14: Developing an Understanding of Mathematics
in All Learners
Learning Outcomes
After reading this chapter, students will be able to:
• 14–1 Identify and explain the big ideas of mathematics instruction.
• 14–2 Give examples of multiple types of mathematical assessments that can be
used to make instructional decisions in mathematics.
INTASC Standards
Standard #2: Learning Differences. The teacher uses understanding of individual differences and
diverse cultures and communicates to ensure inclusive learning environments that enable
each learner to meet high standards.
Standard #3: Learning Environments. The teacher works with others to create environments
that support individual and collaborative learning, and that encourage positive social
interaction, active engagement in learning, and self–motivation.
Council for Exceptional Children
Special educators are to have knowledge of the following:
Standard #3: Curricular Content Knowledge. Beginning special education professionals use
knowledge of general and specialized curricula to individualize learning for individuals with
exceptionalities.
Standard #4: Assessment. Beginning special education professionals use multiple methods of
Chapter Outline
14–1 Establish Learning Goals: Big Ideas in Mathematics Instruction
14–1a Problem–Solving
14–1c Numbers and Operations
14–1e Geometry and Spatial Sense
14–1g Data Analysis and Probability
14–2 Assessment of Mathematics
14–2a Formal Assessment
14–3 Methods, Materials, and Resources That Promote Mathematics for All Learners
14–3b Communication of Mathematic Ideas
14–3d Algebra
14–3f Measurement
14–4 Universal Design for Learning Lesson Planning with Differentiated Instruction for
Mathematics
14–5 Fostering Collaboration in Mathematics Instruction
Key Concepts and Terms
abstract: The level of learning in mathematics in which students manipulate symbols
without the use of concrete objects or pictorial representations.
advance organizer: An outline with prompts for steps or substeps in the concept(s)
scientific, graphing).
classroom performance system: A type of computer–based assessment that collects,
compiles, and displays student data based on student responses delivered via a
response device.
computation fluency: Accurately and efficiently using operations to calculate numbers.
geometry: A type of math that has its own set of language, terms, and symbols to
answer questions about sizes, shapes, angles, lines, and points of figures. It also has
words for their relationships, words that refer to position and motion in space, and words
that refer to theories and formulas.
Global Positioning System (GPS): A navigation system using a constellation of
math literacy.
measurement: A basic life skill that is needed to determine the approximate magnitude
of object attributes.
MMMR Rap: A memory device for remembering the terms mode, median, mean, and
range in mathematics.
supplemental curricular program.
Lecture Notes
Many high–school seniors lack a fundamental, basic understanding of mathematical
concepts. The demands of the twenty–first century make the need to reverse this trend
imperative.
students. Some students will also need adaptations to be successful.
By approaching learning tasks with the UDL principles in mind, teachers ensure that
recognition, affective, and strategic systems can be activated for all learners.
There are many strategies available for students in mathematics. Applying multisensory
Suggestions for In–Class or Online Activities
2. Describe how a calendar can be used to begin to teach algebra.
3. There are many ways to measure objects. Often you cannot find a ruler to use.
4. Have you ever used a mnemonic to remember a mathematical concept?
5. Research the Internet to find at least 3 games learners could play to aid in the
Discussion Questions
1. Why might students who struggle with language have difficulty achieving math
literacy? Include one or two examples in your answer.
2. What is the difference between the concrete and representational stages of
mathematics instruction? Can students perform problem solving at either of
these stages? If so, how? If not, what is missing that prevents them from doing
so?
3. Study Figure 14.16. Invent and describe one additional low–tech and/or high–tech
UDL application(s) extension for the areas of representation, engagement, and
4. How would you modify an activity to use a different intelligence as defined by
Gardner?
5. Describe how you would design two multidisciplinary activities that teach basic
6. Why do you think mathematics is a challenge for learners?
7. What are your memories of math instruction? Were they pleasant or terrifying?
8. Who did you turn to for help with math? If it was not a parent, why not?
9. How comfortable are you with a calculator or a computer to help you solve a
Field Experiences
1. Visit a math class either on campus or at a school. Observe the methods that the
teacher uses. How did the students in the class seem to be reacting to the
material? Would these methods have helped you? Why or why not?
2. Work with a small group using manipulatives to solve a subtraction problem.
How will you help the students understand that they need to take away
manipulatives to solve the problem?
Videos
Watch the MindTap video for this chapter. Use the questions to start a class discussion.
Web Resources
Kentucky Center for Mathematics
