Mathematics Teachers Kindergarten – Grade 2 Joy Donlin & Ryan Dunn October 7, 2013

Welcome and introductions Discussion – how do students learn mathematics? Exploring the paradigm shift Participating in a lesson that meets the shift Translating the standards Designing a lesson Reflections Agenda

Participants will consider their educational platform. Participants will increase their knowledge and understanding of Operations and Algebraic Thinking and the Standards for Mathematical Practice in the CCSSM. Participants will apply their knowledge and understanding to develop a lesson. Outcomes

Design Methodology Standards Interpretation Expected Evidence of Student Learning Text-based Discussion (Research) Model Construction (Trying on the work) Task & Instructional Plan Student Work Examination Revision of Task & Instructional Plan

5 College and Career Readiness SCUSD Strategic Plan Common Core State Standards (CCSS) Focus Pillar One: Career and College Ready Students The focus of the CCSS is to guarantee that all students are college and career ready as they exit from high school.

Common Core Standards Framework Common Core Content Standards Instructional Shifts Practices (Math & Science)/ Descriptors (ELA) Curriculum Equity Assessment Teaching & Learning

Content Focus Areas Content Focus Areas for Teachers Grades K – 2Counting and Cardinality (K); Operations and Algebraic Thinking & Number and Operations in Base Ten Grades 3 – 5Number and Operations – Fractions Operations and Algebraic Thinking & Number and Operations in Base Ten Grades 6 – 7Ratios and Proportional Reasoning The Number System Grade 8Expressions and Equations Functions Grades 9 – 12Integrated Math 1

This is a 2 player game. The idea of the game is to be the person that lands on zero. You begin at the number 10 Each turn you can choose to go back by 1 or 2. Race to ‘0’

What are some questions we could ask to prompt students to think more deeply about this game? Is this a rigorous activity to undertake with kindergarten students? Race to ‘0’

Some questions to prompt deeper thinking: Is there a strategy that can help you win the game? Are there numbers along the way that can help you land on zero? (powerful numbers) Race to ‘0’

How would the game change if we: Started at 12 or 15 Raced from 0 to 10 Could move by 1, 2 or 3 What are some variations…

Why do you think it is so common for students (and adults) to talk about mathematics as being hard? 2 minutes to discuss this with the person next you. 3 minutes to share thoughts with your table. 5 Minute Brainstorm…

Make a list of the top 5 things that support elementary students in learning mathematics. Rank them from 1 to 5.

Share your #1’s with a neighbor. Are your #1’s the same?

There are two major theories on how children think and learn: Behaviorism – has long been associated with mathematics learning. Constructivism – has been shown to promote meaningful learning. How do children learn mathematics?

Has roots in stimulus response and conditioned learning. Asserts that behavior can be shaped through rewards and punishment. Focus on low level thinking, not mathematical thinking. Behaviorism

Behaviorism has had a significant impact on mathematics programs: Students are shown algorithms. Mathematical relationships are illustrated in textbooks. Produces mastery of specific objectives but lacks critical connections that make knowledge meaningful and useful Behaviorism…

Constructivism advocates that: Knowledge is not passively received, but actively constructed by the learner. The learner uses prior knowledge to construct new meaning (Piaget). Learning is a social process (Vygotsky) Constructivism

Think back to your list of top 5 things that support elementary students to learn mathematics. Is there evidence of Behaviorism and/or Constructivism on your list? What is your Educational Platform?

CCSS for Mathematics Paradigm Shift Mathematics learning that goes beyond the demonstration of procedural content by: providing extensive opportunities to reason and make sense of the mathematics students are learning emphasizing student understanding, problem solving and sense making developing deep understanding of content and use of conceptual understanding as a precursor to developing procedural or symbolic fluency.

L Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them 6. Attend to precision 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Reasoning & Explaining Modeling & Using Tools Seeing Structure & Generalizing Overarching Habits of Mind of a Productive Mathematical Thinker Legend

SMP 1,4, SMP 2,3,7 SCUSD SMP Emphasis

Break

Choose a playing card from the materials bag. 1 – Student 2 – Observer for SMP 3 – Observer for use of teacher moves/ questioning strategies 4 - Observer for use of formative assessment

Grade 1 OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., = = = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding by creating the known equivalent = = 13). Grade 2 OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. Lesson

The Task Using only the numbers 3, 4, 5, 6, 7. Place any 4 numbers into the frame below to make a true equation. Try to find other solutions. ___ + ___ - ___ = ___ Number Tiles

How many solutions do you think there are? How would you know when you have found them all? What do we notice from the solutions we have already found? Deepening the Investigation

How could students apply the mathematical knowledge from this investigation? Applying the Knowledge

For the original problem, the tiles are consecutive starting at 3. What happens if you use five consecutive numbers beginning with a different number? (4, 5, 6, 7 and 8) Will there be the same number of solutions? Deepening the Learning

As a school team discuss the following: 1.Describe what the student(s) know, understand and are able to do based on your role during the lesson and provide evidence to support your answer. 2.Describe the implications for instructional design of a mathematics lesson. Debrief

LUNCH

Try these as a warm up after the lunch break. Given the numbers on the edges try to work out the numbers in the vertices. Here is an example: Arithmagons

Try these…

3 Big Ideas: 1.Read 2.Translate 3.Design Units and Learning Activities Wiggins, 2011 Honoring the CCSSM

Domain: Operations and Algebraic Thinking Kindergarten: 1 Cluster Grade 1: 4 Clusters Grade 2: 3 clusters Unpacking the Standards

As the grade level/band teacher leader at your school, you will have a role: 1.As the content expert 2.As a content pedagogy expert 3.As the leader of collaborative planning – units of study and lesson design 4.As the leader of peer observation experiences 5.As the lead learner and sharer of information Taking It Back

“you can’t lead where you won’t go” Barth, 2002

In a lesson that you will be teaching in the next week, will my students be experiencing a similar kind of learning? Work with a colleagues to adjust your lesson design as necessary for the following: 1.How will the problem/task or activity provide students the opportunity to engage in the Standards for Mathematical Practice? 2.How/when will students make sense of problems and persevere in solving them? 3.How/when will students be reasoning abstractly and quantitatively? 4.How/when will students be explaining their thinking to each other? 5.How/when will students be critiquing the reasoning/thinking of others? 6.How/when will students be modeling with mathematics? 7.How/when will students be attending to precision? 8.How/when will students be looking for and making use of the structure of the lesson content? Be prepared to share the lesson with another grade level team and your school team. Lesson Design

Share the lesson(s) with another grade level team. Share the lesson(s) with your school team. Receiving feedback

Reflection One idea that interests me is …Something I plan to try … One step I will take tomorrow to lead other math teachers in my grade is … I wonder …

Enter the following link and complete the online questionnaire: MG Reflection Questionnaire

“Professional development works, if it works at all, by influencing what teachers do...” Instructional Rounds in Education, pg. 24.