Reviewer: Jami
Date of Review: 3/31/03
Summary: This article was about an activity during a geometry unit involving dominoes. Students are supposed to work in pairs for the first part of the activity. Each student is given a grid sheet, as well as 15 dominoes, so that each pair has 30. The students are supposed to work with partners to see if they can find a 5 by 6 grid using those dominoes. Then the students can get back together as a class and discuss their results, to see if they came up with the same results, or if there was more than one way to find the answer. The second part of the activity involves a bit larger groups. The students use 30 dominoes, but with four people this time. Their goal in the second part of this activity is to assume that your Brick-Wall company wants to produce a catalogue of designs to show to customers. If they miss out on a design then a competitor may offer it. So your company had better include all the designs you can. The brick walls are to be two units tall. The bricks are all the same size, 2 units by 1 unit. They are supposed to see how many different ways they can make a wall using one brick, two, three, and any number of bricks.
Reaction: This was a great activity. When teaching a geometry unit, this is a great way to get students out of their daily textbooks and actually doing something fun. Since many students look at dominoes as being a game, this activity is a very good way for them to learn something when they may not even be realizing it. It is also a good way for them to work together with other students, and collaborate their ideas to find solutions to different problems. The activity didn't really say a specific age level, but I would say a high school geometry class would be sufficient for this activity. I liked the way this activity put the students at the spotlight. Many times, the students do the listening and watching, and it is up to the teacher to do the work. This activity allows the students to discover the answers to the problems, and work together to learn as well as have fun.
Keywords: Activities, Statistics, Probability
Ref: Jami11
Author(s): Fendel, Dan; Resek, Diane
Date: 1997
Title: The Game of Pig
Journal or Publisher: Interactive Mathematics Program
Volume, Issue, Pages: Year 1
Reviewer: Jami
Date of Review: 3/17/03
Summary: This teachers guide is about a game called "The Game of Pig." The classroom is focused on the IMP, which is the interactive mathematics program, which is a four-year program of problem-based mathematics the traditional algebra1-geometry-algebra2/trigonometry-precalculus sequence designed to exemplify the curriculum reform called for in the Curriculum and Evaluation Standards of the National Council of Teachers of Mathematics. This book focuses on the first year of the program, where students will go through 32 days of an activity, where they will play "The Game of Pig," and find strategies to the game, and why they think their strategies are the most effective. The way the game is played is that a student is given a die, and they roll the die as many times as they want until they roll a 1, but they can stop at any time. If they stop before they roll a 1, then they can add up their scores, and that is their score for that turn. If they roll a 1, their score for that turn is automatically 0. The students work with probability to determine when they should roll again. They first must define what they think strategies are, and how they can be effective. One thing that is illustrated in the book is the importance of understanding the social issues concerning dice and gambling. This is because some parents may be concerned about school activities that involve dice or seem to involve gambling. This teachers guide goes through each day of the unit, along with homework assignments for each day. Reaction: Since I have never had the chance to actually read out of a teacher's guide, I thought it was very interesting. I always wondered how their book was different from ours, and now that I have seen one, I've noticed how helpful they actually are. I think this activity is great, and can be very effective. I like the way students get to discover things on their own is very good, and that they are able to decide what their strategies are based on the results they see from their data. It allows the students to work together, and to decide whether it is most effective for them to play with each other, or play against each other. This is a great strength for students to develop. Overall, I think that this game is an excellent way for students to gain a better understanding of probability, and how to develop strategies to improve their understanding of mathematics.
Keywords: Activities, Curriculum, Planning
Ref: Jami10
Author(s): Zawojewski, Judith S.
Date: 1991
Title: Dealing With Data and Chance
Journal or Publisher: National Council of Teachers of Mathematics
Volume, Issue, Pages: pages 1/71
Reviewer: Jami
Date of Review: 3/12/03
Summary: This book is a very valuable resource for middle school teachers. It focuses on different activities that will enable students to become more familiar with gathering data, and using it to process their own data through surveys. It discusses good ways of asking questions to make sure that each person taking the survey will be applicable to answer it. The book included five chapters, that focus on communication, making sure that students are able to write good questions, making it look at professional as possible. Two chapters include a focus on problem solving and reasoning, as well as a chapter on connections. Different activities are given for teachers to present to their students, where they will conduct surveys, find their results, and then combine the results with the remainder of the class to see any connections that may exist. Other such activities exist as well. Reaction: I think that this book would be a very valuable tool for middle school math teachers that are intending to teach this type of material. I really like the way these activities connect with real-life situations. The students will look at the activities as being real fun, instead of being an assignment that they have to finish. This will also result in better results because the students are going to put more effort into it, and will end up with more accurate results. I liked the way the book included graphs and ways of displaying the results of different activities because it allows the teacher, as well as the students, to be able to visually see how what to do with their information once they get it. Sometimes students get an assignment and are just overwhelmed by all the information, so when they are able to visually see what to do, they will be more comfortable with it, and eager to begin!
Keywords: Algebra, Planning, Teaching Strategies
Ref: Jami8
Author(s): Cuevas, Gilbert J.; Yeatts, Karol
Date: 2001
Title: Navigating Through Algebra in Grades 3-5
Journal or Publisher: Navigations Series
Volume, Issue, Pages: pages 1-90
Reviewer: Jami
Date of Review: 3/10/03
Summary: This book involves many excellent activities to be used in the classroom involving algebra. The grade levels that could most commonly use these activities are grades 3-5. However, in certain circumstances, all grade levels may be appropriate, depending on the level of depth. The three chapters involved are patterns; variables and equations; and functions. Each chapter is separated with different activities, and ways to teach material in different ways. Following each activity, there is a page for the teacher that explains where to go next in instructions, as well as different ways of assessing the students with the given activity. The activity always begins with the goals for that particular activity, as well as the prior knowledge that is necessary before beginning. Also, a CD-ROM is included, that offers many visual ideas for teachers to use when planning their daily lessons. Reaction: I thought this book is extremely helpful. I really hope that these resources are available when I am planning to prepare lessons for my students. I liked how organized the activities were, and how you could look at the goals and see how they compare to the goals you as a teacher were intending for that particular lesson. I would definitely recommend this book to teachers who are planning on teaching grades 3 and up. It is a very helpful tool, that can help students learn in a different, but effective way.
Keywords: Connections, Problem Solving,
Ref: Jami9
Author(s): Battista, Micheal L.
Date: 2001
Title: Constructivist Learning and Teaching
Journal or Publisher: Internet
Volume, Issue, Pages: http://www.terc.edu/investigations/relevant/html/constructivistlearning.html
Reviewer: Jami
Date of Review: 3/5/03
Summary: This article was about a person's opinion that no one can teach mathematics, but it is effective teachers who can stimulate students to learn mathematics. Also, it describes different proponents of constructivism. The first states that knowledge is actively created or invented by the child, not passively received from the environment. The second states that children create new mathematical knowledge by reflecting on their physical and mental actions. The third states that no one true reality exists, only individual interpretations of the world. These interpretations are shaped by experience and social interactions. The fourth states that learning is a social process in which children grow into the intellectual life of those around them (Burner 1986). The fifth states that when a teacher demands that students use set mathematical methods, the sense-making
activity of students is seriously curtailed. The article goes on to talk about two main goals to make this effective, as well as ways to teach and learn this concept.
Reaction: I thought this article was a very knowledgable article because of the ideas it gave for teachers to use. Constructivism is going to be a very essential part of our teaching, so it is very important that we remain knowledgable about this, and understand exactly when and how to use it. One of the goals that I thought was very important was that we, as teachers, have to make sure that when the students are working on these activities, that they are self-motivated, and that they get their mathematical knowledge from explorations and discoveries, rather than from their teacher. That is very important!
Keywords: Assessment
Ref: Jami6
Author(s): Driscoll, Mark
Date: 1995
Title: The Farther Out You Go..." Assessment in the Classroom
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol 88(5) pg. 420-425
Reviewer: Jami
Date of Review: 2/26/03
Summary: This article was about the importance of integrating assessment with instruction. The writer discusses how he cannot thank one of his students named Billy, who he taught at an alternative high school in the 1970's, for teaching him the importance of integrating assessment with instruction. The title of this article has to do with a discussion he had with Billy. One day in class, the teacher wrote down five decimals between 0 and 1, such as .06, .607, .6, .6707, and .067. She then asked the students which was the smallest, and Billy replied that .6707 was the smallest because he said he had once heard from a teacher that "the farther out you go" the smaller the value. This really made the teacher think. All this time he had learned what he thought was the right way to figure out the answer, when actually he may not have had exactly the right idea. The teacher's reminiscences about Billy will serve as a framework for one model of systematic effort, which involves a process of inquiry that extends through several stages of questioning to form an assessment feedback loop that can help align mathematical goals with teaching practices. When writing this article, the author imagined he was back in Billy's class, and used the hindsight to evaluate the context from his perspective then and his perspective now. Reaction: I enjoyed reading this article. I like reading articles that have to do with students. It allows the reader to remember back to their childhood mathematics classes, and relate the ideas to the ways they were taught, and the teachers they were encountered with. I liked the authors detail that he used. It allowed me to visualize Billy, and the class that he was in. The activity involved in this article can be easily related to classes that I have taken, so it was easy to relate to. Also, it seems very similar that a student thinks they understand how to figure out a particular problem, when in reality, they don't have exactly the right idea. Even though they remembered the right idea, they should still be assessed properly for having that right idea. This gives students confidence, and will allow them to stay focused on current material, and not get down on themselves.
Keywords: Algebra, Problem Solving
Ref: Jami7
Author(s): Hallowell, Kathleen A.
Date: 1995
Title: The Case of the Blue Wooden Flower
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: vol 88(5) pg. 366-370
Reviewer: Jami
Date of Review: 3/2/03
Summary: This article is about a lesson that combines statistics, introductory algebra, and economics. In the lesson, students have the opportunity to create their own mathematical functions and make inferences from those functions. This activity allows students to use problem-solving, and understanding how to apply this to real-world situations. After completing this lesson, students should be able to understand the relationships among profit, revenue, and cost. What the students were doing was they were assigned as financial consultants for a fictional company that produces and sells blue wooden flowers. They would work in groups of three or four students, where each group would be given a blue wooden flower. Then each group would report a cost estimate for producing one flower, and the class would then work together to calculate the mean, and talk about the advantages and disadvantages of each measure. Procedures would then continue, and they would put their information on tables, and graph different functions. Overall, the students really enjoyed this activity, and understood how it could be applied to real world situations. Reaction: I really enjoyed this article. There are so many students who are simply not interested in learning math. They don't find a point to learning it, merely because so much of the time, they cannot find a use for it, so they don't see a point of learning it. However, when they worked on this activity, they were every enthusiastic about doing it. One reason was because it was sort of like they were competing with other groups to make the most profit, which motivated them to want to calculate accurately, and work together effectively in their groups, so they could perform to the best of their abilities. This is a great activity to get students out of their desks, and working on an activity that will actually help them in future real world situations.
Keywords: Connections, Activities,
Ref: Jami4
Author(s): Van Dyke, Frances
Date: 1998
Title: Visualizing Cost, Revenue, and Profit
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: Vol 91(6) pgs. 488-493
Reviewer: Jami
Date of Review: 2/19/03
Summary: This article was about an excellent activity for teachers to use in the classroom regarding cost, revenue, and profit. The sheets that are used in the activity are designed to help students because familiar with the graphs, equations, and tables of these functions. This activity is designed for students from grades 8-11, depending on ability. Instead of students learning how to differentiate among functions from sitting in the desks and reading it out of a book, this activity allows them to actually visualize how and why the graphs and equations are changing. The students are assessed by them writing a paragraph explaining the differences among cost, revenue, and profit and to describe how to recognize each function when the three different ones are modelled by linear functions and graphed together on one set of axes. The way the activity is set up is that they working in groups, and acting like they own a small business, using these different methods to calculate their profits, and so forth.
Reaction: I thought this activity is very good. It applies their knowledge to an actual life
example. This is going to cause the students to be much more active, because they are active,
and able to see what they are learning while they are doing the activity. Also, since they are
working in groups, it allows them to work together, and build from one another to develop the
best plan for them to gain the greatest amount of profit. I would say, though, that this activity
would be for upper high school students. I don't recall learning about such things until the end of
high school, and that was only briefly. I even think that a beginning accounting class, either in
high school or in college, would be able to use such an activity. Also, I think the students are
being assessed in a good way. I think it is beneficial for students who have been working on a
visual, hands-on project with a group of students to have to write about what they saw, and
how they came to their conclusions, because it allows students to think independently, instead of
only listening to the members of their group who tended to speak up a great deal more. Overall
though, if I teach a high school math class, I would highly consider using such an activity.
Keywords: Teaching Strategies, Curriculum
Ref: Jami5
Author(s): Hammock, Richard; Lyons, Davie
Date: 1995
Title: A Simple Way to Teach Logarithms
Journal or Publisher: The Mathematics teacher
Volume, Issue, Pages: vol 88(5) pg. 374-375
Reviewer: Jami
Date of Review: 2/23/03
Summary: This article is about a teacher who has developed an excellent teaching strategy
to teach logarithms. She stated that many students have a very difficult time understanding
logarithms, and often times are not able to put the information together correctly. When
students are just beginning to learn functions, they can get lost in the details of working with
inverses. This approach that he is using is simply replacing log of a, by a, with a box in the
upper right hand side, reading "a-box." They would begin with simple examples such as 2
box(8)=?. The students would then fill in the missing part with a 3, since 2 to the 3rd power is
equal to 8. They would then get into some negative numbers, as well as fractions. When the
students got a good grasp of the pattern involved here, they would go back and input the
logarithm function. Since the students already understood the pattern, it was a lot easier for
them to understand how to do logarithms. They have had tremendous success using the a-box
technique to teach logarithms.
Reaction: This was a great article! I wish teachers would have used this approach when I was
learning how to do logarithms. Making things simpler is the easiest way to teach math,
especially when introducing new material. I liked the way the teacher started out with a simple
example that he knew the students would be able to answer, and then gradually got more
difficult, as he became aware that the students were beginning to understand the patterns
involved. Using techniques like this is a very essential way to teach math. When students first
hear, "we are going to learn how to do logarithms today class", they have no idea what they are,
so they will not be motivated, or have any idea how to start learning how to do them. I will
definitely use this technique in my teaching!
Keywords: Teaching Strategies
Ref: Jami3
Author(s): Allsop, 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: Vol 8 (6) pg. 308-314
Reviewer: Jami
Date of Review: 2/17/03
Summary: This article was about how students that have learning disabilities or special needs have a very difficult time understanding mathematics. It also gives solid advice as to how teachers can help these students. The article specifies four learning problems, which are attention problems, cognitive-processing problems, memory problems, and meta-cognitive deficits. When a student has an attention problem, they will either miss the important information when it presented by the teacher, or they will not attend in a meaningful way to essential cues when attempting to solve a problem. Most people think of a student with an attention deficit to not focus on anything, but it is actually just the opposite. When a student has a cognitive-processing problem, they may be able to see a mathematical problem on the chalkboard, but when they try to write what they see, they will write it inaccurately. This is only one example of this problem. As for memory problems, students who have a difficult time retrieving information accurately even though they may have successfully stored the information at one time. Finally, meta-cognition involves "the ability to apply appropriate learning strategies, to evaluate their effectiveness, and to change strategies when current ones are not successful. When a student has one of these learning disabilities, some instructional strategies include teaching in authentic and meaningful contexts; directly modelling both general problem-solving strategies and specific learning strategies using multi-sensory techniques; ensuring that the sequence of instruction moves from the concrete, to the representational, to the abstract; giving students opportunities to use their language to describe their mathematical understandings; and continually monitoring students' performance and offering meaningful feedback in the form of performance charts.
Reaction: I really enjoyed this article. Throughout my teaching career, I will be faced with students who have learning disabilities. More and more, schools are focusing more on getting these students into the regular classroom, to treat them like the other students. Therefore, as a teacher, we need to know how to recognize these special needs, and how to plan accordingly for these students. These students should feel no different from the others, as far as the amount of information they are given. However, in certain cases, students with special needs may need to be dealt with more individually as far as progress, improvements, and how to continue to improve. This article does an excellent job describing how to help students with special needs in the mathematics classroom, and the importance to have confidence in these students, as well as with the other students in the class.
Keywords: Problem Solving, Probability, Measurement
Ref: Jami1
Author(s): Haug, Mikel
Date: 1998
Title: Up the Creek With a Paddle
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 91(60), 456-460
Reviewer: Jami
Date of Review: 2/10/03
Summary: This article is about an eighth-grade mathematics class who was given a hands-on project, where they were to determine the probability that a local creek would flood. The students were given a packet that included an outline of what their final presentation should include, a list of references, and data sheets. They had a scenario where there was a developer that wanted to build a recreational vehicle park on the banks of a local creek, and the students' consulting firm was hired to evaluate the probability of the creek to flood out of its banks. The students worked in the classroom to determine what was necessary for a creek to flood, and decided that how much water flowed into the creek during a storm and how much water the creek could hold before spilling over the banks was the most general information they needed. "They applied mathematical skills to solve a real-life problem and communicated that process through their written reports" (Haug 459-460). The teacher set due dates for each calculation, and a grade for each calculation was then assigned on the due date on their grade sheet. This allowed the students to stay on task, and corrects any misconceptions quickly. Overall, the students were enabled to learn a mathematical lesson by using a hands-on technique, and learned to work together to solve a problem as a team.
Reaction: I really enjoyed this article. As a student, I have always learned better by getting out of my desk and actually learning visually, hands-on. This project allowed the students to learn how to calculate different areas, and work together with their teams to write up a report that shows how their calculations show their results. It can be effective for students to learn material by reading in their book or listening to their instructor, but they students will gain a broader perspective of why it is important for them to learn the material if they can see what they are learning. This project is an excellent example of a hands-on application to mathematical learning.
Keywords: Planning, Teaching Strategies, Problem Solving
Ref: Jami2
Author(s): Tripp, Joseph
Date: 1998
Title: Getting Students to do Homework
Journal or Publisher: The Mathematics Teacher
Volume, Issue, Pages: 91(6), p.478-479
Reviewer: Jami
Date of Review: 2/12/03
Summary: This article is about a freshman pre-calculus professor from Plattsburg State University College. She wanted an effective way for her students to actually do their homework, so what she did was to have each student be an expert of a homework problem assigned, so that the next day if somebody didn't understand the problem, that person would be responsible for teaching that student how to do the problem. Depending on the amount of homework problems assigned each day, it depended on how many students were experts to a certain problem. She evaluated the students in the way that they would receive 10 points for accuracy and completeness of the solution, and another 10 points for an explanation of the solution. Each student had the opportunity of earning a total of 100 points over the course of the semester, but were not penalized if they did not answer a question. If they were absent on a day when they were supposed to be the expert for a problem, they lost their chance to earn their points for that day. When she used this strategy, the students did need some time in order to get a feel of this type of learning style, but after a short time this strategy was effective in getting students to participate in discussions about assigned homework problems. He stated, "Although this outcome may not seem impressive, it is a significant start, especially toward engaging those students who often do little or no homework" (Tripp 479).
Reaction: This teaching strategy really seemed to have worked for this class. However, when teaching a college course, it seems strange that he would have had a hard time getting students to do their homework. I think this teaching strategy could work for a calculus at St. Olaf, but not in the way of making sure students do their homework. It would be effective for when a student was having troubles with a particular problem. I think this type of strategy would be more effective in a high school math class. Since students in high school math are forced to be there, they are not always as motivated to the work as college students. Students go to college because they want to, so have a better chance of getting their homework done than high school students. Overall, I think this strategy is an effective one, and there's a chance I might use a strategy similar to this!