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Textbook Analysis
Mathematical Tools
Mathematical tools are objects or ideas that teachers utilize to demonstrate and teach concepts in all areas of math. These mathematical tools include hands-on activities such as games, worksheets, additional resources, literature. Textbooks should be evaluated on how they use mathematical tools in each chapter and lesson. Some tools are essential when teaching a lesson out of the textbook and others are optional or for use by the teacher only. It is important to evaluate how well the students use the tools to understand mathematical concepts. And lastly it is important that the text uses a variety of tools to assess one single concept.
In the Silver Burdett Ginn Mathematics textbooks we examined probability and statistics. There are many mathematical tools that are essential in teaching these lessons. The first is Discussion Starters (Grade 4, Chapter 4, pg 1). The textbook gives you exactly five straight forward questions along with their answers. The textbook also gives you specific things to say and do. For example, each lesson has a Problem of the Day that you can write on the board and encourages one right answer. In part of the chapter you can make math connections to the real world with Data Analysis and Probability (Grade 4, Chapter 4, pg. 15). In both the 4th and 5th grade books the chapters include worksheets that help the students practice, re-teach or extend the lesson. Each worksheet has right or wrong answers and gives the answers in the manual. Each chapter also has a chapter test that can simply be copied and given out. All of these mathematical tools are essential for teaching using these textbooks. However there are some tools that are optional and those help individualize each lesson. The Gifted and Talented section gives activities and projects that can help maximize your students learning and keep them busy if they finish early (Grade 4, Chapter 4, pg. 16). Using Technology sections are useful if you have access to computers because they offer more exciting ways to develop multiplication or other problems. At the end of the lessons there are Project Links that are optional if there is more time or a need for extra emphasis (Grade 5, Chapter , pg. 101). There are checkpoints in the middle of each chapter that stop and review what they students have learned. A Vocabulary Review is offered to teachers only if they wish to review the terms before the students begin with the checkpoint (Grade 5, Chapter pg. 104). Also assessment ideas are included at these checkpoints and they include ideas that the students can write about in their journals.
In Silver Burdett Ginn, the tools help emphasize what they have learned but they encourage convergent thinking. The worksheets and tests all have been written and the answers are straight forward. There were very few times where the tools encouraged individuality and creative thinking. There was a variety of tools used in these textbooks including CD-rom, vocabulary reviews and project link ideas. However they still all encouraged one answer and convergent thinking.
In the Investigations Curriculum Unit textbooks we also examined lessons on probability and statistics. The mathematical tools we found in these books differed greatly from Silver Burdett Ginn in many ways. The first way was that the actual materials were less straight forward and more inquiry based. The worksheets included in the back of the book encouraged many answers and were very blank compared to the others. The actual lessons used words like have the students label, brainstorm, relate, distinguish, suggest, and associate. These words all have to do with more thinking and discussing ideas instead of being told the right answer and actual definition. The students came up with their own definition of probability by making a timeline with impossible, unlikely and possible as their points. The students would then discuss and link ideas to each other which encouraged communication and investigation (Grade 5, Session 1, pg. 4). Each lesson gives you questions to ask that lead the students in many different directions. Each question does not lead to one specific answer or activity. For example, the class decides which are the more logical events for the timeline and where to place each event. The teacher is told to list all the suggestions the children give which encourages equal praise for each student's response. These lessons set up a safe environment for the students to participate in without getting cut down or overly praised. One lesson encourages teachers to use math along the course of a day instead of limiting it during the assigned math hour. The final project also gives the students the chance to carry out an extended investigation of data from questions. (Grade 4, sessions 1 and , pg. 5)
In Investigations, the textbook gives Teacher Notes that give heads up for problems or ways to maximize the lessons. The textbook also gives a Dialogue Box in order to help students refine their questions without giving them too much guidance (Grade 4, sessions 1 and , pg. 58). Overall, The Investigations series helps teachers enhance an inquiry based classroom. The activities and lessons encourage divergent thinking and reasoning. Each lesson truly is an investigation of math and prepare students to think on their own and represent data in several ways.
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