Curriculum Guide
Mitchell Schoenbrun
Current Research
Summary
Gender differences in Mathematics are universally accepted as fact, but the proposed reasons are not. A conference in 1993 indicated that in an experiment in Shanghai China a reversal of this trend was found when "teachers adopted a non-sexist attitude in teaching mathematics to girlsÖ" The authors wish to investigate this idea by reviewing TIMSS data for 7th and 8th grade students in four Asian nations. TIMSS data is a multi-country comprehensive study of student's mathematical abilities. The authors discovered results in Singapore in which girls scored better than boys refuting some biological explanations for the gender gap.
Connection to Literacy
An indication that gender differences in mathematical ability are due to cultural biases is quite relevant to the teaching methodology applied. Teachers, both male and female, should be very concerned that their own unconscious biases might affect female expectations and achievement.
Significance of Research
The paper is merely an intelligent speculation on reported data, although it does strongly suggest that follow up research be conducted to reveal the nature of the biases indicated, and methods to overcome them.
2) Peer Assessment in Problem Based Learning, Dominique M. A. Sluljsmans, George Moerkerke, Jeroen J. G. van Merrienboer, and Filip J.R. C. Dochy, Studies in Educational Evaluation, Volume 27, 2001, P 153-173
http://opac.sfsu.edu/search/tStudies+in+Educational+Evaluation/tstudies+in+educational+evaluation/1,3,4,E/l856&FF=tstudies+in+educational+evaluation+online&1,,2,1,0Summary
While problem based learning in mathematics is practiced widely, assessments still focus on content knowledge, rather than the skills that problem based learning promote. The authors believe that this will encourage an attitude in students to focus away from these skills and toward learning to take the tests. In addition, the authors feel that in line with the constructivist point of view of problem based learning, that students should themselves become responsible for their own assessment, and that such assessments can be reliable.
Their first experiment to support this idea was to take 27 university students, engage them in a period of problem based learning, and then have them fill out peer evaluations for their fellow students. The researchers used statistical tests on the data to help in the evaluation. The results of this experiment were promising but inconclusive. In a second similar experiment reported in this paper, they found more positive results.
Connection to Literacy
The research points to the possibility of student evaluations being a reliable assessment tool for problem based learning.
Significance of Research
While the research indicates positive results in this area, there clearly needs to be more investigation in the areas of concern that they report.
Summary
The author proposes a new theoretical approach to understanding the cognitive process of reading Cartesian graphs. The basic idea of this approach is that reading and understanding a graph, like reading text, heavily relies on prior knowledge. In order to understand a graph, you need to be conversant, not just in graphs themselves, but in their subject matter. The author supports his ideas with anecdotal examples that show that graph reading ability is neither age nor experience related, but dependent on whether the reader has proper referents to interpret the material.
Connection to Literacy
The ability to properly read a graph is an important component of literacy.
Significance of Research
This research suggests that in the teaching of graph reading, it is important to use graphs with referential material that will aid in the learning process.
Summary
The author reports on and tries to explain the extremely poor results in the province of Saskatchewan on a Canadian national standardized test in mathematics. Some of his conclusions are that the test evaluated content knowledge over problem solving ability. Other issues were a lack of comfort with mathematics by elementary teachers, lack of parental support, and the weekly amount of time scheduled in school for this subject, and an undemanding curriculum.
Connection to Literacy
Standardized tests as a tool of evaluation have the potential for many biases.
Significance of Research
The reasons behind the poor results of an entire province of school children in Canada in mathematics might lead to significant improved understanding of the learning process.
Note: I'm not sure whether this is a peer reviewed journal or not.
Summary
The article discusses the teaching of technology as one needing an interdisciplinary approach, one that combines mathematics, science, and technology (MST). The author suggests that "from a pedagogical perspective, studying disciplinary concepts via applications adds relevance to the learning experience." Also important to the author's point of view is the inclusion of the societal impact on society as part of its study. The author also reports the drafting of national standards for this area of study.
Connection to Literacy
Understanding technology is an integral part of literacy in our society.
Significance of Research
The importance of this article is to teachers in this field, and it appears to represent some well thought out, if very general, ideas on pedagogy.
Lesson Plan Critiques
Summary
In this lesson, the author teaches students a technique for multiplying two numbers that relies only on addition skills and the ability to multiply numbers by 2. The author claims that this method was invented by ancient Egyptians but is still practiced today.
Positive/Negative Points
The method described does work, but is not very useful. On the other hand, I think that this lesson might be very useful in giving students facility with numbers, i.e. number sense. The lesson plan is a bit thin on directions.
Adaptation
For a low performing class, I would probably use the lesson just as is. For more advanced students, I would like to draw their attention to the connection between this method and the way computers use binary to multiply numbers.
Summary
This lesson claims to review integer operations. I say this with tongue in cheek as after reading the lesson 5 or 6 times, I still could not figure out what was supposed to go on. It does involve breaking the class up into groups of three, each with a specific assignment. It also involves the groups looking at something on an overhead projector, and matching groups of 20 cards. The author wants you to give the winners of the contest a "raise a grade certificate." I guess this is safe since the students probably won't figure this lesson out either.
Positive/Negative Points
The lesson plan is incomprehensible. On the positive side, there isn't a chance I would try to use it or adapt it. I guess one could use it for hazing new teachers, as inÖ Here want to try a surefire lesson that always works.
Adaptation
I would not adapt this lesson. I would start from scratch.
Summary
Students learn about the "Tangram" shapes by starting with a square piece of paper, folding and cutting it, and making observations about the shapes. This is a fairly open ended lesson in which the students are encouraged to explore properties on their own.
Positive/Negative Points
This is actually a very productive type of activity. I've done similar types of things myself early in the year. It helps to get students familiar with a visual type of understanding that many do not start geometry with. A down side is that it fulfills no standards. I've also seen students have trouble bridging the concepts learned in this type of activity to the more formal concepts that occur in a regular geometry course.
Adaptation
I think the basic idea is fine. I would have the students work in groups on their observations. I also think that it would be more productive if the students reported their findings to the whole group, instead of just passing them in to the teacher.
Summary
This lesson is designed to teach students about exponential relationships. It starts with a money question that has to do with compound interest. The students use graphs as a way of investigating this phenomenon. Next the students look at world population and its similarity to the money problem.
Positive/Negative Points
Along with teaching a mathematical subject, this lesson makes students aware of the population problem. Although the author lists 7th-12th grade as the audience, I think that it would be a little too simple beyond 9th grade. Otherwise it seems like a good lesson.
Adaptation
I think that I would make the compound interest problem more realistic and therefore relevant. Something more like, what if you saved $10 every month, and it compounded at %7 monthly. How much would you have saved after thirty years?
5) Geometry Everywhere http://www.kodak.com/global/en/consumer/education/lessonPlans/lessonPlan076.shtml
Summary
This is a very unusual activity lesson. The students are broken up into groups and given cameras to use to photograph various geometric shapes. Afterward the students compile and label photon albums. The author claims that "The creative, inquisitive nature of the average and below average student came out to an unsuspected degree."
Positive/Negative Points
One has to be a little bit skeptical about whether the results reported are real, or whether this is just some good fun for the students.
Adaptation
I would add a little more structure to the assignment. For example I would request that the students look for certain types of shapes to photograph, some rectangles, some circles, maybe some images that clearly show perspective.
Individual Curriculum Activities
Note: I had a lot of trouble finding mathematical lesson plans that tie into popular culture, so I added the two following lessons in Physics, a subject I also am teaching.
Lesson Plan 1
The Physics of Amusement Park Rides (1)
Objective
Students will get some real world experience in Physics problems by evaluating various amusement park "thrill" rides. Using the physical concepts of momentum, energy, and force, they will investigate the physical changes on participants in one of the following rides, or an alternative that they find on the Internet.
Six Flags "Superman Ride".
http://www.ultimaterollercoaster.com/thrillrides/superman/Supreme Scream
http://www.ultimaterollercoaster.com/thrillrides/supremescream/supreme.shtmlFree Fall
http://www.ultimaterollercoaster.com/thrillrides/freefall/Tower of Terror
http://www.ultimaterollercoaster.com/thrillrides/towerterror/Materials
For the first day of this lesson, students will only need calculators, and possibly internet access to the data on each thrill ride.
Prerequisites
This lesson is for Physics students at about the middle of the school year. It should be introduced about the time that the studying of Newton's laws, Energy, and momentum are complete.
Procedures
The teacher will introduce the lesson by picking one of the rides, and demonstrating the type of analysis expected. This will include determining the velocity, acceleration, momentum, and energy on a 150kg passenger on each of these rides.
Students will be divided into random groups of four, and given a choice of rides to investigate. Data for the ride will need to be downloaded from the Internet.
Students will need to produce a poster with a diagram of the salient aspects of the ride, indicating physical parameters at critical points in the ride. The students should differentiate parameters learned from the Internet, and those calculated and/or estimated using their knowledge of Physics.
The teacher will circulate among the groups to make sure that each group is on track. At approximately 10 minutes before the end of the period, each group will present their poster, and describe their results.
Assessment
Each group will be judged on following aspects of the project,
Literacy Aspect
By tying the subject matter into an area of popular culture, I hope to "hook" student's interest in Physics by showing that it is not just an esoteric subject in which perfect objects travel in perfect trajectories, but rather one that is a direct part of their lives.
Students will need to use technology, the Internet, as part of this lesson. The final product is a written cooperative effort.
Outcomes
Students should gain some experience in evaluating some real world scenarios in which physics is useful for analysis.
Lesson Plan 2
The Physics of Amusement Park Rides (2) Lab
Objective
Students will use their work from the previous class, along with dimensional analysis to create laboratory scale models that mimic the speeds, accelerations, and forces experienced on amusement rides.
Materials
Students will need their work from the previous day. The class will be conducted in the physics lab, and students will have access to small cars, tubes, ramps, and ball bearings. In addition, measurement equipment, such as timers will be available.
Procedures
The teacher will explain the objectives of the lab. Groups will remain the same as the previous lesson. Students will first calculate the parameters of scaled down versions of their "thrill" ride using dimensional analysis. After checking these calculations with the teacher, they will plan a construction that will simulate as many of the important features of the ride as possible. Finally, they will construct this model, test it, and analyze the data. Homework will be to complete the write up of the lab.
Note: the lab will probably take more than one 60-minute period to complete. This could be accomplished by extending it over two days, or by using a block period.
Assessment
Each student's individual lab will be graded for accuracy.
Literacy Aspect
By tying the subject matter into an area of popular culture, I hope to "hook" student's interest in Physics by showing that it is not just an esoteric subject in which perfect objects travel in perfect trajectories, but rather one that is a direct part of their lives.
The lab report will be an opportunity for them to use language in a technical, rather than a literary, manner.
Outcomes
Students should gain hands on experience in designing, building and testing a scale model.
Lesson Plan 3
Perspective Transformations as part of Video Games
Objective
To show Geometry students the relationship between geometric transformations and video game technology.
Materials
A video monitor hooked up to a computer loaded with the 3-D game, "Doom".
Procedures
The teacher will start the class by showing a short session with the video game in which the game arena will be walked around in. This will be the game "Doom" which uses a 2-D virtual world model that appears 3-D to the viewer.
Next the teacher will show how various objects on the screen change shape as the point of perspective moves around.
The teacher will draw a two dimensional representation of what is on the screen on the blackboard, and show how the transformations work graphically.
Students will then be given some transform problems to work on.
After completing these problems, individual students will be asked to come to the board to show their work.
Homework will be to draw a 2-D layout of a room, and then to draw what the room looks like from two different perspectives.
Assessment
Teacher will observe black board presentations, and any classroom discussion that ensues. Homework will be checked on the following day.
Literacy Aspect
Student will be encouraged to see the connections between technology, in this case computer games, and mathematics. Students will also have an opportunity to engage in discourse on a technical subject.
Outcomes
I hope that students will see a more direct connection between mathematics and a part of their lives, entertainment.
Lesson Plan 4
Pythagoris as both a mathematician, and as a historical figure.
Objective
To give students an historical perspective on the work of an important mathematician.
Materials
A two page historical description of the mystical cult of the Pythagoreans.
Procedures
Prerequisite, the class will have already worked with and proved the Pythagorean theorem.
The teacher will start the class by reviewing the Pythagorean theorem on the board. Namely for a right triangle, A2 + B2 = C2. The teacher will then ask the class to consider what kind of person they think Pythagorus and his colleagues must have been. Presumably they will think that he was learned and somewhat stuffy, what one might expect from a college professor. After no more than 5 minutes of discussion, the teacher will hand out the historical article.
Approximately 8 students will be chosen sequentially at random to read a paragraph from the article out loud. The article will describe how the cult of Pythagoreans believed that numbers/integers were what the world was made of. How they discovered that the square root of 2 was incommensurable, and how they eventually murdered one of their own for disclosing this fact.
Teacher will then show the simple proof that the square root of 2 is not a rational number, which was the cause for the murder. Then the teacher will ask some open-ended questions to the students, e.g. how do you feel now about Pythagorus and his followers? What do you think about their actions and beliefs?
Students will use the end of the period to write a short essay on how their knowledge of the Pythagoreans affects their feelings toward mathematics. If necessary, the can finish this essay for homework.
Assessment
Teacher will observe the discussion, and read the essays.
Literacy Aspect
Students will learn a connection between mathematics and history. Students will engage in a discussion on this connection, and will have to write about it.
Outcomes
I hope that students will see mathematics as not just a dry boring subject, but one in which historical figures were willing to murder each other over important ideas.
Lesson Plan 5
Geometric Evaluation of the McAteer Architecture
Objective
To give geometry students an appreciation for the need for geometry in architectural design.
Materials
We will use the McAteer Campus at 555 Portola drive an example of geometric architecture.
Protractors.
Procedures
Students will be broken up into groups, and given assignments to map out distance and angular relationships between the buildings of McAteer, with emphasis on the central atrium area between the buildings. Students will be given about 20 minutes to make their measurements. Then will reconvene in the classroom and come up with an overall design document.
Teacher will then lead the class in discussion considering the geometric relationships, and their importance to the ambiance of the school.
Homework will be an essay in which each student will be asked to give their ideas on how the geometry of the school affects them personally.
Assessment
The essays will be graded for effort and insight.
Literacy Aspect
The lesson, although somewhat informal, will stress the relationship between mathematics and work spaces. There also will be an
opportunity for students to practice their writing skills.
Outcomes
Hopefully students will make the connection between the physical structure of the school, how it functions, and geometry.
Resources
This organization provides high quality videos about important mathematical subjects. The video's may be obtained at cost, and then copied legally. Video's that I use in my own classes include, The Pythagorean Theorem, The Story of Pi, Similarity, and The Tunnel of Samos.
This site features lots of resources for math teachers including discussion groups and a problem of the week.