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Massachusetts Department of Education

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Guiding Principles

The Guiding Principles summarize a broad vision of adult numeracy that guides all instructional efforts. They address the specific and unique characteristics of both the subject of math and the adult mathematics learner.

Curriculum: A real life context for mathematical concepts and skills across mathematical content areas is the driving force behind curriculum development. Within that setting, mathematics instruction transcends textbook-driven computation practice to include experiences in understanding and communicating ideas mathematically, clarifying one’s thinking, making convincing arguments, and reaching decisions individually and as part of a group.
Assessment: Mathematical assessment occurs in a framework of purposes for learning relevant to the successful performance of a variety of everyday adult mathematical tasks and the pursuit of further education. Learners are active partners in identifying these purposes, in setting personal learning goals, and in defining measures of success.
Equity: Adult numeracy learners at every level of instruction have access to all mathematics domains (number sense, patterns, relations and functions, geometry and measurement, probability and statistics).
Life Skills: Adult mathematics literacy education strives to create instruction that helps learners become less fearful and more confident in tasking risks, voicing their opinions, making decisions, and actively participating in today’s world.
Teaching: Mathematics instruction mirrors real-life activity through the use of both hands-on and printed instructional materials, group as well as individual work, and short-term and long-term tasks.
Technology: Adult numeracy instruction offers all learners experience with a broad range of technological tools (such as calculators, rulers, protractors, computer programs, etc.) appropriate to a variety of mathematical settings.

Habits of Mind

Habits of Mind are practices that strengthen learning. In numeracy instruction, habits of mind involve reflection, inquiry and action. They are developed by teachers and programs that offer challenging mathematical tasks in settings that support learners’ curiosity, respect for evidence, persistence, ownership, and reflection about what is learned and how it is learned. These habits flourish in instructional environments that favor uncovering mathematical concepts and connections rather than mimicking algorithms.

The following chart defines the habits of mind crucial to adults’ numeracy development. It also lists questions students and teachers may share to assess their own mathematical habits.

Habits of Mind
Learner Question

A curious and open attitude towards the presentation of new ideas or ways of approaching problems, even when confusion arises, facilitates learning.

Do I ask “Why,” “How,” or “What If” questions?

Respect for Evidence

To evaluate reasoning, it is essential to see evidence. Reasoning is demonstrated by the appropriate use of verbal and visual mathematical evidence to support solutions and ideas.

Do I listen carefully for others’ use of

evidence, and do I include evidence to support my solutions and ideas?


Solutions in mathematics are not always apparent at first glance. Persistence is necessary to work through challenging problems that stretch our understanding.

Do I keep going when I feel lost or discouraged while solving problems?


What we own has meaning for us, and taking ownership of our work encourages us to do our best. Although someone else might assign a mathematical task to us, we must treat the problem as important to us, as though it was our own, if we are to produce high quality work and learn from experience.

In what ways do I show that my work is purposeful and important to me?


To become an autonomous learner, it is necessary to think about how our learning happens. We need to consider how we learn from mathematical experiences.

Do I notice and analyze how and what I learn?

Content Strands and Learning Standards

Following is a chart that outlines the content strands and learning standards for the Mathematics and Numeracy curriculum framework. After this chart, you will find a more detailed explanation of each content strand and the learning standards that go along with it.



Learners will demonstrate the ability to…

Number Sense

N-1 Represent and use numbers in a variety of equivalent

forms in contextual situations

N-2 Understand meanings of operations and how they relate

to one another

N-3 Compute fluently and make reasonable estimates

Patterns, Functions and Algebra

P-1 Explore, identify, analyze, and extend patterns in

mathematical and adult contextual situations

P-2 Articulate and represent number and data relationships

using words, tables, graphs, rules, and equations

P-3 Recognize and use algebraic symbols to model

mathematical and contextual situations

P-4 Analyze change in various contexts

Statistics and Probability

S-1 Collect, organize, and represent data

S-2 Read and interpret data representations

S-3 Describe data using numerical descriptions, statistics, and

trend terminology

S-4 Make and evaluate arguments and statements by applying

knowledge of data analysis, bias factors, graph

distortions, and context

S-5 Know and apply basic probability concepts

Geometry and Measurement

G-1 Use and apply geometric properties and relationships to

describe the physical world and identify and analyze the

characteristics of geometric figures

G-2 Use transformations and symmetry to analyze

mathematical situations

G-3 Specify locations and describe spatial relationships using

coordinate geometry and other representational systems

G-4 Understand measurable attributes of objects and the

units, systems, and processes of measurement and apply

appropriate techniques, tools, and formulas to determine


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