Number Sense: Foundations for children’s early math skills develop long before kindergarten. An ability to represent approximate quantities, which is evident in early infancy, predicts children’s performance on standardized measures of mathematics across their lifespans (measures at 6 months old predicts performance at 3- and 14-years old). Representations of approximate quantity improve over the course of development, and can be facilitated by practice and intervention.

• Activity/Application: Equality and Inequality (Leveraging Multiple Mathematical Competencies)

Exact Number Concepts: The ability to large exact numbers (natural number system) is constructed as children learn individual number words and counting procedures. Children’s ability to demonstrate their understanding of equity, equality, and fairness is limited to their ability to represent and compare quantities.

• Activity/Application: Fairness & Equity (Multiple Sources of Knowledge)

Language & Math: Exposure to number language facilitates children's acquisition of number word meanings (Gunderson & Levine, 2011; Levine et al., 2010). The language we speak influences how we think about number. Number knowledge transfers across languages for bilingual learners.

Activity/Application: Talk about it… (Affirming Mathematics Learners’ Identities)

MULTIPLICATION of Whole Numbers

Leveraging multiple mathematical competencies.

Linear Equations in Context:

What is a Fair Living Wage?Part 1

In this activity, we will use linear functions and their graphs to interpret the affordability of housing for families with different circumstances and incomes. We will use technology for graphing, and we will interpret features of the linear functions in context: slope, intercept, and points of intersection of different lines.

We will pay attention to the equity practices of going deep with mathematics, leveraging multiple competencies, affirming identities, and drawing on multiple resources of knowledge.

Modeling with Data Part 1

Brief intro to modeling. Dietary Change and Cholesterol. Participants formulate questions for given data on cholesterol levels of people who changed to a vegetarian diet, choose appropriate graphs to analyze the data, and if time permits, use simulation and informal inference procedures to make inferences and justify conclusions.

Session will involve participants in going deep in mathematics. In addition, it will necessitate that participants draw on multiple resources of their knowledge, particularly relative to use of technology in analyzing data.

Play-Based Learning: Children enjoy learning when it is playful and there is movement involved. Teachers can integrate math instruction into play-based activities across the curriculum.

• Activity/Application: Examples of play-based math instruction

Physical Activity: Physical activity has been shown to promote and enhance learning. There may also be a relationship between gross motor skill development, visual/spatial perception, and later mathematical skill development.

• Activity/Application: How to ensure activities are inclusive and developmentally appropriate?

What is a Fraction?

In this session we will investigate how to conceptually teach fractions. We will explore concrete examples and representations for understanding basic fractions, equivalent fractions and LCM/GCF. The CCSS Progression Documents will be used for sequencing and instructional models. We will explore strategies designed to meet the needs of all students and how to tie them to aspects of equity, agency and language.

Linear Equations in Context:

What is a Fair Living Wage? Part 2

In this activity, we will use linear functions and their graphs to interpret the affordability of housing for families with different circumstances and incomes. We will use technology for graphing, and we will interpret features of the linear functions in context: slope, intercept, and points of intersection of different lines.

We will pay attention to the equity practices of going deep with mathematics, leveraging multiple competencies, affirming identities, and drawing on multiple resources of knowledge.

Modeling with Data Part 2 - note independent of Part 1

Brief intro to modeling if the group is different. Titanic 1, 2 and 3. On April 15, 1912, the Titanic struck an iceberg on its first voyage and rapidly sank with only 710 of her 2204 passengers and crew surviving. Some believe that the rescue procedures favored the wealthier first class passengers. Data on survival of passengers are given, and participants ask and answer questions about the data. Then they are given data broken down by gender and age within each class and are asked to investigate what might be concluded from the given data.

Session will involve participants in going deep in mathematics. In addition, it will necessitate that participants draw on multiple resources of their knowledge, particularly relative to use of technology in analyzing data.