Keywords: Problem Solving, Proof...
Ref: Brian1
Author(s): Perlwitz, Marcela D.
Date: 2005
Title: Dividing Fractions: Reconciling Self-Generated
Solutions with Algorithmic Answers
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: 10, 6, p.278
Reviewer: Brian
Date of Review: February 15, 2005
Marcela Perlwitz writes about a lesson that was given where the students are supposed to solve a problem that required using division with fractions. In the problem, ten yards of fabric is to be used to make pillowcases. Each pillowcase consists of three-fourths of a yard and from this, the students are supposed to determine how many pillowcases can be made using the amount of fabric given. In this lesson, the students need to explain their answer. Hence, simply using the division algorithm is insufficient. At first the students struggle with the problem. Eventually, one student comes across a possible solution but it contradicts the solution given by the algorithm. The students become confused, as they do not understand why there is an inconsistency. The algorithm gives them the remainder of one-third. However, when they use there own method of solving the problem they get a remainder of one-fourth which seems more logical to them given the fact that a pillowcase only requires three-fourths of a yard of fabric. Yet, the students seem to trust the answer that the algorithm gives them over their own. Finally, one of the students figures out why the remainder is different and finds the relation between the “two solutions.”
Perlwitz admits that this lesson was used in a college class. Nevertheless, she does explain that the lesson is still relevant to middle school. Students should not learn algorithms just so that they can solve problems. Students need to learn how an algorithm works.
This lesson could have been easily made into a hands-on lesson that could be used to show middle school students how to divide using fractions. I think this might help steer students away from thinking that math is all numbers and possibly prevent some students from fearing the word “math”. This article also made me realize that it is odd how sometimes things are taught without an explanation being given. In all reality, I shouldn’t expect students to really remember or care about algorithms that aren’t given an explanation for how they work. As a result, I will need to remember this the next time I teach someone an algorithm.
Keywords: Connections, Geometry, Measurement
Ref: Brian2
Author(s): Bergner, Jennifer A., Groth, Randall E.
Date: 2004
Title: Making Mathematical Connections by Constructing
Tetrahedra
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 98, No. 5, p 298 - 305
Reviewer: Brian
Date of Review: February 17, 2005
The article was about a lesson that includes algebra, geometry, measurement, and data analysis. For the lesson, the students would spend five class days constructing tetrahedrons that are 5.5 feet tall. To start the lesson, students need to cover some of the basics of geometry. For example, students will need to know the definitions of an edge, midpoint, and trapezoid. In addition, students will need to know what a tetrahedron is and how to construct one. When this lesson was taught, the class discussed what they thought each definition was and eventually came to a conclusion about what the actual definitions are with the help of the instructor. Since the tetrahedrons were constructed from circles, students found the measurements of each of the tetrahedron. Then to find the correct dimensions based on the radius, students compiled their data and found the arithmetic mean. Students had measurements for the tetrahedron’s height, the radius of the circle, the tetrahedron’s slant height, and the tetrahedron’s edge length. Once students knew all of the correct dimensions, students were able to figure out the formulas to compute what a certain measurement would be given one of the tetrahedron’s measurements. On the last day, students finished the construction of their tetrahedrons.
While this lesson appears to be a fun project and incorporates
several content standards, I think the main focus of this project is
geometry and that it should be remain the focus. It seems that the
connections made limit the material covered for each of the content
standards. Furthermore, I think the connection between data analysis
and geometry is a little awkward. To show connections in math, it seems
like it would be important to show that one area is dependent on
another. In this lesson, I don’t fully grasp how constructing a
tetrahedron is dependent upon data analysis. However, I do really like
the fact that this is a lesson that doesn’t require a textbook and that
it is a hands-on project.
Keywords: Statistics, Activities...
Ref: Brian3
Author(s): Goldsby, Dianne S.
Date: 2003
Title: "Lollipop" Statistics
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 9, No. 1, p. 12 - 15
Reviewer: Brian
Date of Review: February 21, 2005
This article described a lesson that is centered on the Chordettes’ song “Lollipop”. For this lesson, the teacher played the song “Lollipop” for the students and afterward the students were asked what parts of the song were repetitive. The students identified phrases and sounds that repeated throughout the song. Then the teacher played the song again and the students were asked to count the number of times they heard each repetitive part. Having the students count the repetitions helped the teacher establish the concept of frequency. Students then displayed the number of times they counted each repetitive item in the song by making bar graphs. Goldsby suggests that this lesson can be made more advanced by only playing a small portion of the song and having the students estimate the total number of times that the each repetitive part is heard throughout the entire song. In addition, the author suggests that students can further investigate statistics by conducting surveys about music.
I think this lesson is an excellent way to introduce statistics to students. However, instead of playing “Lollipop”, I would choose an appropriate popular song that I know my students have heard and are familiar with. That way, I know that they would be engaged in the lesson. I also think this lesson can easily be adapted for a wide range of students from different ages and skill levels.
Keywords: Teaching Strategies, Algebra...
Ref: Brian4
Author(s): Steele, Marcee M; Steele, John W.
Date: 2003
Title: Teaching Algebra to Students with Learning Disabilities
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 96, No. 9, p. 622 - 624
Reviewer: Brian
Date of Review: February 28, 2005
This article gives tips on how teachers can help students with learning disabilities to learn algebra. Across the nation it is expected of high school students to learn algebra. In fact, some states require all high school students to take algebra in order to graduate. For students with learning disabilities this can be very challenging. In order for teachers to accommodate a student’s special needs it is important for the teacher to know about the student’s specific disability. This will help a teacher plan around what he/she might anticipate as being a difficulty for the student. The article recommends that teachers have students self-question and self-monitor themselves as they learn algebra. Students should create a checklist of the procedures they need to complete for each problem and the students should also explain why each step is performed. It is also recommended that teachers give students prompts to guide them, correct mistakes, remember the order of steps, and help them answer questions. In addition, teachers should help students create mnemonic devices.
Helping students understand algebra is crucial to a student’s ability to progress into the world of higher mathematics. It is very valuable for teachers to understand the basics about learning disabilities so that teachers aren’t preventing students from achieving. While this article was geared towards algebra, I don’t see why it can’t be applied towards any other area in math.
Keywords: Activities, Geometry, Connections
Ref: Brian5
Author(s): Schooler, Susan Rodgers
Date: 2004
Title: A “Chilling” Project Integrating Mathematics, Science and Technology
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 10, No. 3, p. 116 - 121
Reviewer: Brian
Date of Review: March 1, 2005
In this article, Susan Rodgers Schooler writes about how a technology class and a seventh grade advanced math class paired up to work on a project. To introduce the project the classes had a theme based off of the television show Survivor and the students were given a Tribal Council’s Challenge. For the challenge, the students were asked to form groups of three to four students and construct a container that would keep ice frozen the longest. Students were given specific rules to follow. Class time was divided into time for research, presenting designs, and constructing the containers. Overall the project took nine class days. At the end, the students tested their constructions. Students used math to create scaled drawings as well as measure the surface area and volume of their containers.
I remember participating in a project similar to this one when I was in high school. I think it is definitely educational but I feel that it is geared more towards science than it is geared towards math. However, I still feel this project has some value for a junior high math class but I would be hesitant to allow nine class days for it.
Keywords: Representations, Statistics...
Ref: Brian6
Author(s): Kranendonk, Henry A.
Date: 2004
Title: People Count: Analyzing a Country's Future
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 97, No. 1, p. 58 - 66
Reviewer: Brian
Date of Review: March 7, 2005
This article details a lesson involving applying data analysis to a real world situation. In the lesson, students analyzed United States population data. From the data, students were asked to predict future population growth. Students created linear, exponential and recursive models to extrapolate what the population size might be in the future. Throughout the lesson the students used calculators to graph their equations and create histograms. Furthermore, students used their calculators to find the projected population size from their recursive models. As a result of using the various models, students learned when each model should be used. Students compared their results with the Census Bureau’s project growth rates. In addition to working with the data, students discussed many issues related to population growth such as birth, immigration, and death rates.
I think this lesson is excellent example of using a real world problem with mathematics. Using data from the Census Bureau seems to give the lesson a greater importance than a worksheet with a hypothetical situation. In addition, having the students discuss issues relevant to population growth helps show how math is important to other disciplines. If I have to teach a lesson on creating models to represent data, I would definitely use this lesson.
Keywords: Connections, Algebra, Geometry
Ref: Brian7
Author(s): Kahan, Jeremy A; Wyberg, Terry R.
Date: 2002
Title: The Spot Problem: Connecting Points, Connecting Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 95, No. 1, p. 26 - 31
Reviewer: Brian
Date of Review: March 9, 2005
Kahan and Wyberg explain how a discrete math problem can connect geometry, algebra, graph theory, and combinatorics. They write about a lesson where students are given a circle with n spots where line segments connect each spot to all the other spots. Once all the spots are connected, the students need to find an equation that calculates the total number of regions that the circle is divided into. One method of solving the problem is by using a fourth degree polynomial function to model the pattern of differences of regions between circles with increasing number of spots. Another method involves using Euler’s formula for vertices and edges. Also, student may use combinatorics to find the function as well. Surprisingly, one student found his own formula using a previous problem, where the maximum number of pieces of pizza needs to be determined for n cuts. The student’s solution ended up being a lot quicker than the other methods. In addition, another solution can be found using Pascal’s triangle.
Personally, I find discrete math to be a lot of fun. I think this lesson is excellent for students who like mathematical puzzles and are learning proof by induction. My only hesitation regarding this lesson is that it requires the students to have prior knowledge of basic combinatorics and graph theory. However, if the students have a solid math background and are ready for a challenge then this might be the perfect lesson for them.
Keywords: Management, Issues...
Ref: Brian8
Author(s):
Thurston, Cheryl Miller
Date: 1975
Title:
Junior High? Good Grief!
Journal or Publisher:
Today's Education
Volume, Issue, Pages: Sept.-Oct.
Reviewer: Brian
Date of Review: March 15,
2005
Cheryl Miller Thurston’s article is filled with advice and warning for anyone who thinks they are capable of teaching junior high students. She explains that young adolescents are at a socially awkward stage in addition to their physically awkward stage. Thurston informs teachers to be prepared to ignore some of their student’s inappropriate behavior, dodge flying objects, be ready to made fun of, and understand the social relations of teenage boys and girls. She also gives advice on how to handle situations that may arise.
I remember junior high well enough to know that young teenagers do act differently than the rest of the population. Many of the things that Thurston mentions I remember experiencing some aspect of when I was in junior high. However, now that I am older and have some maturity I think it will be easier to handle those situations as a teacher than when I was a student.
Keywords: Number and Operation......
Ref: Brian9
Author(s): Roach, David; Gibson, David; Weber, Keith
Date: 2004
Title: Why is √25 Not ±5?
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 97, No. 1, p. 12 - 13
Reviewer: Brian
Date of Review: March 17, 2005
This article explains that it is important for students to realize that the root of 25 is not both positive five and negative five. The true answer is that x is equal to 5. The reason is that the function actually reads “the unique positive real number whose square is 25” (12). To clarify things, the article features a graph of the function and it shows that when x is equal to –5 then y is equal to 5 . The authors suggest that students should add in a step into their solution and write that since the root of 25 is equal to the absolute value of five, then x can be equal to both positive and negative five.
I have to admit that I find this issue to be rather subtle. At first I would have thought that the root of 25 is equal to both positive and negative five because I think of the problem as x^2 = 25. Even after reading the article the first time through, I didn’t fully understand. However, after looking at the graph it makes sense. Yet, I’m not too sure how important this correction is. I believe then when I teach roots, I will explain it according to the process given in this article but I still don’t think it is the end of world if my students don’t fully understand the concept. I would rather cover other material than dwell on this specific issue.
Keywords: Algebra, Curriculum
Ref: Brian11
Author(s): Friel, Susan; Rachlin, Sid; Doyle, Dot
Date: 2001
Title: Navigating Through Algebra in Grades 6-8
Journal or Publisher: Principles and Standards for School Mathematics
Volume, Issue, Pages:
Reviewer: Brian
Date of Review: April 6, 2005
The Navigating Through Algebra book introduces students to patterns, functions, and relations. The book is full of activities that help teach students with these topics. Many of these activities are hands-on and have the students working a lot with collecting, plotting, and analyzing data. The book starts out with having the students work with data and then eases them into creating linear relations with the data.
Overall, I think this is an excellent book because of the activities. I specifically remember students saying they liked science class when I was in middle school because of all the hands-on activities. If math classes became more hands-on, I'm guessing some students that didn't really care for math in the past might start to enjoy it a lot more.
Keywords: Geometry, Measurement...
Ref: Brian12
Author(s): Cuicchi, Paul M; Hutchinson, Paul S.
Date: 2003
Title: Using a Simple Optical Rangefinder to Teach Similar Triangles
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 96, No. 3, p. 166 - 168
Reviewer: Brian
Date of Review: April 12, 2005
This article presents a fun lesson that works with similar triangles. In the lesson, students using optical range-finding golf scopes to measure how far away they are from some flagsticks. Students line up the eight-foot flagsticks in the viewfinder slot of the rangefinder. Then using a ratio for similar triangles, the students calculate the distance from the flag using the height of the flag, the height of the viewfinder slot, and the distance from their eye to the slot. According to the article, the students' findings were quite accurate. In addition, the class decided to explore the problem further. Since the students were not measuring from the ground level, thus they weren't making a perfect ninety-degree triangle, they found a way to calculate the error in their findings.
The part I like the most about this lesson is that it has the students use a practical application of similar triangles. The only downside of this lesson is that in order to teach it you need to have access to some rangefinders.
Keywords: Proof......
Ref: Brian13
Author(s): Knuth, Eric J.
Date: 2002
Title: Proof as a Tool for Learning Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 95, No. 7, p. 486 - 490
Reviewer: Brian
Date of Review: April 12, 2005
Eric J. Knuth writes about how students can benefit from working more with proofs. Outside of geometry many math students rarely work with proofs. He states that the real educational value of proofs comes from presenting them and not necessarily developing them. Knuth continues on by saying that students should work more with presenting proofs so that students can become better at making conjectures, developing and evaluating arguments, and honing reasoning skills. All of these mathematical skills are a part of NCTM's principles and standards. He even shows that students can learn a lot from presenting the various ways to complete even a simple proof.
A lot of the work that I first did with proofs was on developing them. I don't remember learning much mathematics from them. However, after really working with proofs in college, especially my geometry class, I found that analyzing the content of the proofs really helps with understanding mathematical concepts. I agree with the author and I think that math teachers should try to incorporate more proofs into their classes and change the focus of proofs towards presenting them.
Keywords: Number and Operation, Curriculum...
Ref: Brian14
Author(s): Reys, Barbara J., et al.
Date: 1996
Title: Developing Number Sense in the Middle Grades
Journal or Publisher: Curriculum and Evaluation Standards For School Mathematics Addenda Series, Grades 5-8
Volume, Issue, Pages:
Reviewer: Brian
Date of Review: April 6, 2005
One of the focuses of this text is "number sense". With "number sense", students take new information they have learned about the characteristics of numbers and connect it to old information they have already obtained. Throughout the book, students are presented with various situations to help them learn about numbers. Many of them are practical to everyday life and feature subjects that students might be interested in such as video games and television. One of the main concepts taught in this book is magnitude. The other big concept is fractions and decimals. Overall, the book's lessons are short and straight to the point. As a result, the teacher will need to adjust the lessons to generate launches, incorporate manipulatives, and create additional problems.
If I had the choice, I don't think I would hesitate to use this book. I really like the conscious effort by the authors to make the problems interesting. I think students prefer to do problems that are applied to something that interests them. Furthermore, the ideas and activities in this book are laid out well.
********************
Keywords: Puzzles, Discrete, Representations
Ref: Brian14
Author(s): Fujimura, Kobon
Date: 1978
Title: The Tokyo Puzzles
Journal or Publisher: Charles Scribner's Sons
Volume, Issue, Pages:
Reviewer: Brian
Date of Review: April 19, 2005
The Tokyo Puzzles is a book full of puzzles that requires the use logic, geometry, graph theory, and combinatorics to solve them. One thing that sets this book apart from other puzzle books is that The Tokyo Puzzles was written by Kobon Fujumura, who had established celebrity status in Japan for his love and wisdom of puzzles. The book's introduction, written by Martin Gardner, says, "If you hated math in school, it wasn't because the subject is dreary but because you had dreary teachers who in turn disliked mathematics. Mr. Fujimura is not a dreary teacher."(p. 4) Many of the book's puzzles seem similar to other puzzle problems I have seen. However, Fujimara had several geometrical puzzles that involved matches that were unfamiliar, which definitely shows his ability to translate mathematical concepts into creative puzzles. It also should be noted that the answers along with their explanations are featured in the back of the book.
I think one of the reasons that puzzles are great ways to teach math is that a good puzzle comes with a good launch and it involves applying mathematical skills. At first, I was skeptical that all of these puzzles could be used to effectively teach people mathematics. After opening the book, I began looking at a problem that required logic to solve it. In the process of solving it, I had to write some things down to sort my thoughts. While doing so, I inadvertently used mathematical symbols to abbreviate my ideas. After noticing what I had wrote, I had realized the full power of puzzles as a teaching tool.
Keywords: Teaching Strategies, Representations, Connections
Ref: Brian15
Author(s): Bay Williams, Jennifer M.
Date: 2005
Title: Poetry in Motion: Using Shel Silverstein's Works to Engage Students in Mathematics
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 10, No. 8, p.386 - 393
Reviewer: Brian
Date of Review: April 19, 2005
Jennifer M. Bay Williams writes about a way to use literature to help teach mathematics. Her article tells how Shel Silverstein's poems can be used to help teach middle school math. One of the lessons uses "Eighteen Flavors", a poem that revolves around an ice cream cone with eighteen scoops of ice cream, to get students to analyze data and create algorithms. In this lesson, the students attempt to figure out the height of the eighteen-scoop cone by creating a model. From the model, the students make a chart and then write out in words a method of solving the problem from what they notice in their chart. After their method is put in words, the students are asked to write it out using symbols instead of words. Using the poem "One Inch Tall", students use their own height to investigate a world where a character is only one inch tall. The students cut a string the same length as their height and then fold the string so that it is only an inch. Then the students try to estimate what the height of other objects would be by measuring them with their string. After the students estimate their measurements, they are able to compare them to ones that they obtain with measuring tape. In another lesson, students use a poem about shoes to learn about statistics and probability. The article also features a lesson from the book The Missing Piece to teach arc lengths and angles.
For the right age level, using Shel Silverstein poems seems like an excellent way to launch a math lesson. In addition, these lessons seem pretty ideal for middle school math teachers who work in core teams. Depending on what the English class is doing, the math class could try to use the same content as a launch. However, this could cause some discontinuity in the order in which math lessons are taught. Since Silverstein's poems have varying topics, his poems might not form a cohesive math unit.
Keywords: Technology, Teaching Strategies, Statistics
Ref: Brian16
Author(s): Baker, Paul L.
Date: 2003
Title: Using FreeCell to Teach Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 16, No. 6, p.406-410
Reviewer: Brian
Date of Review: April 20, 2005
Paul L. Baker shows how he has been able to incorporate his love for the game FreeCell, a computer card game that can be set up in 32,000 different ways, to help teach mathematics. Baker first brings up the topic of whether or not the level of difficulty increases with the number of games played. Since the game keeps statistics of games lost and won, students can attempt to find a solution to this question by setting up an experiment. In the experiment, students can keep track of which number game or way that the game is set up comes after each won or lost game. In addition, students can see if the ways the cards are stacked are actually random. Moreover, students can investigate if the way that FreeCell selects each new game is actually random. Baker's class used the central limit theorem to analyze this and found that the standard deviation was too great for the game to be random. Besides probability and statistics, FreeCell can be used to study proof. Some of the games in FreeCell are rather difficult and it may cause students to wonder if winning the game is even possible. With this in mind, students can try to find a counterexample by determining a way to win the game or find a way to prove that winning the game is impossible.
I really do not have much experience playing FreeCell but it does seem like an interesting way to present math problems. Obviously, it would be difficult to have a unit on FreeCell but the game still does have its usefulness for informal problems outside of class and introducing problems and topics in class. Most importantly, this article shows that teachers can look into their own hobbies and technology that they use and find the mathematics involved so that they can find new ways of teaching.
Keywords: Puzzles, Connections, Discrete
Ref: Brian17
Author(s): Yolles, Arlene
Date: 2003
Title: Using Friday Puzzlers to Discover Arithmetic Sequences
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 9, No. 3 p.180-185
Reviewer: Brian
Date of Review: April 25, 2005
This article tells of a way to utilize puzzles in order to help students learn arithmetic sequences. Arlene Yolles gave her students five different puzzles and spread them out over several weeks. The first puzzle was introduced to the students as a problem that wasn't impossible and can be done using mathematical knowledge that they already know. For the first puzzle, the students were asked to sum the integers from one to one hundred. A few weeks later, the students were asked to find out for a group of ten people how many handshakes need to take place for each person to shake everyone else's hand. After few more weeks, students were presented with a problem that centers on how many candles are burned on one menorah during Chanukah. A few weeks after that puzzle is given, students were asked to find out how many presents are give out on the twelfth day of Christmas according to the song "The Twelve Days of Christmas". Finally, the students were given the problem of finding the number of ways to divide a clock into two equal halves so that the sums of the numbers on each side are equal. Following, the students were asked to connect the solution to the clock puzzle to previous puzzles. Eventually the students saw the pattern and were able to establish a formula.
One thing I really like about this lesson is that it is an ongoing project. I think high school and junior high classes can sometimes become monotonous. Therefore, I think it is good to have an activity that can be integrated into the syllabus so that at least one Friday a month is spent working on a different type of activity than the other class days. Additionally, by spreading the activity out over several weeks, students are able to develop their own problem solving skills.
Keywords: Problem Solving, Probability...
Ref: Brian18
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: Vol. 96, No. 5, p.328-332
Reviewer: Brian
Date of Review: May 2, 2005
This article details a problem that can be evaluated in several different ways. In the problem, students investigate a problem where the New York Mets are playing the New York Yankees in a series where the winner needs to win four games in order to win a monetary award. So far, the Yankees are up two games to one. Due to an umpire strike, the money is to be divided based on the probability of each team winning. One method that students can use to find a solution to the problem is to simulate the games played using a calculator or a computer. A second way of solving the problem is to create a tree diagram and find out what events can happen next after each team wins. Moreover, a third way to solve the problem involves using a generating function in the form of (y+m)^x. While all of these methods are different, they all yield the same answer, which shows students that there is more than one correct way to solve a problem. The authors write that even if the students are not interested in baseball, a similar problem can be created using another topic.
I personally think that this problem looks like it would be fun to solve but if
I didn't have any interest in baseball I probably wouldn't agree. Since the
students in a class will most likely have a variety of interests, if I were to
teach this lesson, I would try to make a few different versions of the problem.
I also really like how this problem can be solved using more than one method.
Too often, it seems that students are confined to think a certain way in order
to solve a problem. This problem allows them to explore different approaches
for finding a solution
Keywords: Teaching Strategies, Equity...
Ref: Brian19
Author(s): Deitte, Jennifer M.; Howe, R. Michael
Date: 2003
Title: Motivating Students To Study Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 96, No. 4, p.278-280
Reviewer: Brian
Date of Review: May 2, 2005
In order to help motivate first-year college students in an algebra class, students were assigned to complete a project to help inform them of the importance of mathematics. The students could choose from several different projects. For one of the projects, students could gather information about a contemporary mathematician. In another project, students could analyze data of the level of math completed by students and compare it to the level of education attained by each student. Moreover, another option was to investigate a career in math. Lastly, students could interview their advisor or another faculty member about what math they use in their lives. After completing the project, students were asked to rate how much they enjoyed each project. Of all the projects, students were motivated most by interviewing a faculty member.
While this project was used at a college level, it could easily be used in a
high school or a middle school. In fact, this assignment might be better for
younger students. It seems that students strictly rely on learning math from
their math teacher and their math book. I think it is valuable to have students
to learn mathematics and its importance from outside sources so that students do
not think that math is only important because they need to take it in order to
graduate. Probably one of the reasons that interviewing another faculty member
was so successful is that the faculty member was probably able to convey how
useful math is even though learning it may seem irrelevant or tedious. A goal
for all math teachers is to teach math to students in an exciting manner that
shows the relevance of the material to the students' lives. Combining this goal
and the project in the article should really help improve the how students
perceive math.
Keywords: Probability, Connections, Statistics
Ref: Brian20
Author(s): Lyublinskaya, Irina E.
Date: 2003
Title: How Fair is the Drug Test?
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 98, No. 8, p.536-543
Reviewer: Brian
Date of Review: May 8, 2005
Lyublinskaya writes about a lesson to teach conditional probability which can also be easily integrated with other areas of math. In the lesson, students investigated drug testing. Using a drug test where 3% of the population is assumed to be drug users, students applied their knowledge of probability to figure out the percentage of false positive tests. To start, students assumed that the test is 99% accurate. Then the students found the probability for a 95% accurate test. According to Lyublinskaya, students were amazed at how high the percentage of false positives there were with a 95% accurate test. Students then tested what the probability is for an individual to test false positive twice consecutively. After figuring out the conditional probability, students used the formula that they had to calculate iterations. From the iterations, students moved on to graph logistic growth models from the iterations. In addition, students also looked at differential equations involving the iterations that they had calculated.
This is a pretty interesting lesson on how to connect several mathematical concepts to a real world problem. However, all of the math used in this lesson might be a little advanced for some high school math classes. Yet, the conditional probability part could be done as a group project during a probability unit. Furthermore, students could be guided to learn some of the basics of the other math ideas tied into the conditional probability.