Introduction
Book Style
## Targeted Users of This Curriculum
*Numeracy* is for adult mathematics learners who want to learn to use and appreciate mathematics in a daily life context. This curriculum may be used in college as a prerequisite course for Quantitative Reasoning or Quantitative Literacy.
# Philosophy of Curriculum Design
This curriculum is designed according to a set of principles on adult literacy, real-life based content selection, and situational and group discussion based instructional methods. These principles are explained below.
There are 3 major components that form and construct adult literacy and we have developed this curriculum around these components:
1. Context––the use and purpose for which an adult takes on a task with mathematical demands
2. Content––the mathematical knowledge that is necessary for the tasks confronted
3. Cognitive and Affective––the processes that enable an individual to solve problems, and thereby, link the content and context
The focus of this curriculum is to make sense of numbers in real-life, in other words, Numeracy. There are no abstract numbers in everyday life. Numbers exist with measurement units, in various forms, and can be computed, estimated, and transformed.
This curriculum is designed around realistic, in-situ instruction where each mathematical concept is taught using small, useful realistic mathematical situations. In other words, students will learn at what time and in what situation or scenario people should use different mathematical ideas or skills to solve problems. Therefore, this curriculum is a mathematical toolbox for real-life problem solving. This curriculum also helps students *appreciate* mathematics from a realistic problem-solving perspective. Each mathematical idea or skill covered in this curriculum can be applied to specific real-life situations.
## The Content
This curriculum is neither mathematics nor skills oriented. It is not anchored with comprehensive mathematical structures or skills (e.g., performing operations on fractions by hand, solving various types of linear or exponential equations, or doing complicated multiplication or division in scientific notation). Rather, selected mathematical concepts and skills that are important and frequently used in everyday life are embedded in realistic contexts, where students learn and appreciate how mathematics facilitates problem solving in everyday life.
This curriculum assumes that calculators, computer software, and the Internet are available for student use, and that they are used as tools for understanding.
## The Curriculum Structure
Each chapter section is laid out using the following structure:
**Introduction** of the topic
**Explore––**students walk through a realistic problem that uses constructivist model building to exemplify the use and appreciation of mathematical knowledge in everyday life. The problems are especially suited for small interactive group work or discussions between students and the teacher.
**Reflect––**students reflect on mathematical and modeling concepts, skills, and strategies they have learned in the Explore section.
**Examples––**students familiarize themselves with the new concepts, skills and strategies that they learned from the Explore and Reflect sections. The context and difficulty level of examples are similar or slightly higher to those in the Explore sections. Solutions are given in detail.
**Practice Exercises––**students practice newly learned concepts and strategies on their own. Only answers are given.
**Perspectives––**the newly learned concepts and strategies are used in new situations, and the difficulty level may be slightly higher than the Examples. Answers are given.
**Practice Skills––**skill problems that are needed for further study in mathematics are provided out of context for practice. Answers are given.
A project at the end of each chapter aggregates ideas and skills developed in that chapter. This is to help students put mathematical thinking into realistic practice on a larger scale. It may also help students develop a disposition for mathematics in their everyday lives. These projects may involve hands-on activities that students complete in groups or online research, as necessary.
# How to Teach this Curriculum
This curriculum is designed for realistic problem and group discussion-based or teacher-student discussion-based instruction. Teachers who prefer to use traditional or direct instruction may need to make some adjustments when teaching this curriculum. The recommended and alternative instructional methods for teaching this curriculum are explained below.
## The Recommended Instructional Method
This curriculum is designed for problem and discussion-based teaching. The authors believe adults (e.g., college students) have some existing knowledge regarding Numeracy (e.g., integers, fractions, decimals, measurement, rate, linear equations etc.) and possess different ways of understanding and solving a given problem. Afterall, at some point (usually in K-12), most students have taken courses in this material before, and possibly used numeracy in a job or their daily lives without realizing it. Therefore, instead of reteaching the mathematical knowledge they have seen before, a teacher may facilitate students’ recall of their existing knowledge, evaluate their ways of solving a problem, and make sense of and appreciate their mathematical abilities in realistic contexts. Each section of the curriculum was designed to achieve these goals.
**Explore––**This section is designed to be facilitated as a realistic problem solved by whole-class or small group discussion. A whole-class discussion is led by the teacher where the teacher help students express their ideas and help students complete their reasoning attempts. Small groups of students will interact with each other to talk about how a realistic problem can be solved. They will discuss issues or difficulties they encounter while solving the problem. Teachers will facilitate the students’ discussions so that they learn the intended mathematical ideas used to solve the problem. The intended mathematical knowledge a teacher must uncover is written in the solution of each Explore.
**Reflect––**After students have solved problems in an Explore section, the students should reflect as a group (whole-class or small groups) what they have learned. This section is designed as a summary of what was learned in the Explore section. Teachers should make sure that the students have learned what was intended.
**Examples––**Teachers may use Examples as in-class exercises to help students familiarize themselves with the new concepts, skills and strategies that they learned from the Explore and Reflect sections. They can be done individually, in small groups, or through class discussion led by the teacher.
**Practice Exercises––**Students practice newly learned concepts and strategies on their own. Only answers are given. These can be used in class as further Examples, or can be left for students to complete at home before they tackle the homework assignments.
**Perspectives––**This section contains realistic examples that mix the concepts and skills students learned in the section. This is the level that students should be assessed at on quizzes or tests. Teachers may use the examples in this section as classroom examples or assign them as homework.
**Practice Skills––**Teachers may use questions in this section to help students develop mathematical skills out of context so that they achieve fluency in the basic skills required to solve realistic problems. Teachers may want to help students focus on making sense of the skills (e.g., operations) because students may use calculators to complete questions in this section.
