Keywords: Standards, Keyword 2, Optional..., Keyword 3, Optional...
Ref: Nathan13
Author(s): Burrill, Gail
Date: 1998
Title: Changes in Your Classroom: From the Past to the Present to the Future
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 91, #9, p. 800-6
Reviewer: Nathan
Date of Review: 28 April 2003
Burrill looks at how we taught math and how we teach math. She lists some of the misconceptions about math that are held by students and teachers today as stated by Loats and Amdahl in Algebra Unplugged. There is only one answer. Problems are solved step by step. Some people are good at math, some are not. Math is too hard for some to learn. Problem that take a long time are not solvable. Math is mostly memorizing. Only geniuses can understand formulas and equations. As we know, these are not true, but they are believed by many students none the less. Burrill also points out that we seem to track students too often and too early. Each school teaches different. One school’s A may be another’s C. This is the present for Burrill. Things must be changed for the future, and that is why the NCTM standards were created.
For the future, we must work with our fellow teachers, include technology, and change the way we address problems. We should be representing and creating relationships between the material and the students. Burrill states that NCTM’s role is to help math teachers meet the challenges that they face everyday. NCTM aims to give an equal opportunity to each student, get better prepared teachers in the classroom, and aid in what is taught. Good teachers are able to remove the fear of math from the students. But to do this, we have to adapt to the new ways the students learn. Math is changing, and is not scary.
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Keywords: Probability, Games
Ref: Nathan12
Author(s): Ismeal, Abdulcarimo
Date:
Title: The effect of use of cultural games in teaching probability syllabus in secondary school in Mozambique on students' performance and attitudes towards mathematics
Journal or Publisher:
Volume, Issue, Pages: Draft
Reviewer: Nathan
Date of Review: 23 April 2003
Ismeal's study was conducted in two towns in northern Mozambique. One town was taught using cultural games while the other was taught without the physical use of any of the games. Both a pre-test and post-test were administered and compared with interviews.
Ismeal pointed out that multiple studies have been conducted, aimed at improving the education methods in improving countries in Africa. One of the popular theorists had said that in order to teach effectivly, teachers must include cultural influence. Games have been used to teach every subject, especially mathematics in Mozambique. Ismeal implamented the use of the cultural games in the classroom to observe the effect on test results and the student's attitude to probability.
Suprisingly, Ismeal's results were not quite what was expected. The students as a whole improved from the pre-test to the post-test. The suprising result was that both the control, the non-game classrooms, and the classrooms with the game integrated methods showed very similar improvements in raw scores on the post-tests. The students that were taught using the games did score better on questions about the general concepts and did better overall even though their improvement amount was the same as the other students. Students who learned using the games said they enjoyed class when interviewed after the post-test. Overall, the students who were taught by using cultural games did better and enjoyed the class more. This is always a goal of teachers. If the students enjoy the material, they are more likely to learn it better and remember it. This is an effective teaching method in Mozambique and the US.
Keywords: Activities, Measurement, Connections
Ref: Nathan11
Author(s): Alvarez, Richard
Date: 1996
Title: How High Is the Water Tower
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 89, number 4, p. 274-278
Reviewer: Nathan
Date of Review: 9 April 2003
Students often wonder why they learn mathematics. This activity gets the students out of the classroom and using their math. Students are taught how to solve a series of problems and then given a related task. Students are to measure the height of a water tower. The problem is that it is impossible to drop a tapemeasure down. They must use equipment that measures angles to get numbers that can be used in conjunction with the math they learned in the classroom.
To teach measurement, we do not have to teach measurement directly. Sometimes, many times, when we want to measure something, there is not an easy way. Students should know how to measure objects in the most effective manner. Sometimes the most effective manner is not a direct means of measurement. This method has practical use and a historical perspective. For a long time, using multiple angles with the horizontal to determine the height of an object was the only way possible with technology.
Keywords: Geometry, Teaching Strategies,
Ref: Nathan10
Author(s): Lilbow, Herb
Date: 1997
Title: Exploration in Geometry: The "Art" of Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 90, Number 5, p. 340-342
Reviewer: Nathan
Date of Review: 2 April 2003
In this article, Libow identifies an instance when he had an idea that connected two theorems in geometry concerning a circle and its chords and extended chords. After noticing that both of the theorems state that the result of the equation in a constant when the variables are altered, he wanted to know what this constant was. By doing these side by side, he noticed that the constant was identical. He continued on to write his own theorem which he called "The Chord-Line Theorem.
Now, this article mainly focuses on Liblow's discovery, but that is not the reason for the article. The article actually is to draw our attention to the fact that we teach too much mathematics and not enough of how math is interesting. Liblow states that math gets boring for all involved, the students and the teacher, if we do not show the artistic experience that exists within math. Students like it when the teacher is learning something at the same time. They like it when the light bulb goes on in the teacher's head as well as their own. We should not just teach mathematics, we should also teach the reason why we enjoy it. We should teach that it is interesting and innovative people thrive in it. New ideas come from people who are curious. And students can be very curious if allowed.
Keywords: Assessment, Teaching Strategies,
Ref: Nathan8
Author(s): Blanton, Patricia
Date: 2003
Title: Action Research to Evaluate Student Achievement
Journal or Publisher: The Physics Teacher
Volume, Issue, Pages: April 2003, Vol 41, #4, p. 552-553
Reviewer: Nathan
Date of Review: 31 March 2003
The ways in which we look at the results of assessments is important to how we view the progress of students. Should we look at the overall class average, the number of passing students, the existence of the bell curve? High-stakes assessment tests uses overall scores to designate scholarships, allowing acceptance to programs, and effectiveness of instructional methods. With the new "No Child Left Behind" legislation will cause teachers to show that they are providing instruction that is helping students meet the NAEP standards according to Blanton. To do this, we can not only look at the numerical results of exams. We have to write exams that actually look at the standards taught and analyze the student responses for understanding.
Blanton outlines 6 areas to work on that will identify specific areas of instruction that need to be improved by each teacher. 1) We must know the objectives of the curriculum so that we can use our time in the most effective manner by covering the important topics with more time then the ones that are not as essential in the curriculum. 2) Identify the method that will be most effective to teach the topic. 3) After each class, write some assessment questions so that the ideas of how the class went are fresh in your head and it will be easier to compile the finished assessment when the time comes. 4) Write assessment questions that address the goals and analyze the assessment for overage of the topics relative to the amount of time spent teaching them. 5) After correcting the assessment, look at the questions students did not do well on and make connections to their actual understanding of the topic individually and as a class. 6) Ask for more then the response to a question, as for the reasons why the students responded such. These methods can help to refine teaching strategies.
I think this is a effective way to look at the results of assessment. From my experience, the percentage or numerical result is looked at too much and not the actual responses. A student can understand the material and not get a good composite score on an exam and vice versa. Also, some exams ask too many questions about material that was covered briefly and few questions on material that was covered for a longer time. By actually looking at the exam itself and what the students did on the exam, we can better teach to our students and be aware of their understandings of the material.
Blanton, being a physics professor, makes an analogy between teaching physics and a house. "A good foundation must be established before continuing with the structure. Identifying the flaws requires careful inspection. If you ignore the flaws in the foundation, the resulting structure will be weakened. The ultimate goal of assessment is to identify the strength of the foundation and determine the instructional strategies that are effective in helping students construct a solid foundation."
Keywords: Teaching Strategies
Ref: Nathan9
Author(s): Singer, Jonathan E., Tai, Revital (Tali), Wu, Hsin-Kai
Date: 2003
Title: Students' Understanding of the Particulate Nature of Matter
Journal or Publisher: School Science and Mathematics
Volume, Issue, Pages: Vol 103(1), January 2003
Reviewer: Nathan
Date of Review: 17 March 2003
This report of research was part of a large-scale urban reform. This portion looks at the AAAS' standards for middle school science concerning the knowledge of the matter. The study looked at the progress made by multiple classrooms when project-based science was implemented. The results are extremely positive, but I am left wondering how much of the progress is because of the methods used and how much of it is because of the normal learning of the students because the article does not reference any data taken from a classroom when project-based science was not used. < P>Project-based science is aimed at constructivist learning methods by engaging students in investigations of the material. These investigations are usually started with a driving question the opens the door to foster student conative thought and collaboration. T he project-based instruction contained four components; context for the concepts, taking advantage of learning technologies, making multiple representations (one of the core ideas in project-based science as I understood from the article), and having the students learn the events in a logical manner.
The unit was initiated by a driving question about air quality during a walk outside as a class. Back in the classroom, the students were involved in a variety of activities. They drew pictures as a means of pre-assessment, sharing and explaining them to the class, followed by a range of activities following the "predict-observe-explain" inquiry method. The students were engaged in activities that focused on all three properties of air; macroscopic, microscopic, and molecular. No activity was used to teach all three, but each had it's speciality. For example, looking at the macroscopic level, students were packed tightly together and told to move slowly to represent the atoms and molecules in a solid. The students did take a midterm exam during this process and a final exam 10 days after finishing the unit.
The results were very encouraging. All the classrooms showed progress, even with the final exam being 10 days after the completion of the unit. This shows that the students actually learned something and are more likely to remember it because of their involvement. I think it is well known that we learn better when involved. This is another example of such and another example of the fact that urban students can learn just as well as students that are considered better off. The use of a variety of representations (verbal descriptions, drawings, models, and equation-like expressions) proved to be an effective means by with to teach middle school students the properties of matter. This article offers some general guidance to using project-based science and a good amount of factual support that can be used to influence administration.
Keywords: Curriculum, Algebra, Technology
Ref: Nathan7
Author(s): Heid, M. Kathleen
Date: 1996
Title: Curriculum and Evaluation Standards for School Mathematics: Algebra in a Technological World
Journal or Publisher: National Council of Teachers of Mathematics
Volume, Issue, Pages: Addenda Series, Grades 9-12
Reviewer: Nathan
Date of Review: 10 March 2003
This is a good reference for teachers looking to take advantage of technology in their algebra classroom. The book goes into six areas of the combination of algebra and technology with activities that can be used in the classroom. The six sections also contain small examples of what is being referred to.
The six sections include the following; The Future of Algebra in a Technological World, Changes in Learning and their Consequences for Teaching and Assessing, A Functions Approach to Algebra, Extending a Functions Approach, Matrices, and Symbolic Reasoning. These cover uses of the technology, how it effects the classroom, and applications in some large curriculum areas.
This does look like a good reference for algebra teachers in the advancing world including technology. The activities are great for the teacher that is searching for activities to incorporate the new movements in technology in the algebra classroom.
Keywords: Standards
Ref: Nathan6
Author(s): Martinez, Joseph G. R.; Martinez, Nancy C.
Date: 1998
Title: In Defense of Mathematics Reform and the NCTM's Standards
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 91, Number 9, pp. 746 - 748
Reviewer: Nathan
Date of Review: 6 March 2003
Martinez and Martinez defend the current national standards for mathematics education. They state facts about the progress that has occurred since the standards have been released. American students are improving in every category. They state that it is because the standards call for a higher lever of education, that we are improving. The standards also include teaching strategies that will continue this increase.
Martinez and Martinez do bring up one problem supposedly related to the standards. There are complaints that they so no promote multiculturalism. The evidence that the standards are not promoting the education of multicultural, minority groups is that fact that the gap between achievement is not changing as rapidly as hoped. To counter this, Martinez and Martinez point out that all groups are improving, including minority and white students.
Many people are concerned with the results of TIMSS in connection with American student's achievement in mathematics, but, according to tests among only our students, we are continuing to approve. Because of this, we should have faith that the reforms that have previously occurred are of help and we should continue to reform to continue improvement on all fronts.
Keywords: Assessment,
Ref: Nathan4
Author(s):
Date: 1997
Title: Improving Classroom Tests as a Means of Improving Assessment
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol 09, #1, p. 58 - 64
Reviewer: Nathan
Date of Review:
Using tests and exams as a means for assessment is common place in mathematics. Most of the time, the tests contain simple questions that are easy to grade and easy to see if the student knows a particular fact. This article calls for a change in that. Teachers, especially math, should try to move forward in their means of assessment. Testing what facts a student can memorize for one class period is not a good means by which to measure the progress in the classroom. Thompson and all call for "A shift toward judging the progress of each student's attainment of mathematical power, and away from assessing student's knowledge of specific and isolated skills." And "a shift toward using multiple and complex assessment tools, and away from sole reliance on answers to brief questions on quizzes and chapter tests."
The article makes reference to some statistics about the importance of tests on the grades of high school students in math classes. Most students are driven by the grades they receive. That is the means in which they are used to receiving feed back from the teacher. To make these tests actually examine how much the student is learning, we should move away from "solve this problem," multiple choice, and closed short answer questions and move to open-ended, real context oriented, technology-oriented, reasoning, and representative questions.
This is a good article for when you need some alternatives to test questions. The questions advised are not as easy for the students to answer, they are forced to think. They will take more time to answer and more time to correct. That is the trade off of actually discovering what the students have learned. This article offers many alternative to a main stay in assessment, tests, that can actually discover what the students have learned towards the standards.
Keywords: Technology, Activities,
Ref: Nathan5
Author(s): Picciotto, Henri
Date: 1996
Title: Make These Designs
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 89, Number 5, p. 424-427
Reviewer: Nathan
Date of Review: 3 March 2003
Technology is increasing in the classroom. Picciotto offers an exercise to investigate the effect of changing the variables in the equation y=mx+b on the graphs. Students are given sample screen shots that they are to duplicate.
Picciotto made an effort to present this exercise as a means in which students will become greatly involved and excited about. I can see how it can aid in the teaching of the equation for a line, but I am unsure about potential effectiveness in encouraging the majority of students to explore on their own.
Picciotto does make an important disclaimer; technology is not a substitute for teaching. This exercise is an aid, not the a stand alone way to teach an equation. Students that do get involved in the discovery process can increase their understanding, but I do not see this as the original idea that is usually looked for when attempting to include technology in the classroom.
Keywords: Activities, Games, Problem Solving
Ref: Nathan3
Author(s): Larson, Anne. Koca, Robert M Jr. Weening, Fredrick
Date: 1999
Title: Developing Mathematical Reasoning Using Attribute Games
Journal or Publisher: Mathematica Teacher
Volume, Issue, Pages: Vol. 92, Number 9, p. 768 - 775
Reviewer: Nathan
Date of Review: 19 Feb. 2003
The card game called Set can be used to help develop mathematical reasoning skills. Set was played with groups of junior high, senior high, college freshman, and sophomores and a set of questions was asked about the game. The game consists of 81 cards with four categories that need to be combined to make a set. The questions ranged in difficulty and need for analytical thinking. There were a variety of methods and problem solving techniques that were used at the various levels. Strategies were developed to play the game and to answer the questions. Overall, the students enjoyed the game and seemed to enjoy the problem solving that was added to the game while developing reasoning skills.
I found this to be a great method to develop skills and I had never heard of Set. Any method of teaching specific skills during an entertaining activity is great, but a game that helps develops problem solving skills is even better.
Keywords: Teaching Strategies, Calculus
Ref: Nathan1
Author(s): Hammack, Richard; Lyons, David
Date: 1995
Title: Mathematics Teacher
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: Vol. 88, # 5, pg. 374-375
Reviewer: Nathan
Date of Review: 11 Feb 2003
A good alternative for teaching logarithms. If students are stuck with the concept of
visualizing the y=log(a) x, try using what Hammock and Lyons call the "a-box" method of
looking at the inverse. A good refresher on ideas that there is always an alternative way.
Keywords: Technology, Teaching Strategies,
Ref: Nathan2
Author(s): Slavit, David; Cooper, Kevin; LoFaro, Tom
Date: 2002
Title: Understandings of Solutions to Differential Equations Through
Contexts, Web-Based Simulations, and Student Discussion
Journal or Publisher: School Science and Mathematics
Volume, Issue, Pages: 102(8), December 2002, pg 380-388
Reviewer: Nathan
Date of Review: 12 Feb 2003
A study was conducted to investigate the benefit of using technology, specifically web-based technology, to improve the instructional methods of teaching elementary differential equations. It is known that students learn better when they are involved in the discovery process. This study was aimed at using the technology as a tool to discovery. The results of the study could conclude that web-based technology no only make the job of creating applications for teachers easier, but has made learning easier by supplying real-world contexts. Of the questions asked in pre-course and post-course exams, all but one improved greatly. The authors conclude that technology, specifically the WWW, can improve student understanding with simulations of meaningful representations.