Greg Soldatenko's mini-course: Singapore Math Formative Assessments (SMFA)

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Singapore Math Formative Assessments (SMFA) Course Description

In highly practical terms, this course will define Singapore Math Formative Assessments (SMFA), equip you with the formative assessment tools to teach mathematics for understanding and help you prepare your students for State tests.

SMFA Course Objectives

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By the end of this course you will be able to:

1. Define Formative Assessments process in the context of the Singapore Math framework.

2. Understand the relationship between the Singapore Math Framework and the Common Core State Standards (CCSS-M).

3. Develop SMFA strategies to assess students’ prior knowledge and identify students’ misconceptions.

4. Assess students’ current problem solving abilities.

5. Design SMFA for the Singapore Math lesson plans.

6. Design SMFA rubrics to measure students’ progress toward meeting learning goals, CCSS-M and State tests.

7. Use SMFA rubrics to differentiate instruction and to provide feedback to students


The ultimate learning objective of this mini-course is for you to design Singapore Math Formative Assessments for a unit of instruction in the grade that you teach.

The SMFA Course Pre-requisites

Teachers in Grades K-2 should take the following courses listed below prior to registering for this course:

  • Introduction to Singapore Math in K-2
  • K-2 Number Sense
  • Building Fluency in K-2

Teachers in Grades 3-5 should take the following courses listed below prior to registering for this course:

  • Introduction to Singapore Math in Grades 3-5
  • Introduction to Bar Modeling
  • Multiplication & Division in Grades 3-5
  • Fractions in Grades 3-5

SMFA Course Introduction

Welcome to Singapore Math Formative Assessments (SMFA)!

Singapore Math is a constructivist approach (developed in Singapore) to teaching students mathematics for understanding. Problem Based Learning (PBL) is at the heart of this method. Singapore Math became very popular in the United States due to Singaporean students’ consistently ranking top on the international benchmark tests (TIMSS and PISA) over the last twenty years.

SM Pentagon.png

The Singapore Math framework was a model for developing the Common Core State Standards in Mathematics in the United States.

The constructivist Concrete-Pictorial-Abstract pedagogy and model drawing lay the foundation of the most popular K-5 mathematics programs used in the United States today. They include the NYS Math modules, Eureka Math, Primary Mathematics and Math in Focus.

Singapore Math Formative Assessments (SMFA) are teaching strategies designed to make students’ mathematical thinking visible in the context of the Singapore Math Framework and the Common Core State Standards in Mathematics.

The powerful SMFA teaching strategies that you will learn in this course will help you navigate multiple challenges that you face, not only in teaching Singapore Math, but also in preparing your students for State tests and in meeting the Common Core State Standards in Mathematics.


Specifically, this course will answer the following questions:

1. How can SMFA help you teach mathematics for understanding?

2. How can SMFA help you meet your State Standards and prepare your students for State tests?

3. How to design SMFA rubrics for Units in your grade that help you differentiate instruction, provide students with formative feedback and meet desired learning goals?

Enjoy your journey!

SMFA Course Structure

Organization

This course is organized into three units each of which contains three lessons. In each unit, I will provide you with a “Study Guide” section. The Unit Study Guide will contain the Big Ideas of the Unit and an overview of the three lessons that follow. I will also provide you with an Overview for each lesson. The Overview section will focus your attention on main ideas, provide you with learning objectives and ask you to complete assignments in each lesson.

Learning Activities

In learning about SMFA you will engage in four major activities:

1. Readings and Watching short Videos [and Power Point Presentations]

You’ll need to study Singapore Math textbooks, teacher editions, and other materials to deepen your content knowledge of Singapore Math and Formative Assessments. You’ll also watch selected video clips to build your knowledge about Singapore Math.

2. Critical Analysis

You will investigate a series of the Singapore Math content tasks and pedagogical tasks focusing on SMFA strategies to make student thinking visible. To build a solid understanding of SMFA, you’re encouraged to seek connections between SMFA’s big ideas and lesson plans in your Teacher Editions. You’re encouraged to actively seek conceptual connections among topics in your grade and vertically across all K-5 grades. You’ll analyze SMFA strategies and relate them to each of the five areas in the Singapore Math framework and the Common Core Standards in Mathematics.

3. Discussions and Reflections

You’ll share your new knowledge of SMFA and your teaching experience through online discussions. You’re encouraged to discuss how the same mathematical idea (for example, Place Value concept) evolves over time not only in your grade, but also in prior and subsequent grades. You will reflect on your learning experiences and relate them to your teaching practices in your Math Journal.

4. Designing SMFA

You’ll design lesson plans and design SMFA rubrics to assess students’ prior knowledge, current problem solving abilities and progress toward meeting unit goals and State tests. You’ll work individually and in groups to develop SMFA for a unit of instruction in your Grade.

To get the most out of this course you should:

  • Read and watch all of the required materials
  • Build connections between SMFA’s Big Ideas and daily lesson plans
  • Actively engage in discussions with your colleagues
  • Develop SMFA for various lessons
  • Thoughtfully reflect on your learning experiences in your Math Journal

Reflection: Keep Your Math Journal

EWM Math Journal.png

Any time you see this image, you should write down your thoughts in a Math Journal.

A Math Journal is an important Formative Assessment tool that students use in Singapore to solve mathematical problems and keep daily records of lessons during the school year.

I recommend that you use a Math Journal to solve mathematical problems, draw models and record your thoughts over the duration of this course.

I will provide you with a Math Journal as part of this course.

SMFA Course Units: Begin Here

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Unit 1: How can SMFA help you teach mathematics for understanding?

Learning Objectives

After completing this unit, participants will be able to:

  • Define Singapore Math Formative Assessments
  • Create a sequence of learning progressions in the Singapore Math curriculum
  • Identify the key concepts that students need to learn in each grade
  • Explain how to devote the majority of instructional time to teaching mathematics for understanding


Unit 2: How can SMFA help you meet your State Standards and prepare your students for State tests?

Learning Objectives

After completing this unit, participants will be able to:

  • Identify critical instructional areas and major clusters for the grade, as described in the CCSS-M
  • Explain success criteria that will show evidence that students are meeting the goals in the major clusters
  • Combine questions from the Singapore Math materials similar to the State test type questions to imitate the State exam
  • Plan SMFA Strategies that will show evidence of student learning in the CCSS-M major clusters

Unit 3: How to design SMFA rubrics for Units in your grade that help you differentiate instruction, provide students with formative feedback and meet desired learning goals?

Learning Objectives

After completing this unit, participants will be able to:

  • Explain how to differentiate instruction and scaffold in the ZPD to meet desired goals
  • Design the SMFA rubric for anchor and guided practice type lessons in a unit
  • Create scenarios to provide students with formative feedback to meet desired learning goals

References and Resources

  • Ban Har, Y. (2014). Bar Modeling: A Problem-solving Tool. Singapore: Marshall Cavendish Education.
  • Ban Har, Y., Edge D. (2011). Teaching of Whole Numbers. Singapore: Marshall Cavendish Education.
  • Bransford, J. D., Brown, A. L., & Cocking, R.R. (2000). How People Learn: Brain, Mind, Experience, and School. Washington, DC: National Academy Press.
  • Heritage, H. Margaret (2010). Formative Assessment: Making it Happen in the Classroom. California: Corwin.
  • Heritage, H. Margaret (2015). Improving Teaching and Learning Through Effective Formative Assessment. New Jersey: NCTM Regional Conference.
  • Hong, K. H, Mei Y. S., Lim, J. (2009). The Singapore Model Method for Learning Mathematics. Singapore: Marshall Cavendish Education.
  • Hammond, L. (2008). Powerful learning : what we know about teaching for understanding. San Francisco, CA: Jossey-Bass.
  • Ma, Liping (2010). Knowing and Teaching Elementary Mathematics. Anniversary Edition. New York: Routledge.
  • National Council of Teachers of Mathematics (2014). Principals to Actions: Ensuring Mathematical Success for All. Reston, Virginia: NCTM.
  • Rubrics
http://rubistar.4teachers.org/
http://www.rubrics4teachers.com/
  • Stigler, J. W., Hiebert, J. (2009). The Teaching Gap. New York: Free Press.
  • Teaching Channel:
https://www.teachingchannel.org/videos/daily-lesson-assessment
  • You Tube:
https://www.youtube.com/watch?v=ekvAE7K3mmA
https://www.youtube.com/watch?v=vxJSCwcnac8&index=1&list=PL3ttUbu6au68Z1LWv8SCoBVy64tU1uS1W
  • Vygotsky, L.S. (1978). Mind and society: The development of higher mental processes. Cambridge, MA: Harvard University Press.