This course focuses primarily on whole-number concepts and operations, including sense-making strategies for single-digit and multidigit addition, subtraction, multiplication, and division. Other topics include various number systems (Babylonian, Egyptian, Mayan) and base-5 arithmetic, which are used to help diagnose difficulties children face as they learn our Hindu-Arabic number system. The course follows a problem-solving approach, in which participants learn to express solutions to problems in multiple ways: visually, algebraically, numerically, and verbally (the fourfold way). Prerequisite: Intermediate Algebra

GETTING STARTED (GSPS)
Participants register and ascertain the purpose, philosophy, and requirements of the Math Content Program for Teachers. Participants then solve a variety of problems looking at the different problem solving strategies along the way. Participants take a pre-test, and for homework read a math issues article and write a math autobiography.

LINEAR PATTERNS (LINPATT)
Participants examine patterns, concentrating on those that are linear. They express solutions to problems using multiple representations, referred to as the fourfold way.

NUMBER SYSTEMS (NUMSYS)
Participants analyze number systems with features and properties different than our own. The process of contrasting number systems helps us develop better understanding of our own system. At the same time, in our struggle to decode unfamiliar systems we are likely to acquire some appreciation for the processes children experience as they learn about our number systems structure and conventions.

ARITHMETIC PROBLEM TYPES (PT)
Participants focus on the structure of word problems involving addition and subtraction. They discuss the features that make word problems difficult for students, and they classify word problems according to these features. Participants examine word problems in their adopted textbooks.

SINGLE-DIGIT ADDITION/SUBTRACTION STRATEGIES (COMP1A)
Participants identify strategies that children use to solve computation problems in sense-making ways. They view video clips of children who use a range of computational strategies to do single-digit problems. Finally, they discuss questioning techniques and instructional approaches that promote sense-making computational fluency in children.

PLACE VALUE (PV)
Participants explore number concepts and operations associated with base-5. By focusing on base-5, participants get insight into the workings of the place value system and into the meanings of conventions and procedures in base-10 arithmetic. They learn to count in base-5, perform operations in base-5, and convert between bases. Further, they diagnose obstacles confronted by children in learning to compute in base-10.

MULTIDIGIT ADDITION/SUBTRACTION STRATEGIES (COMP2)
In part one of this lesson, participants identify strategies that children use to solve problems in sense-making ways, they view and discuss video clips of children using a range of multidigit computational strategies, and they examine some computation algorithms used around the world. In part two of the lesson, participants focus on intervention strategies. They examine the work of one child that was completed over a period of time, and they discuss what the teacher might have done to encourage growth. Then participants create intervention plans for specific student misconceptions, using their textbooks as resources.

SINGLE-DIGIT MULTIPLICATION AND DIVISION (COMP4)
Participants learn about problem types associated with multiplication and division. They focus on the meaning of multiplication and division, and they develop sense-making strategies for computation. Through video clips, student work samples, and discussion, participants examine a range of primary multiplication and division strategies. They also share ways to teach and practice number facts.

MULTIDIGIT MULTIPLICATION AND DIVISION (COMP5)
Participants examine multidigit multiplication and division strategies that build on students’ understanding of single-digit multiplication and division. Participants examine the meaning of the traditional multiplication and division algorithms and variations. They learn about area models and algorithms from around the world. Participants share ideas for Parent Math Night.

NUMBER THEORY (NUMTH)
Participants explore divisibility properties of numbers. They use the sieve of Eratosthenes to find prime numbers, and they use factor trees to factor composite numbers.PRE

COMPUTATION NUMBER CONCEPTS (PNC)
Participants identify and define several pre-computation number concepts and consider an appropriate order for introducing them. Then participants use the basic number concepts in an adult counting activity that extends the “Hundreds Chart.” Through this activity we focus attention on the importance and challenges of teaching counting as well as on some features of our base-10 number system. Finally, participants examine their books to see how and when these concepts are addressed. Universal Access Strategies are included.

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