Several national professional groups, the National Mathematics Advisory Panel and the Institute for Educational Sciences in particular, have concluded that all students can learn mathematics and most can succeed through Algebra 2. However, the abstractness and complexity of algebraic concepts and missing precursor skills and understandings–number conceptualization, arithmetic facts, place value, fractions, and integers–may be overwhelming to many students and teachers.

Being proficient at arithmetic is certainly a great asset when we reach algebra; however, how we achieve that proficiency can also matter a great deal. The criteria for mastery, Common Core State Standards in Mathematics (CCSSM), set for arithmetic for early elementary grades are specific: students should have (a) understanding (efficient and effective strategies), (b) fluency, and (c) applicability and will ensure that students form strong, secure, and developmentally appropriate foundations for the algebra that students learn later. The development of those foundations is assured if we implement the Standards of Mathematics Practices (SMP) along with the CCSSM content standards.

** In these workshops, we provide strategies; understanding and pedagogy that can help teachers achieve these goals. **All workshops are held on the

**Framingham State University campus**from

**8:30am to 3:00pm**. Cost is

**$49.00 per workshop**and includes breakfast, lunch, and materials.

*PDP’s are available through the Massachusetts Department of Elementary and Secondary Education for participants who complete a minimum of two workshops together with a two-page reflection paper on cognitive development.*

*A. Creating A Dyscalculia Friendly Classroom
*

**Learning Problems in Mathematics (including math anxiety)**

*For special education, regular education teachers, interventionists, and administrators*

**September 28, 2018
**In this workshop, participants will learn (a) why learning problems in mathematics (e.g., dyscalculia, etc.) occur, (b) how children learn mathematics, (c) what are effective methods of teaching mathematics, and (d) how to fill gaps in mathematics learning. The major aim is to deliver mathematics instruction that prevents learning problems in mathematics from debilitating a student’s learning processes in mathematics.

*B. Number Concept, Numbersense, and Numeracy Series
*

**Additive Reasoning (Part I): How to Teach Number Concept Effectively**

*For K through grade second grade teachers, special educators and interventionists*

**October 26, 2018
**Number concept is the foundation of arithmetic. Ninety-percent of students who have difficulty in arithmetic have not conceptualized number concept. In this workshop we help participants learn how to teach number concept effectively. This includes number decomposition/recomposition, visual clustering, and a new innovative concept called “sight facts.”

**Additive Reasoning (Part II): How to Teach Addition and Subtraction Effectively**

*For K through grade third grade teachers, special educators and interventionists*

**November 30, 2018
**According to Common Core State Standards in Mathematics (CCSS-M), by the end of second grade, children should master the concept of Additive Reasoning (the language, concepts and procedures of addition and subtraction). The mastery means (a) understanding, fluency, and applicability. In this workshop, the participants will learn effective, efficient, and elegant ways of achieving this with their students.

**Multiplicative Reasoning (Part III): How to Teach Multiplication and Division Effectively**

*For K through four second grade teachers, special educators and interventionists*

**December 14, 2018
**According to CCSS-M, by the end of fourth grade, children should master the concept of Multiplicative Reasoning (the language, concepts and procedures of multiplication and division). The mastery means (a) understanding, fluency, and applicability. In this workshop, the participants will learn effective, efficient, and elegant ways of achieving this with their students.

*C. Proportional Reasoning Series
*

**How to Teach Fractions Effectively (Part I): Concept and Multiplication and Division**

**January 25, 2019 **

*For grade 3 through grade 9 teachers and special educators*

According to CCSS-M, by the end of sixth grade, children should master the concept of Proportional Reasoning (the language, concepts and procedures ratio and proportion). The concepts of ratio and proportion are dependent on the mastery of the concept of fractions. The mastery means (a) understanding, fluency, and applicability of fractions and operations on them. In this workshop, the participants will learn effective, efficient, and elegant ways of achieving the concept of fractions and multiplication and division of fractions and help their students achieve that.

**How to Teach Fractions Effectively (Part II): Concept and Addition and Subtraction**

*For grade 3 through grade 9 teachers*

**February 15, 2019
**According to CCSS-M, by the end of sixth grade, students should master the concept of Proportional Reasoning (the language, concepts and procedures ratio and proportion). The concepts of ratio and proportion are dependent on the mastery of the concept of fractions. The mastery means (a) understanding, fluency, and applicability of fractions and operations on them. In this workshop, the participants will learn effective, efficient, and elegant ways of achieving the concept of fractions and operations on fractions-from simple fractions to decimals, rational fractions and help their students achieve that.

*D. Algebra*

**Arithmetic to Algebra: How to Develop Algebraic Thinking**

*For grade 4 through grade 9 teachers*

**March 15, 2019
**According to CCSS-M, by the end of eighth-grade, students should acquire algebraic thinking. Algebra is a gateway to higher mathematics and STEM fields. Algebra acts as a glass ceiling for many children. From one perspective, algebra is generalized arithmetic. Participants will learn how to extend arithmetic concepts to algebraic concepts and procedures effectively and efficiently. On the other perspective, algebraic thinking is unique and abstract and to achieve this thinking students need to engage in cognitive skills that are uniquely needed for algebraic thinking. In this workshop we look at algebra from both perspectives: (a) Generalizing arithmetic thinking and (b) developing cognitive and mathematical skills to achieve algebraic thinking.

*E. General Topics
*

**Mathematics as a Second Language: Role of Language in Conceptualization and in Problem Solving**

*For K through grade 12 teachers*

**April 12, 2019
**Mathematics is a bona-fide second language for most students. For some, it is a third or fourth language. It has its own vocabulary, syntax and rules of translation from native language to math and from math to native language. Some children have difficulty in mathematics because of language difficulties. Most children have difficulty with word problems. In this workshop, the participants will learn how to teach effectively and efficiently this language and help students become proficient in problem solving, particularly, word problems.

**Learning Problems in Mathematics (including dyscalculia)**

*For special education and regular education teachers *

**May 17, 2019
**In this workshop, participants will learn (a) why learning problems in mathematics (e.g., dyscalculia, etc.) occur, (b) how children learn mathematics, (c) what are effective methods of teaching mathematics, and (d) how to fill gaps in mathematics learning.

**Standards of Mathematics Practice: Implementing Common Core State Standards in Mathematics**

*For K through grade 11 teachers (regular and special educators)*

**June 7, 2019
**CCSS-M advocates curriculum standards in mathematics from K through Algebra II. However, to achieve these standards, teachers need to change their mind-sets about nature of mathematics content; every mathematics idea has its linguistic, conceptual and procedural components. Most importantly, these standards cannot be achieved without change in pedagogy-language used, questions asked and models used by teachers to understand and teach mathematics ideas. Therefore, framers of CCSS-M have suggested eight Standards of Mathematics Practice (SMP). In this workshop, we take examples from K through high school to demonstrate these instructional standards with specific examples from CCSS-M content standards.