Keywords: Curriculum, ,
Ref: Lisa1
Author(s): Bedford, Crayton
Date: 1998
Title: The Case for Chaos
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 91(4), pp.276-281
Reviewer: Lisa
Date of Review: March 28, 1999
Chaos theory and fractal geometry are beginning to be taught as units in many high schools. Crayton Bedford makes a case for offering a semester-long class which incorporates chaos theory with students' knowledge of algebra and trigonometry. Students leave the class with a new way of seeing the world, and it helps them reflect on aspects of order and disorder, searching for patterns, and working with rigorous mathematical techniques. After outlining the basics behind chaos theory, dynamical systems, and fractals, Bedford gives a brief summary for the following 8 units to be used for a high school course:
I thought this article is an excellent source for information on teaching fractals and chaos. A class on chaos combines the beauty of math with rigorous demands in a relatively new and useful branch of mathematics. I was introduced to this topic as a high school student and feel that other students may be fascinated and motivated by studying math in this context. Offering a class on chaos theory also relieves those teachers who wish to squeeze in a unit of their already full schedule.
Keywords: Geometry, Activities,
Ref: Lisa2
Author(s): Kennedy, Joe; McDowell, Eric
Date: 1998
Title: Geoboard Quadrilaterals
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 91(4), pp.288-290
Reviewer: Lisa
Date of Review: 3/31/99
Geoboards are helpful tools for students to explore the properties of geometric figures. Beginning with a 3x3 peg geoboard, students can find specific geometric shapes (trapezoids, non-square rectangles, etc.) and progress to more general quadrilaterals on larger boards, recording their findings. As more figures become possible, the students must organize their findings and divise ways to account for all possible figures. Counting the quadrilaterals on each size geoboard and coming up with ways to check congruence will help a student's understanding of the principles behind quardrilaterals. These properties can be checked against the triangle theorems, which students will realize do not hold.
Geoboards also help visualize rotations, reflections, and translations. In addition, parallel lines with equal slope and the Pythagorean theorem can be confirmed using geoboards.
After reading this article, I realize how geoboards may help
visualize aspects of geometry that many students may have
difficulty with. If properly guided, the activity may be
great in promoting hands-on exploration, creativity, and
thoughtfulness. Many of the properties of quadrilaterals can
be discovered using a geoboard, and students have an opportunity
to check their hypotheses and work at their own pace.
Keywords: Technology, Teaching Strategies,
Ref: Lisa3
Author(s): Zucco, Cathleen
Date: 1998
Title: Evaluating Mathematics Videotapes for Use in the Classroom
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 91(4), pp.348-351
Reviewer: Lisa
Date of Review: 3/31/99
Videotapes are not often used in the math classroom, and Cathleen Zucco believes that video technology could enhance instruction at the high school level. This article contains criteria for evaluating and effectively using a videotape in the high school math classroom. The tape should contain the elements of a good math lesson: specific math objectives, introductions and summaries, labelling of properties and figures, examples with step-by-step solutions, real-life applications and a historical perspective.
The pace should be moderate so that students are able to understand the material but are not bored. Engaging the students in problems and questions encourages student participation and attentiveness. In addition, the narrator should sound enthusiastic and appealing, with the aid of music, graphics, cartoons, or other stimuli.
If used properly, mathematics videos could be a helpful addition to
a classroom. However, the teacher needs to use the video as a lesson
aid and not a replacement for the lesson itself. It needs to be
discussed by the teacher at appropriate intervals, practiced by the
students, and integrated into classroom activities. Although, I don't
believe that videotapes should be used extensively in a math class,
occasional use in a creative and appropriate manner may add to a math
curriculum. This article was also helpful in listing good math videos
under subject headings.
Keywords: Communication, Assessment, Teaching Strategies
Ref: Lisa4
Author(s): Mayer, Jennifer; Hillman, Susan
Date: 1996
Title: Assessing Students' Thinking Through Writing
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 89(5), pp.428-432
Reviewer: Lisa
Date of Review: 4/3/99
Writing is an important means of communication between the math student and teacher. The ability to effectively explain mathematical reasoning and pinpoint difficulties is a learning tool for students and helps develop their math skills. Journals, laboratory reports, and portfolios are all types of writing which encourage thought and provide valuable information about the students' thinking not as evident through traditional assessment methods.
Journals monitor a student's progress and reflect attitudes towards math. The teacher is also aware of the level of understanding or confusion the student has about a particular concept. Laboratory reports follow a group activity, and allow reflection on their discoveries as well as any difficulties, solutions, and conclusions. Portfolios that include entries for different problems encourage clear explanations of their solutions and problem-solving strategies. Students meet with peers to review and edit their work. The teacher uses these to evaluate students' achievement and growth.
Writing builds confidence and enables students to demonstrate their understanding. As the year progresses, their logic becomes more focused, they are able to ask more specific questions in class, and they challenge themselves to ask "why" and "how."
I believe that journals, lab reports, and portfolios are extremely effective and informational to both teachers and students. Although a substantial time commitment is required, a committed teacher will find the information they receive beneficial for lesson structuring and better communication with their students.
Keywords: Assessment, Standards, Teaching Strategies
Ref: Lisa5
Author(s): Driscoll, Mark
Date: 1995
Title: "The Farther Out You Go...": Assessment in the Classroom
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 88(5)
Reviewer: Lisa
Date of Review: 4/5/99
In order to make the NCTM Standards a reality in the schools, assessment must be combined with instruction in the classroom. Many students develop alternate ideas from a teacher's intended meaning that lead to lasting misunderstandings. A system of assessment which uses the process of inquiry to question and receive feedback can help determine whether mathematical understanding is met. Making instructional decisions and monitoring the progress of students take place in this process. The four steps include planning the activity, gathering evidence, interpreting evidence, and using evidence.
The planning of activities should include a reflection of the teacher's personal beliefs about math and his/her students.
An awareness of gaps in prequisite knowledge and the giving of more broad understanding-based questions (through different means of communication, more open-ended or thoughtful explanation questioning) will help structure activities. Evidence should be gathered from complex and challenging tasks which show what a student can do and demonstrate their connections to previous concepts.
Interpreting the evidence is one of the most challenging aspects of the process, since students's answers may not adequately expose their true understandings and intentions and more information may be needed. Teachers can use various indicators to determine whether the student has sufficient understanding of the concept. After feedback is given to students and they have a chance to revise or correct their thinking, evaluative assessment can take place.
Throughout the process, the teacher should be evaluating the activity, evidence, and mathematical priorities. It is important to remind themselves why it is important for students to learn mathematics.
This article has excellent ideas for implementing the mathematics standards. A process with communication and feedback is needed to ensure the students and teacher's ideas are aligned and learning goals are met.
Keywords: Standards, Research, Teaching Strategies
Ref: Lisa6
Author(s): Galbraith, Peter
Date: 1995
Title: Mathematics as Reasoning
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 88(5)
Reviewer: Lisa
Date of Review: 4/10/99
The Curriculum and Evaluation Standards for School Mathematics strives for reasoning to take place in all levels of mathematics classes. Typically, proof is seen in geometry where the teacher shows examples, discusses how to write a proof, and then assigns similar problems for homework. Yet proof should be integrated early into a student's thinking and progress from a verification of truth of a statement, to illumination into why it is true or false, until the student is advanced enough to organize and present the results.
Research done in British and Australian secondary schools revealed misunderstandings in counterexamples and a lack of appreciation for the proof process. Many students did not accept that only one counterexample could disprove a statement and that counterexamples must satisfy the conditions but not the result of the mathematical statement. One study revealed the distinctive response groups of students' reasoning. The first reasoned only empirically, based purely on numerical evidence without generalization. The second group also reasoned empirically and was unable to articulate a proof but had a feeling for the argument and gave thought-out examples. The third group generalized the argument and gave examples of the identified principle involved in the problem. Although empirical proofs may be acceptable to some students, a clear process of reasoning is needed to convince others of the validity of a statement. Other problems noted through tests showed that students often use previous notions or knowledge not given or may even ignore given information if it conflicts with their beliefs. The structure of the proof is also difficult for students to grasp.
This evidence is important information for teachers. They must realize that preconceived ideas are mixed with classroom teachings and may explain why some students are not understanding certain ideas of proof. Classroom discussion involving student interchange and reasoning could expose and clarify some misunderstandings and demonstrate the importance of a clear convincing proof.
Keywords: Technology, Activities, Algebra
Ref: Lisa7
Author(s): Picciotto, Henri
Date: 1996
Title: Make These Designs
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 89(5)
Reviewer: Lisa
Date of Review: 4/11/99
An activity that helps students understand the equation y=mx+b involves recreating designs on their graphing calculators. They must find the correct values for x and b to reproduce designs of parallel lines (with negative, positive, and zero slope), lines with the same y-intercepts, intersecting lines, and other graphs. This activity is good because it allows students to create their own paths and all students have an understanding of the question. The amount of experience the class has with linear functions will determine the depth of the activity and the level of accuracy in matching each picture.
The students should keep notes on how each image was produced and a follow-up discussion will help each student contribute and learn of ideas they may have missed. Questions like "How do you make the lines steeper? farther apart? Can you make a parallel line below this one?" etc., make the students think about how they came up with their images. This activity is a reversal of traditional ways to present the graphs of lines. Given the graph, students produce the equation instead of looking at graphs of given equations. The students have a chance to discover what role m and b have and how changing the values for each affects the graph.
This activity is a creative way to use technology in the classroom. Combining this with class discussion and written explanations of results will give the students a strong foundation for understanding y=mx+b. It could also be extended to quadratic, trigonometric, or other functions for upper-level students.
Keywords: Activities, Discrete, Teaching Strategies
Ref: Lisa8
Author(s): DeTemple, Duane; Walker, Dean
Date: 1996
Title: Some Colorful Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 89(4)
Reviewer: Lisa
Date of Review: 4/14/99
This article explores the possibilities for using color in classroom learning. Three activities in discrete math are given which involve the coloration of geometric objects: overlapping simple closed curves, coloring triangulations of polygons, and finding the necessary number of colors to paint a plane given a distance rule. Colors can also be used in real-world problems, such as traffic flow, scheduling, and inventory control. Students are able to discover unexpected patterns and ask questions to help a group discussion.
This article looks beyond traditional activities to encourage creativity and diversity in learning. Since students learn in many different ways, using color is a strong visual aid to motivate understanding.
Keywords: Teaching Strategies, Standards,
Ref: Lisa9
Author(s): Arvold, Bridget; Turner, Pamela; Cooney, Thomas
Date: 1996
Title: Analyzing Teaching and Learning: The Art of Listening
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 89(4)
Reviewer: Lisa
Date of Review: 4/14/99
In order to reach students, we must understand their thinking and teach according to the ways they learn. By listening carefully to students' thoughts, we can evaluate their thinking processes and discover their level of mathematical understanding, means of mathematical communication, and the attributes that affect students' ability to do math. The article suggests tape recording group conversations to see who the dominant personalities of the class are, whether there are gender or other inequities, and see if a few designated students are targeted for the higher-level questions.
Involving students in problems that require individual and critical thinking and a formulated written response will reveal much about their level of understanding of a concept. If they are going the wrong direction, they can be led to counterexamples or asked to explain their reasoning. By taking the time to listen to students, teachers are able to reason with the students and create lessons that are compatible with their thinking.
Keywords: Assessment, Statistics,
Ref: Lisa10
Author(s): Schloemer, Cathy
Date: 1997
Title: Some Practical Possibilities for Alternative Assessment
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 90(1)
Reviewer: Lisa
Date of Review: 4/21/99
Alternative assessment allows students to communicate understanding in different ways than traditional short-answer and multiple choice tests. It begins with the teacher asking questions and finding creative ways to see the level of student understanding. One of Cathy Schloemer's concerns was whether her students were connecting mathematical concepts to real-world situations. At the end of a statistics unit, she designed a miniproject to test understanding of ordered pairs as numbers in the everyday world. By asking specific, guided questions, she had a basis for grading, yet the students could apply the project to their own interests in real-world situations and demonstrate their understanding of statistics beyond rote problems.
Another means of assessment is classroom conversation about a thought-provoking problem or activity. Size and scale changes, for example, can be explored by looking at different size photographs from the same negative. The students are to determine the relationship between the two pictures and explain their insights. However, a hands-on activity applying the same concepts may be more appealing, educational, and provide the insights the teacher is looking for if just thinking about the problem is not successful. Through exploration of different types of activities and assessment techniques, teachers can gain a better perspective of their students learning and give them experience with challenging questions that test conceptual understanding.
Keywords: Technology, Algebra,
Ref: Lisa11
Author(s): Pelech, James; Parker, Jacquelyn
Date: 1996
Title: The Graphing Calculator and Division of Fractions
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 89(4)
Reviewer: Lisa
Date of Review: 4/25/99
Graphing calculators can be helpful technological aids for students struggling to understand reciprocals of fractions. By graphing several equations and comparing their results, the concept of dividing by a fraction or multiplying by its reciprocal becomes apparent when only one graph appears for the two equations. After several examples, students record their observations and explain their results. A similar activity can demonstrate binomial expansion since students often leave out the middle term when squaring a binomial. The trigonometry identities can also be explored visually. Students will be more likely to remember that sin(2x)= 2sinxcosx when they can discover the property for themselves.
This article has good, simple ideas that can be applied to lessons at all levels of math. By visually demonstrating properties and equations, students comprehend abstract concepts more concretely and increase their chances for retention. The use of the graphing calculator to demonstrate ideas that students normally learn by rote will involve and engage the visual learners as well reinforce the understanding by all students.
Keywords: Connections, Teaching Strategies, Activities
Ref: Lisa12
Author(s): Hansbarger, J. Clark; Stewart, Eric
Date: 1996
Title: Merging Mathematics and English: One Approach to Bridging the Disciplines
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 89(4)
Reviewer: Lisa
Date of Review: 4/25/99
Although high school students should be able to connect disciplines in real world problems, students (especially those at the lower levels) seldom see the connection of math to other fields. Clark Hansbarger and Eric Stewart discovered ways to integrate math and English in classroom activities. In two projects, they combined a ninth-grade math class with a tenth-grade English class to observe and record data, analyze their findings, and publicize their results. The students in both classes were responsible for both the math and English portions of the work. The first project was a statistical study of their school-- countable behaviors, like tardies, running in the hall, etc. The classes then represented their data collection in graphs and scatterplots, and created documents to share with others.
The second project involved surveying soldiers in the Gulf War and analyzing and reporting on surveys sent to American military soldiers. The personal connection of this project excited the students as well as its connection to the outside world. The students were introduced to new equipment and tools which encouraged responsibility and curiousity. The students received grades based on their participation and completion of their part both in math and writing.
These projects were successful in several respects. Many of the students were "at risk," yet they acted responsibly and had fewer incidences of misconduct. They encouraged exploration of technology, team building, and independence. Teachers had opportunities for alternative assessment and integration of disciplines.
I thought this was a very creative way to combine two seemingly different disciplines and demonstrate their conncections. While these projects were short-term (6 weeks) and involved students from 2 classes of different disciplines, I would also be curious to know if a similar project could be done by creating a double class that incorporated both math and English (or another subject) for a semester.
Keywords: Issues, Teaching Strategies,
Ref: Lisa13
Author(s): Fiore, Greg
Date: 1999
Title: Math-Abused Students: Are We Prepared to Teach Them
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 92(5)
Reviewer: Lisa
Date of Review: 5/1/99
All students enter high school or college math classes with a pre-conceived idea about math and their own personal histories of success in math. Some students have math anxiety as a result of the attitudes of teachers and parents towards math. Occasionally there are math abused students, those who have negative experiences, verbal or physical, relating to doing mathematics. To get a feel for past math history, (especially in older people returning to school) the author suggests having students write an essay "Math and Me" describing attitudes toward math and past difficulties. The teacher can then use the information to determine how to treat students in class, see who will need more encouragement, or who could be challenged more.
For the students with math anxiety, teachers must provide the support the student needs to succeed. Teaching content of math so that students understand will draw them from their fears as well as encouraging diversity of learning styles in the classroom-- small groups, manipulatives, encouraging questioning and classroom discussion. However, I think that most importantly, teachers need to watch their attitudes towards math in the classroom and in how they treat students, especially in the lower grades. Students' experiences determine how they respond to math and their ability to succeed in the future.
Keywords: Standards, ,
Ref: Lisa14
Author(s): Garet, Michael; Mills, Virginia
Date: 1995
Title: Changes in Teaching Practices: The Effects of the Curriculum and Evaluation Standards
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 88(5)
Reviewer: Lisa
Date of Review: 5/3/99
Since the Curriculum and Evaluation Standards for School Mathematics was published, people have been trying to judge to what extent changes are occurring in the schools. Several years ago, a survey was taken of 550 public secondary schools about practices in first-year algebra classes. They found that most schools were moving in the right direction, but some reforms are difficult to implement without adequate time and teacher training.
The structure of number systems, functions, discrete mathematics, and probability and statistics have been emphasized more because of recommendations by the Standards, while factoring, which had previously been given the most emphasis, has been reduced. Although lecture-discussion and in-class problem sets are still the most prevalent form of instruction, but there is an increase in cooperative learning and writing. The use of technology, calculators and computers, has increased greatly since 1986, as called for by the Standards. However, forms of assessment, from short answer or multiple choice tests to oral or written reports or projects had not significantly changed at the time of the survey.
While it appears that improvement is being made overall, variations between individual schools have become more substantial. Urban and suburban schools have a higher level of consistency with the Standards than rural and city schools, where software packages are less common and fewer math educators attend NCTM annual meetings. The department chair greatly determines whether changes will take place by supporting change, acquiring the resources needed, and linking teachers to professional groups outside the school.
Although this survey is several years old and may not accurately reflect the role of the Standards in current classrooms, the article is helpful in identifying key items that are important to look at in the classroom. It also acknowledges differences in schools of differing demographic characteristics so that others are aware of the need to remove the level of diversity of Standards implementation between schools.
Keywords: Problem Solving, Teaching Strategies,
Ref: Lisa15
Author(s): Jones, Graham; Thronton, Carol; McGehe, Carol; Colba, David
Date: 1995
Title: Rich Problems-- Big Payoffs
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: 1(7)
Reviewer: Lisa
Date of Review: 5/11/99
One way to get students involved in math is to give real-life problems that creative opportunities for discussion, extensions, and learning beyond the textbook. This article is about problem-based learning, a problem which becomes an activity with many different ways to solve it and many paths for understanding. The problem here dealt with architecture and the amount of brass needed to enclose a maximum area. Students approached the question in several ways-- relating areas and shape, comparing numeric and geometric patterns, plotting points on a graph, and using calculators to investigate the maximum. The teacher had the groups of students justify their answers and present them to the class. <P>
Extension problems came from student questions and interest in the problem. One involved a slightly different architectural design, another added more complicated factors (elevators), and others could involve different shapes and sizes of area. Students were encouraged to generalize their cases and discovered that squares and equilateral triangles maximized the area of a fixed perimeter. <P>
Problem-based learning is important in that it leads to other problems and may be applied to many different levels of mathematics. It also leads to generalizations, additional questions, the use of technology, and various methods for solutions for all types of learners.
Keywords: Problem Solving, Standards,
Ref: Lisa16
Author(s): Showalter, Millard
Date: 1994
Title: Using Problems to Implement the NCTM's Professional Teaching Standards
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 87(1)
Reviewer: Lisa
Date of Review: 5/12/99
Some teachers are having difficulties finding problems that promote investigation of stimulating mathematical ideas and promotion of understanding as set by the Professional Standards for Teaching Mathematics. But teachers can choose situations not in the traditional mathematics textbooks that lend themselves well to classroom discussion and student investigation. This article gives several problems that are interesting to students, have strong mathematical content, and may lead to extensions.
The first problem is the challenge of folding a piece of paper 8 times. Students realize by analyzing the thicknesses after each fold that an unaided person will not have enough strength to make the last fold. Another similar idea involves cutting and stacking the paper instead of folding. Students estimate how high the pile will be after fifty times, and then compute the answer-- 35,540,000 miles high! Other questions, like snapping fingers with twice as much time between each snap, gives a reversal of thought, as the answer will be much lower than the previous problems.
Problems can be found from discussions in class or something a student or teacher finds mathematically interesting or unusual. It is important to have problems which have solid content as well as opportunities for various problem-solving methods and attractiveness. I think the problems in this article would be worthwhile for class activities and investigations.
Keywords: History, Communication,
Ref: Lisa17
Author(s): Jennings, Edward
Date: 1999
Title: Quote the Student, Evermore
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 92(2)
Reviewer: Lisa
Date of Review: 5/12/99
This is a short article but has a great idea for getting students involved and seeing their attitudes towards mathematics. Edward Jennings had his students bring in quotes from famous mathematicians and an original statement about math. After discussing the quotes for an entire class period, students were engaged in the creative and serious ideas that the mathematicians implied. Discussion included looking at different approaches to problems, what mathematics really is, and exposed the students to math history. Many thoughtful ideas were reflected in the individuals' quotes, which enabled the teacher to listen to their thoughts, structure future classes on their responses, and create opportunities for althernate assessment. All students actively participated and the activity promoted interest and variety in the curriculum.
Keywords: Connections, Standards,
Ref: Lisa18
Author(s): Bartels, Bobbye
Date: 1995
Title: Promoting Mathematical Connections with Concept Mapping
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: 1(7)
Reviewer: Lisa
Date of Review: 5/12/99
With the standards promoting connections in instruction, concept maps help students develop deeper understandings of mathematics. A concept map describes the relationships and connections between concepts. It promotes thinking and reasoning when figuring out how the concepts should be arranged and the direction and placement of the concepts. Depending on age and experience, there are several activities that can be done with concept maps. The first consists of a list of concepts and an incomplete and students are to fill in the blanks. A second method is providing a list of concepts but no map, and the most difficult is to have the students make a map using the concepts they believe are the most important.
Concept maps can be used in groups or individually. Then they should be discussed or critiqued by others, so that the students have to communicate their ideas and reason mathematically. Students can clarify misunderstandings and develop and explain new meanings for ideas. The concept map is a good form of alternative assessment because it can divulge a lot of information about someone's understanding and connections between concepts. Another advantage is the visual representation of math it gives. The maps can be reference tools or be hung in the classroom.
I think concept maps are an excellent way to generalize and summarize concepts and test for understanding between ideas. It also gets students actively thinking and participating in defending and constructing their mathematical understanding.
Keywords: Communication, Activities,
Ref: Lisa20
Author(s): Leitkin, Roza; Zaslavsky, Orit
Date: 1999
Title: Cooperative Learning in Mathematics
Journal or Publisher: Mathematics Teacher
Volume, Issue, Pages: 92(3), pp. 240-245
Reviewer: Lisa
Date of Review: 5/14/99
This article describes cooperative learning and gives guidelines for implementation in the classroom. Cooperative learning is defined as learning in small groups (2-6 students), doing tasks in which members are dependent on one another, having an environment encouraging communication and interaction of ideas, and promoting individual responsibility by each group member. The exchange-of-knowledge method lets the student work individually and as a "teacher" in problem-solving activities. Study cards are used in partners to solve and explain problems to one another. Parts of the cards contain examples and then problems to work. When arranging students in groups, I found it interesting that they advise putting high achievers in groups together so they can learn additional material, and middle and low achievers together so that low achievers can feel more comfortable and middle-level students can develop confidence as they help others.
Studies show that student activeness increased, attitudes were positive, and student-student relationships dominated in cooperative learning activities. Their learning seemed just as strong as those in traditional settings. But in order to implement this effectively, teachers need to structure the activity carefully and take into consideration the amount of students in each group, the heterogeneity of the group, student interactions and cooperativeness, interactions between groups, the teacher's role, and assessment of the activity.
This article helped convince me that with proper attention and planning, cooperative learning can be used successfully in the classroom. This activity promotes communication of ideas, cooperation between students, and the importance of sharing ideas.