Foundations in Mathematics: Number

Grades Pre K - Grade 2

This course is designed to explore early childhood mathematics concepts, with a focus on number.  Critical learning experiences necessary to build a strong foundation in mathematical understanding will be explored. Specific topics to be covered include counting and cardinal meaning of number, number relationships, place value, and additive thinking. Throughout the course, teachers will engage with learning activities that build conceptual knowledge. Furthermore, teachers will work with problem solving and assessment tasks that reveal common student misconceptions. Through the examination of video footage, articles, and student work, teachers will create solutions to revealed misconceptions, and design appropriate instructional plans for moving children to a deeper level of understanding.

Developing Numbers Sense

Grades 3 – 5

This course is designed to enhance teachers’ understanding of foundational ideas of number that are critical for student success in grades 3 through 5. Topics to be covered include place value, multiplicative thinking, multi-digit computation, and fractions. Participants in the course will engage with technology, hands-on workshops and activities, relevant research, and the analysis of student work. Participants will make connections between research and classroom practice, and will develop assessments for use with their students. A focus will be placed on analyzing student errors and misconceptions with the planning of appropriate interventions.

Understanding Fractions

Grades 3-5

This course is designed for teachers grades 3-6 with a focus on fractions. Specific topics to be addressed include models for fractions, equivalence and comparison of fractions, working with all 4 operations with fractions, and real world applications of fraction problems. This course balances content and pedagogy, including elements and strategies of effective instruction and application of the Standards for Mathematical Practice. Teachers will engage with learning activities that strengthen their own conceptual knowledge. Through problem solving and examining student work, teachers will critique the reasoning of others.

Understanding Rational Numbers

Grades 3 – 7

This course is designed to enhance teachers’ foundational mathematics knowledge in the area of rational numbers: fractions, decimals, percents and ratios for those who teach either in a regular or an inclusion classroom. The need to strengthen teacher and student understanding of this topic is a key finding of the National Math Panel. Elements and strategies of effective standards-based instruction will be modeled and incorporated into the class. Participants will gain a deeper knowledge of how children understand rational numbers, what underlies common errors and misconceptions, and which activities and resources are helpful in developing a strong conceptual understanding of this topic.

Developing Proportional Reasoning

Grades 6-8

This course is designed for teachers grades 6-8 with a focus on fractions, decimals, percents, and ratios and the overall development of proportional reasoning. Specific topics include a study of rational numbers, division of fractions with an understanding of the traditional algorithm, equivalent ratios using the support of visual models, and ratio and percent problems. This course balances content and pedagogy, including elements and strategies of effective instruction and application of the Standards for Mathematical Practice. Teachers will engage with learning activities that strengthen their own conceptual knowledge.

Exploring the Standards for Mathematical Practice in the K-8 Classroom

Participants will unpack the Standards for Mathematical Practice, developing a deep understanding of their applications in the math classroom. Instructional models and specific strategies will be discussed and exemplified through the analysis of critical grade level content. Instructional models include: developing questioning techniques, utilizing specific talk moves to enhance mathematical discourse, differentiation instruction through a guided math model, developing learning targets for conceptual understanding, and teaching strategies for problem solving that uncover meaning and understanding. Activities in the course include presentation of research and ideas, solving rigorous math problems, analyzing teaching practice via video footage, and participation in exemplary classroom activities.  Participants will be engaged in self reflection and analysis of their own practice, and will be create an action plan to implement course ideas into their classrooms.

Unlocking the Standards: Expressions and Equations and Statistics and Probability

Grades 6 - 9

This is designed to explore the Expressions and Equations (EE), Statistics and Probability (SP) and Algebra I (A-CED, A-REI) standards for grades 6 - 9. Particular attention will be paid to the expressions and equations across the grades, with a focus on developing conceptual understanding in order to help students develop a solid foundation for entering a formal Algebra I course. The SP standards will be explored through application problems. Strategies for solving problems with high cognitive demands will be shared, including differentiating instruction using a guided math approach as well as utilizing tiered problems. Participants will unpack standards, participate and solve aligned tasks, and look at patterns of student errors, with an eye to planning appropriate interventions.

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