GUIDED MATH KERI STOYLESPRING 2012 Effective use of classroom

instruction, meeting the individual needs of students in mathematics

Thinking about MathematicsTrue of False?

T F 1. A number with three digits is always bigger than on with two

T F 2. To multiply 10, just add zero. T F 3. Scales identify intervals of one unit. T F 4. ‘Diamond’ is a mathematical term

used in learning shape geometry. T F 5. When you multiply two numbers

together, the answer is always bigger than both of the original numbers.

BONUS : If you draw a square, right-triangle, rhombus, trapezoid, and hexagon. Will your shapes look exactly like your neighbor’s shapes? Try it!

*Questions taken from TIMMS report of top 4th grade misconceptions

What is Guided Math? Guided Math is a structured, practical

way of matching math instruction to the diverse individual learners in the classroom

Assist students in using reasoning and logic, as well as basic skills necessary to solve problems independently

Differentiated, meeting the needs of all learners

Fluid groupings Target instruction/interventions

“Effective Mathematics teaching requires

understanding what students know and need to learn and then challenging

and supporting them to learn it well.”

~ NCTM, 2000

NCTM(National Council of Teachers of Mathematics)

Process Standards Problem Solving  Reasoning and Proof  Communication  Connections  Representation 

Adding it up (2001, Center for Education)

Strands of Mathematical Proficiency conceptual understanding—comprehension of

mathematical concepts, operations, and relations procedural fluency—skill in carrying out

procedures flexibly, accurately, efficiently, and appropriately

strategic competence—ability to formulate, represent, and solve mathematical problems

adaptive reasoning—capacity for logical thought, reflection, explanation, and justification

productive disposition—habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.

Intertwined Stands of Proficiency

Adding it up (2001, Center for Education)

Strands of Mathematical Proficiency

Adding it up Continued (2001, Center for Education)

These strands are not independent; they represent different aspects of a complex whole.

The most important is that the five strands are interwoven and interdependent in the development of proficiency in mathematics

CCSS (Common Core State Standards)Standards in Mathematical Practice 1. Make sense of problems and

persevere in solving them. 2. Reason abstractly and

quantitatively. 3. Construct viable arguments and

critique the reasoning of others. 4. Model with mathematics. 6. Attend to precision. 7. Look for and make use of

structure.

A Guided Math Session Before:

3-6 students per grouping Teacher decides on the focus of the session based

on assessments Teacher chooses math activity or problem that will

support selected learning target (“I CAN”)/ Big Idea Genuine questions are used to prompt student

thinking Focus Free Write KWHL Chart Concept Check

Arrange a functional room You may sit at one table or you may travel from group

to group Stations are clearly labeled

During Introduce problem/activity Question:

What do you notice?” What do you know about today’s ______________? What does the problem tell us? What words are tricky? (Anticipate vocabulary

challenges) What do you predict will happen next? What connections to other ideas do you see in

today’s activity? Students solve problem/begin activity

independently Teacher observes the group and coaches individuals

as needed.

Teacher observes and takes anecdotal notes.

After Teacher and student discuss the problem as a group to

explore strategies and understandings of the problem solving process. EMPHASIS ON PROCESS.

Students share strategies, partial thinking, and solutions. Teacher may clarify, re-teach, review skills or vocabulary

used in the session. Teacher records observations and evaluates student

problem solving/basic skills Based on performance, teacher plans next

session Students may be involved in self evaluation

Rubrics Exit Tickets (Assessments) Likert/ Feeling of Knowing Scale

What Makes Guided Math Different from Traditional Math Groups?

The focus is on skills and strategies that students construct and communicate through the activity

Session is based on one or two problem-solving opportunities

Flexible math groups change based on teacher’s ongoing assessments, therefore students are provided with immediate or next day (exit tickets) feedback

Students gain knowledge of vocabulary in context Instruction is based on student needs Students solve problems independently with

strategies that make sense to them Selection of math activity/problem is differentiated

based on student needs

Effective Uses for Math Workshop(Adapted from Sammons 2011)

Component

Review of Previously Mastered Concepts

Math Fact Automaticity

Math Games Problem-Solving Practice

Objectives

•Ensure retention of understandings previously achieved

•Increases computational proficiency of students through math fact fluency

•Reinforces math standards previously and currently taught, prior to Math Workshop

•Requires the use of strategies or related to concepts previously modeled, taught, and practiced.

Examples

•A.M. Math•Entrance Slips•Pre-Assessments•Hands on Activities•Problems to solve•Games•Activity sheets•Computer Activities•Differentiated Learning Tasks

•Math Add+ Vantage Games•Rocket Math to assess•Computational Fluency Games•First in Math •Greg Tang Math

•Investigation games for each Unit•Teacher Created Games•Commercially prepared games

•Problem of the day•10- minute Math•Problem of the Week•“Good Question” of the Day•Menus

Effective Uses for Math Workshop Continued(Adapted from Sammons 2011)

Component

Investigations Math Journals Computer Use Math Related to Other Subject Areas

Objectives

•Similar to problem-solving practice, but requires the gathering of data or other information by students

•Enhance mathematical process skills

•Supports the understanding of math concepts•Resource for investigation and for creation of presentation of findings

•Help students realize the interrelatedness of the disciplines•Focus on the real-life applications of math

Examples

•Real-life, relevant investigations provided by the teacher or generated by students•Test out conjectures•Discovery Questions•I have, who has•Concept Maps•Matrix

•Mathematical observations•Definitions of math-specific vocab•Recording of conjectures•Log of prob. Solving steps or strategies•Explanation of mathematical understandings

•Math games•Math fluency practice (First in Math)•Compass Learning•Smart Tech•Blogs•Wikis

•math activities tied to current events•Science projects•Math connections from social studies, language arts, and science text books

Planning Problem-Centered Lessons

Define the Heart of Your Lesson (Content and Task Decisions) Determine the Mathematics

Think in terms of mathematical concepts not skills Describe mathematics, not student behavior The best tasks will get at skills through concepts.

Think about what your student bring to the mathematics What do you students know or understand about the concept? Are there background ideas they have not developed? Is the scaffolding of the learning appropriate for your students?

Deign or select tasks Keep it simple! Good tasks often come from the text you are using Children’s Literature can impose great tasks Resources should be problem centered and rich mathematically

Predict student’s approaches to a solution Use what you know about your students to predict responses Can all engage at some level in the problem solving Plan for modifications, adjust tasks accordingly

Define How You will Carry out the Plan in Your Classroom

(Teaching Actions)

Articulate student responsibilities Discuss and define expectations of

dialogue, writing “S.E.W.” box, and journaling about thinking

Students should be able to tell you: What they did to get the answer Why they did it that way Why they think the solution is correct

Plan the BEFORE activities Plan the DURING activities Plan the AFTER dialogues (MOST

important)

List the Critical Decisions Made(Completed Plan)

Write out the plan Goals/ Big Ideas/ Target Skills/ “I CAN” Task and Expectations Before Activities During Hints and Extensions After-Lesson discussion format (Be sure to

have ample time for this) Assessments (I enjoy exit tickets as quick

formative/summative checks to best prepare for the following session)

Stations (Centers)

7 (6 + 1 Computer ) stations are ideal for a K-6 Classroom

I chose the term stations for the 5th grade setting, however the term centers could be used.

Stations activities should be introduced first, then placed in rotation

Some stations may stay all year to refresh skills

Rotations do not need to change all at once It is best to change out one station at a time

Possible Station Ideas Concept Games

• Depending on Unit of study example may include:• Close to 100, Close to 1,000, Close to 7,500, Close to 0 ot 1• Decimal Duel• Capture 5• War with equivalent fractions, decimals, and percents• Order of Operations Game

Math Add+Vantage Games Number Battle (addition and subtraction) Rolling Groups (multiplication) Speed (multiplication) Treasure Chest

Marcy Cook Thinking Tiles

Possible Station Ideas Continued

Critical Thinking/Logic Games to encourage Conjectures• Number Puzzles, Tantrix, Rubrics cube• Qwirkle, Yatzee, and Mancalla• Math Analagies

Fluency and Graphing Mosaics Computer Station Number Sense

Today’s Magic Number (TMN, I created for 3rd grade) Target Number (Similar to TMN) Math Dice Game Multiplication (Juniper Green) Leap Frog (Math Add+Vantage) Student created Problems

Build a Community of Learners Listen to others and respect their thinking Ask thoughtful questions Disagree with others in a respectful way Volunteer your ideas in group discussion Take risks with challenging ideas and

problems It’s ok to be wrong, no one is perfect, this

is how we think and learn. Confusion leads to new learning!

Enjoy discovering new things about math

Groupings Heterogeneous groups lead to higher

quality experiences for all children Groups should not be based on overall

math ability, they should be based on content of point in time

Groups should be fluid and flexibile

Reflections of Stations (Centers)

Center Visited Date Comments/Reflections about this center (station)

• I staple a copy of this on the outside of student math journal•I keep all student journal in a colored crate in number order. • Folder up, ready to check or grade• Folder down, graded

Suggested Possible Schedule for Guided Math (Sammons 2011)

Teacher Facilitated/Student Directed Whole Group

30-40 minutes

Math Learning Centers 20-30 minutes

Closure/Sharing 10 minutes

Whole Group Lesson 4 days a week 45-60 minutes

Math Learning Center 1 day a week 45-60 minutes

OR

K. Stoyle Schedule (2011-2012)

Activity Time

Math Fluency Practice 5-10 minutes

Problem Solving Review and Focus (A.M. Math) 5-10 minutes

Sm. Group Instruction & Problem SolvingLearning Centers

30-45 minutes

Independent Practice and Assessments (Exit Tickets, common formative and summative assessments)

10-20 minutes

Discussion 10-20 minutesThis schedule is flexible, whole group instruction takes place as needed. Introduction to new content may lead to a day of more discovery and activation of prior knowledge.

Journaling Good Questions or Story Problems given 1-

2x per week. Students are provided with a 4 point rubric I try to give prompts Tue and Thur. to support

mathematical comprehension Should incorporate process standards On current content topic

Released question from state assessments Open ended questions How to questions Evaluation questions R.A.F.T.S.

Resources Adding it Up: Helping Children Learn Mathematics. Strands of

Mathematical Proficiency. http://www.nap.edu/openbook.php?record_id=9822&page=115

Blanke, B. (2010) Guided Math Seminar , Cleveland, Oh. Common Core State Standards Initiative. Common core state standards:

Mathematics. Http://www.corestandards.org/the-standards/mathematics Linden, T. (n.d.) Teacher created A.M. Math Problem Solving Questions. NCTM. NCTM process standards:

http://www.nctm.org/standards/content.aspx?id=322 Sammons, L. (2009) Guided math ; A framework for mathematics

instruction. Huntington Beach, CA: Shell Education. Sammons, L. (2011) Building Mathematical Comprehension. Huntington

Beach, CA: Shell Education Small, M. (2009) Good Questions; Great Ways to Differentiate

Mathematics Instruction. Teachers College, Columbia University, New York.

Stoyle, K. (n.d.) Teacher created materials Wright, R., Martland, J., Stafford, A., Stanger, G. (2006) Teaching

Number in the Classroom with 4-8 year olds. Thousand Oaks, CA: Sage Publications.

Wright, R ., Martland, J. Stafford, A., Stranger, G. (2011) Teaching Number; Advancing Children’s Skills and Strategies. Thousand Oaks, CA: Sage Publications.

Wright, R.,Ellemor-Collins, D., Tabor, P.(2012) Developing Number Knowledge; Assessment, Teaching & Intervention with 7-11 year-olds. Thousand Oaks, CA: Sage Publications.