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What is the best way to teach math to high school and college students? Conventional classroom teaching has included explanation of the subject matter accompanied by a limited number of examples, after which students are assigned unsolved problems to work out. Recent research has investigated the effect of increasing the use of “worked out” examples of math problems, and the results have revealed that this teaching method produced more effective results.

This manuscript includes a brief review of research findings suggesting that providing students with worked out examples is more effective than the conventional math instruction method a discussion of the probable reasons for this effect comments on what this body of research suggests for teaching today’s math students, with specific consideration of a recently developed math-learning resource.

Research

mathHotmath is a new approach for mathematics homework assistance for high school and college students. It is a Web site that provides students with a means of learning mathematics by giving step-by-step solutions to the textbook homework problems assigned by their teachers.

Students are given a complete path from the problem statement to the solution showing each step to take to reach that solution, along with hints, and explanations of each step. Students can work at their own pace through the solutions and move back to replay steps. Hotmath asks questions during the problem solving process as well. This encourages more thought on the part of the students and ensures that the process is interactive.

Hotmath provides solutions to relevant and pertinent problems-the ones that students are given by their teachers to solve. Teachers know that students are focusing on the exercises that are important to students, and students are getting help with their homework while still learning the important material.

The challenge is to create instruction that is effective to the challenged students. Hotmath does this by providing accessible, worked solutions to problems. Students using Hotmath focus on the correct series of steps needed to reach the solution.
The theory of knowledge integration as described by Linn (2000) and others is one such technique. There are four tenets in knowledge integration: make science accessible, make thinking visible, promote autonomy, and encourage social supports.

Hotmath’s instructional approach helps to make science accessible by presenting relevant problems to students to promote integration of the ideas obtained while learning how to solve these problems with the students’ existing knowledge and ideas. Hotmath helps to make the expert’s problem solving thought process more visible by clearly showing the sequence of steps taken and providing explanations, discussions of alternative paths and approaches, and showing a complete history of the steps taken to reach the solution. Hotmath promotes autonomy by prompting students with questions that encourage them to reflect on the information presented. This promotes an inquiry process that will help students to learn autonomously.

Hotmath uses graphs and diagrams to explain the solutions when applicable and necessary. These additional sources of information are integrated within the HotMath instructional environment to reduce cognitive load that would be imposed by having to integrate them (Ward Sweller, 1990). The use of multimedia to provide alternative forms of representation has been shown to be effective when properly presented (Mayer, 1997). HotMath is looking into providing narrations of the explanations to provide instruction that is easier to follow.

Hotmath uses ideas founded in principles of constructivism and knowledge integration, and that leverage off of the effectiveness of worked examples and multimedia. The goal is to provide instruction that reduces cognitive load and results in knowledge that is integrated with students’ existing ideas such that it can be more effectively used in a wide range of contexts.

Why do worked examples work better than conventional methods?

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    Reduced cognitive overload. Solving problems imposes a high degree of cognitive load on the learner. Students lose track of the key issues to be learned as the process of solving problems is so cognitively demanding; this interferes with learning of the desired information.

     

     

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    Reduced frustration. Students often feel frustrated as they struggle trying to reach the solution. Providing step-by-step solutions can create a “scaffolding” or schema around which to organize challenging concepts, making them more manageable and less overwhelming.

     

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    Opportunity for great problem variability. A greater number and range of examples can be presented, which facilitates abstraction, especially for students with low achievement.

     

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    Shifted responsibility. Worked examples encourage active mental participation on the part of the students by providing the student with the tools needed to reach a solution on their own without needing to rely on others such as a parents or tutors, resources that may not always be available.

     

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    Immediate correction. Correctly worked examples reduce the risk of “faulty learning” or practicing incorrect solutions and the learning of incorrect associations (Siegler, 1988).

     

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    Greater feeling of accomplishment and confidence. Knowing that it will be possible to complete schoolwork correctly makes learning math less daunting. Knowing that work has been completed correctly contributes to confidence and the desire to continue.

     

How does Hotmath use this research to help students?

mathHotmath is a new approach for mathematics homework assistance for high school and college students. It is a Web site that provides students with a means of learning mathematics by giving step-by-step solutions to the textbook homework problems assigned by their teachers.

Students are given a complete path from the problem statement to the solution showing each step to take to reach that solution, along with hints, and explanations of each step. Students can work at their own pace through the solutions and move back to replay steps. Hotmath asks questions during the problem solving process as well. This encourages more thought on the part of the students and ensures that the process is interactive.

Hotmath provides solutions to relevant and pertinent problems-the ones that students are given by their teachers to solve. Teachers know that students are focusing on the exercises that are important to students, and students are getting help with their homework while still learning the important material.

The challenge is to create instruction that is effective to the challenged students. Hotmath does this by providing accessible, worked solutions to problems. Students using Hotmath focus on the correct series of steps needed to reach the solution.
The theory of knowledge integration as described by Linn (2000) and others is one such technique. There are four tenets in knowledge integration: make science accessible, make thinking visible, promote autonomy, and encourage social supports.

scienceHotmath’s instructional approach helps to make science accessible by presenting relevant problems to students to promote integration of the ideas obtained while learning how to solve these problems with the students’ existing knowledge and ideas. Hotmath helps to make the expert’s problem solving thought process more visible by clearly showing the sequence of steps taken and providing explanations, discussions of alternative paths and approaches, and showing a complete history of the steps taken to reach the solution. Hotmath promotes autonomy by prompting students with questions that encourage them to reflect on the information presented. This promotes an inquiry process that will help students to learn autonomously.

Hotmath uses graphs and diagrams to explain the solutions when applicable and necessary. These additional sources of information are integrated within the HotMath instructional environment to reduce cognitive load that would be imposed by having to integrate them (Ward Sweller, 1990). The use of multimedia to provide alternative forms of representation has been shown to be effective when properly presented (Mayer, 1997). HotMath is looking into providing narrations of the explanations to provide instruction that is easier to follow.

Hotmath uses ideas founded in principles of constructivism and knowledge integration, and that leverage off of the effectiveness of worked examples and multimedia. The goal is to provide instruction that reduces cognitive load and results in knowledge that is integrated with students’ existing ideas such that it can be more effectively used in a wide range of contexts.

Who Are We?

We are math teachers and professors who believe that immediate help with assigned homework improves math learning. We know that math is a gateway subject for success in school and careers. Our mission is to help every student succeed in math.

Our Corporation , today serves over a million students with instant explanations for odd-numbered homework problems for over 250 math textbooks.

Independent scientific research shows that tutorial help with homework improves math learning. Math scores have improved when Hotmath is used. We have been the topic of an education journal article and a teacher article. Math teachers support the use of Hotmath.

In addition to our for-pay step-by-step answers, math videos, and online math tutoring, we offer free practice tests, math workbooks, graphing calculator tutorials, learning activities, and math games.

Math Textbook Answers

  • We explain the actual, odd-numbered math problems, step-by-step, from your math textbook. We have math answers for virtually all math publishers .

  • You click your textbook cover from our library pages, and then select the page and problem number to instantly begin our self-paced, step-by-step explanation to your actual homework problem. And, if desired, you can click for a review lesson, a math video, or even an online math tutor.

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