Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis.

Teacher Guide for Book 1 of the Principles of Mathematics - Biblical Worldview Curriculum for junior high! Math is a real-life tool that points us to God and helps us explore His creation, yet it often comes across as dry facts and meaningless rules. Here at last is a curriculum that has a biblical worldview integrated throughout the text and problems, not just added as an afterthought. The resources in the Teacher Guide will help students master and apply the skills learned in the Student Textbook. What does this Teacher Guide include? Worksheets, Quizzes, and Tests: These perforated, three-hole punched pages help provide practice on the principles taught in the main student textbook.Answer Keys: The answers are included for the worksheets, quizzes, and tests found in this Teacher Guide.Schedule: A suggested calendar schedule is provided for completing the material in one year, though this can be adapted to meet individual student needs. There is also an accelerated schedule for completing the material in one semester. Are there any prerequisites for this course? This curriculum is aimed at grades 6-8, fitting into most math approaches the year or two years prior to starting high school algebra. If following traditional grade levels, Book 1 should be completed in grade 6 or 7, and Book 2 in grade 7 or 8. In Book 1 students should have a basic knowledge of arithmetic (basic arithmetic will be reviewed, but at a fast pace and while teaching problem-solving skills and a biblical worldview of math) and sufficient mental development to think through the concepts and examples given. Typically, anyone in sixth grade or higher should be prepared to begin. The focus of the course is actually learning math for life, not simply preparing to pass a test.

This title has been endorsed by Cambridge Assessment International Education Master the essential mathematical skills that underpin the new Cambridge Primary Mathematics curriculum framework (0096), with specifically sign-posted tasks and activities rooted in the mastery approach. - Get learners thinking mathematically with engaging activities designed to focus on key skills and principles. - Embed knowledge across all areas of learning, enabling learners to make connections between different areas of mathematics. - Develop vocabulary with probing questions designed to encourage learners to use accurate language to describe how they solve particular problems.

With full coverage of the theory and practice required for effective and creative mathematics teaching, this text is an essential guide for all trainees working towards QTS (Qualified Teacher Status).

The key to students' success in math lies in a way of teaching that provides clear evidence of how students are thinking about problems and builds on that thinking to take them to a deeper level of understanding. Seasoned math educators Ted Hull, Don Balka, and Ruth Harbin Miles offer teachers a sequential and developmental plan for integrating visual thinking into current classroom practices, and gradually, but steadily, initiating successful instructional changes in mathematics. Their new book provides teachers with numerous sample problems and classroom scenarios, showing successful teacher interventions at work, and offers guidance on how teachers can adapt traditional problems to promote visible thinking in their own classrooms.