QUESTIONS FOR DISCUSSION
FOLLOWING ARE SOME IMPORTANT QUESTIONS TO CONSIDER WHEN REVIEWING
INTEGRATED MATHEMATICS CURRICULUM/TEXTBOOKS
Program Organization and Structure
How is this curriculum based on the NCTM Standards, state standards, and
Is it intended to be a core curriculum for all high school students?
Is there a coherence to the curriculum or is it a series of isolated topics?
Are all the strands of mathematics (algebra, geometry, functions, trigonometry,
statistics, probability, discrete mathematics) represented in each year
of the curriculum?
How is the mathematics in each of the strands developed and deepened within
a unit, across the units, and over the years?
How are the various strands connected and interrelated to each other?
How are concepts, skills, and problem solving balanced within the development
of the mathematical ideas?
What is the balance between cooperative learning, direct instruction, inquiry-based
learning, investigations, etc. and is each strategy being used appropriately?
Are there indicators that the classroom environment is primarily a student-centered
Is assessment integrated in the instructional program?
Are students encouraged to use the tools, such as graphing calculators
and manipulatives while carrying out assessment tasks?
Do students have ample time to work on assessment tasks?
Are the assessment tasks varied; short response, performance-based, self-assessment,
take-home, long term problems or projects, etc.?
Are the assessment tasks embedded, ongoing and reflect the knowledge of
The Work Students Do
Are students asked to think and communicate, to draw on mathematical ideas,
and to use mathematical tools and techniques?
Do students encounter a varied program, including all the strands, and
a balance between exercises, problems, and investigations?
Are a large portion of assignments open-ended and encourage multiple approaches?
Do some tasks require time and deliberation which is continued over several
days or weeks?
Are students asked to formulate mathematical questions and assess what
is known and what must be determined?
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?
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?
Do students have access to a graphing calculator at all times for use in
Are students consistently asked to communicate their findings orally and
Are students asked to explore a situation, gather data, or interact with
members of their families for homework assignments?
Are students asked to develop problems or projects to apply what they have
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?
Does the curriculum account for different learning styles?
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?
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
How are the teacher materials structured? What are the components of the
What kind of background information is provided for each lesson? Is there
a description of the important mathematical ideas in the units of instruction?
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?
Are there suggestions on helping students work together productively; improve
their writing; make quality presentations?
Are the teaching materials detailed enough to help teachers present material?
Support for the Teacher
Is there an ongoing professional development program for teachers?
What is essential for professional development? What do teachers need that
they don't have?
Is there a way for teachers new to the program to gain from the experienced
- What is the evidence that students are learning mathematics?
- Is there evidence that colleges and universities will accept the curriculum
as satisfying their mathematics entrance requirement?
- Is there evidence that states will accept the program?
- Do students use technology in meaningful ways to deepen their understanding
of mathematical content and processes?
- Do teachers use technology in meaningful ways to deepen their understanding
of mathematical content and processes?
- Does the curriculum employ technology that is accessible to students?
- Do students have access to a graphing calculator at all times for use in
- Is care taken to ensure that technology does not replace basic mathematical
understanding and intuition for students?
- Does the curriculum clarify limitations as well as benefits of technology
as a mathematical tool?
Copyright © 1997
COMPASS - All rights reserved
Last Revision: 11/07/05