Trudy Denton
Curriculum Coordinator Math/Science
Email: dentong@wiltonps.org
Phone: 203-762-0381 ext. 8329

Chris Shpak
9 - 12 Instructional Leader - Math
Email: shpakc@wiltonps.org
Phone: 203-762-0381 ext. 6021

Mathematics Program Goals (adapted from Catalyzing Change NCTM 2018, NCTM Principles to Action 2014 and Common Core Standards for Mathematical Practice 2010)

Mathematics is one of the significant gatekeepers of success in modern society (Visible Learning for Mathematics, 2016). A well-designed and well-implemented math program enables students to use math to think critically, analyze a range of situations quantitatively, and make decisions based on thoughtful analysis in both their personal and professional lives. Learning mathematics should enable students to see themselves as capable lifelong learners and practitioners of mathematics and statistics. 

Mathematical proficiency encompasses the following components: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition (National Research Council, 2001). These capacities also address the future ready skills identified and described in Wilton Public Schools Portrait of a Graduate as contained in the Contemporary Literacies Philosophy 2022 . As students advance through the grades and make individual progress towards mastery of mathematics content and practices, they are able to exhibit with increasing fluency these processes and proficiencies of quantitative literacy along with the development of the specific attributes of the Vision of a Learner.

1. They learn mathematics conceptually.

Mathematically proficient students achieve procedural fluency from the conceptual understanding of mathematics. Procedural fluency enables students to use mathematical procedures flexibly and meaningfully to solve problems. Contemporary, Multiliterate Scholar

2. They make sense of problems and persevere in solving them.

Mathematically proficient students can explain problems and identify entry points towards arriving at a solution and plan a solution pathway.  They analyze givens, constraints, and relationships. They check their answers. Mathematically proficient students can explain the correspondence between different representations of mathematical situations (graphs, tables, diagrams, manipulatives, equations, etc.) Self-Navigating Expert Learner

3. They reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. Quantitative reasoning entails habits of  creating a coherent representation of the problem; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Creative, Entrepreneurial Designer

4. They construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They are able to analyze situations by breaking them into cases and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. Students at all grades can listen to or read the arguments of others, decide whether they make sense, and ask questions to clarify or improve the arguments. Contemporary, Multiliterate Scholar, Self-Navigating Expert Learner, Courageous Ethical Leader

5. They model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, and possibly improve the model as needed. Self-Navigating Expert Learner

6. They use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. They are able to use technological tools to explore and deepen their understanding of Concepts. Self-Navigating Expert Learner, Creative, Entrepreneurial Designer

7. They attend to precision.

Mathematically proficient students communicate precisely to others. They use clear definitions in discussion with others and in their own reasoning. For example, they state the meaning of the symbols they choose and are careful about specifying units of measure and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, and express numerical answers with a degree of precision appropriate for the problem context. Self-Navigating Expert Learner

8. They look for and make use of structure.

Mathematically proficient students look closely to find a pattern or structure. For example, they recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. Self-Navigating Expert Learner

9. They look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated, and look both for efficient and effective methods. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details which can lead to discovery of formulae, theorems and conventions. Self-Navigating Expert Learner

10. They demonstrate mastery of the CT Core Content Standards for Mathematics.

These standards define what students should understand and be able to do in their study of mathematics, and are a balanced combination of procedural and conceptual understanding. Students develop this understanding and procedural fluency through the mathematical practices delineated above. For grades K-5 the content standards include: Counting and Cardinality, Operations and Algebraic Thinking, Number and Operations Base 10, Number and Operations Fractions, Measurement and Data, and Geometry. In grades 6-8 they include Ratio and Proportions, Functions, Expressions and Equations, the Number System, Statistics and Probability, and Geometry. At the high school level they include Algebra, Functions, Number and Quantity, Statistics and Probability, and Geometry. Contemporary, Multiliterate Scholar, Self-Navigating Expert Learner

Core Principles for Mathematics Instruction (adapted from NCTM Principles to Action 2014)

The Mathematics Program Goals are realized through the following core principles, which embody three components of the instructional core for mathematics:  Standards (what students learn), Mathematical Practices (how students learn) and Classroom Instruction (how teachers teach). These components are essential to high quality math instruction. 

1. Mathematics instruction in Wilton is based on the fundamental belief that every student is a capable learner. The development of a strong conceptual understanding and mathematical mindset requires an engaging, student-centered learning environment that connects content standards to mathematical practices, incorporates meaningful problem-solving, and promotes reasoning and discourse between and among students and teachers.  

2. The teacher’s understanding of mathematics and his/her ability to make insightful instructional decisions are the most influential factors in student mathematics achievement. Teacher effectiveness in providing quality mathematics instruction is greatly enhanced by purposeful, job-embedded professional learning and reflective practice including teacher collaboration and various types of targeted professional learning experiences.  

3. Teachers of mathematics establish clear goals for the mathematics that students learn, situate goals within learning progressions, and use the goals to guide instructional decisions on a unit-by-unit and lesson-by-lesson basis. Establishment of clear goals not only guides teachers’ decision making during a lesson but also focuses student attention on monitoring their own progress toward the intended learning outcomes.

4. Mathematics instruction in the Wilton Public Schools is provided using a consistent student-centered framework for learning throughout the school year, this will most often include the following components: 

• Exploration and Problem Solving
  • Students explore math, notice patterns, build on prior knowledge and make connections.
• Teacher Facilitated Synthesis (consolidation)
  • Teachers highlight student work and use direct instruction to facilitate  students’ understanding of the math learning goals.
• Independent Practice and Small Group Instruction
  • Planned individual practice and small group instruction based on student needs.

5. Mathematics instruction includes a strong focus on using multiple mathematical representations (modeling) to deepen understanding of mathematics concepts and procedures as tools for problem-solving.

6. Mathematics instruction engages students in discourse to advance the mathematical learning of the whole class. Mathematical discourse includes the purposeful exchange of ideas through classroom discussion and questioning, as well as through other forms of verbal, visual, and written communication. Discourse in a mathematics classroom gives students the opportunity to share ideas, clarify understandings, construct viable arguments about how and why things work, and learn to see things from another perspective.

7. Mathematics instruction focuses on the development of both conceptual understanding and procedural fluency so that over time students become skillful in using procedures flexibly as they solve contextual and mathematical problems.

8. Teachers of Mathematics support students as they struggle productively to learn mathematics. This approach views “struggle” as an opportunity to delve more deeply into understanding the mathematical structure of problems and the relationships among mathematical ideas. Instead of simply seeking correct solutions, students develop the ability to make sense of the math they are learning and are able to transfer their learning to new situations.

9. Teachers of Mathematics use inclusive instructional strategies designed to engage all students and support them in sustained learning. Successful application of mathematics demands significant cognitive effort, so all students must be provided with equitable opportunities to learn math. This includes sufficient instructional time and access to quality space, equipment, and resources to support and motivate their engagement and learning.

10. Scientific Research-Based Interventions (SRBI):  A clearly defined and data-informed collaborative team process will be used to identify and monitor students in need of SRBI. Individualized, intensive instructional support and enhanced opportunities to learn must be provided to students who need additional support to develop mathematical skills.  

11. A productive partnership between home and school positively affects student 

achievement in mathematics. Teachers, students, and families need regular opportunities for dialogue and inquiry around student performance and instructional needs.

Common Core Standards for Math

Curriculum Materials

K-8 and Algebra I math classes in grade 8 use a problem based instructional resource, Illustrative Math. At the high school, Algebra I also uses a problem based program, Amplify/Desmos Algebra I. Both programs utilize similar structures and routines. 

Each unit begins with a pre-assessment that helps teachers gauge what students know about both prerequisite and upcoming concepts and skills, so that teachers can gauge where students are and make adjustments accordingly. The initial lesson in a unit is designed to activate prior knowledge and provide an easy entry to point to new concepts. By starting with what students already know, teachers invite all students to contribute to mathematical learning, center their students’ thinking, and respond as students develop conceptual understanding.

As the unit progresses, students are systematically introduced to representations, contexts, concepts, language and notation. As their learning progresses, they make connections between different representations and strategies, consolidating their conceptual understanding, and see and understand more efficient methods of solving problems, supporting the shift towards procedural fluency. The distributed practice problems give students ongoing practice, which also supports developing procedural proficiency.

Algebra Classes at WHS utilize the Amplify Desmos Algebra program. Like IM Amplify Desmos is a problem based instructional resource that combines interactive digital activities with printable materials to deepen conceptual understanding and procedural fluency. 

Resources

Students in kindergarten through grade 5 experience math through common core aligned grade level math courses

Math Course Sequence 6-8 (for detailed course description please refer to MB Program of Studies and Math Course Outlines)

Math Course Sequence 9-12 (for detailed course description please refer to WHS Program of Studies and Math Course Outlines)