QUESTIONS FOR DISCUSSION

FOLLOWING ARE SOME IMPORTANT QUESTIONS TO CONSIDER WHEN REVIEWING INTEGRATED MATHEMATICS CURRICULUM/TEXTBOOKS
 

Program Organization and Structure

  1. How is this curriculum based on the NCTM Standards, state standards, and local standards?
  2. Is it intended to be a core curriculum for all high school students?
  3. Is there a coherence to the curriculum or is it a series of isolated topics?

Content

  1. Are all the strands of mathematics (algebra, geometry, functions, trigonometry, statistics, probability, discrete mathematics) represented in each year of the curriculum?
  2. How is the mathematics in each of the strands developed and deepened within a unit, across the units, and over the years?
  3. How are the various strands connected and interrelated to each other?
  4. How are concepts, skills, and problem solving balanced within the development of the mathematical ideas?

Instructional Strategies

  1. What is the balance between cooperative learning, direct instruction, inquiry-based learning, investigations, etc. and is each strategy being used appropriately?
  2. Are there indicators that the classroom environment is primarily a student-centered classroom?

Assessment

  1. Is assessment integrated in the instructional program?
  2. Are students encouraged to use the tools, such as graphing calculators and manipulatives while carrying out assessment tasks?
  3. Do students have ample time to work on assessment tasks?
  4. Are the assessment tasks varied; short response, performance-based, self-assessment, take-home, long term problems or projects, etc.?
  5. Are the assessment tasks embedded, ongoing and reflect the knowledge of the students?

The Work Students Do

  1. Are students asked to think and communicate, to draw on mathematical ideas, and to use mathematical tools and techniques?
  2. Do students encounter a varied program, including all the strands, and a balance between exercises, problems, and investigations?
  3. Are a large portion of assignments open-ended and encourage multiple approaches?
  4. Do some tasks require time and deliberation which is continued over several days or weeks?
  5. Are students asked to formulate mathematical questions and assess what is known and what must be determined?
  6. Are students asked to interact with one another and often work in small heterogeneous groups? Are they expected to share approaches, conjectures, difficulties, results, and evidence with their group and with other groups?
  7. Are students asked to formulate and test generalizations as they become apparent and make connections among the mathematical ideas within a lesson or among lessons?
  8. Do students have access to a graphing calculator at all times for use in class?
  9. Are students consistently asked to communicate their findings orally and in writing?
  10. Are students asked to explore a situation, gather data, or interact with members of their families for homework assignments?
  11. Are students asked to develop problems or projects to apply what they have learned?

Student Diversity

  1. How does the curriculum address a classroom of students with diverse mathematical backgrounds? Are there problems and exercises for students who need reinforcement? Are there problems and exercises for students who would like to explore a concept in greater depth?
  2. Does the curriculum account for different learning styles?
  3. Are the tasks and problems students work on accessible to all students? Are they rich and open and can be investigated at many different levels?
  4. Will all students be able to see their cultural background reflected in the curriculum or be able to bring their own cultural experience to the mathematical situation?

Teacher Materials

  1. How are the teacher materials structured? What are the components of the teacher materials?
  2. What kind of background information is provided for each lesson? Is there a description of the important mathematical ideas in the units of instruction?
  3. Are there suggestions on questions to ask and ways to respond that keep students' thinking open and help students reflect on what they have done?
  4. Are there suggestions on helping students work together productively; improve their writing; make quality presentations?
  5. Are the teaching materials detailed enough to help teachers present material?

Support for the Teacher

  1. Is there an ongoing professional development program for teachers?
  2. What is essential for professional development? What do teachers need that they don't have?
  3. Is there a way for teachers new to the program to gain from the experienced teachers?

Evaluation

  1. What is the evidence that students are learning mathematics?
  2. Is there evidence that colleges and universities will accept the curriculum as satisfying their mathematics entrance requirement?
  3. Is there evidence that states will accept the program?

Technology

  1. Do students use technology in meaningful ways to deepen their understanding of mathematical content and processes?
  2. Do teachers use technology in meaningful ways to deepen their understanding of mathematical content and processes?
  3. Does the curriculum employ technology that is accessible to students?
  4. Do students have access to a graphing calculator at all times for use in class?
  5. Is care taken to ensure that technology does not replace basic mathematical understanding and intuition for students?
  6. Does the curriculum clarify limitations as well as benefits of technology as a mathematical tool?

Copyright © 1997 COMPASS - All rights reserved
compass@ithaca.edu

Last Revision: 11/07/05