Effective use of classroom instruction, meeting the individual needs of students in mathematics
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
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
Problem Solving Reasoning and Proof Communication Connections Representation
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.
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
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.
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
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
Review of Math Fact Math Games Problem-SolvingComponent Previously Mastered Automaticity Practice Concepts •Ensure retention of •Increases •Reinforces math •Requires the use understandings computational standards previously of strategies orObjectives previously achieved proficiency of and currently taught, related to concepts students through prior to Math previously math fact fluency Workshop modeled, taught, and practiced. •A.M. Math •Math Add+ Vantage •Investigation games •Problem of the •Entrance Slips Games for each Unit day •Pre-Assessments •Rocket Math to •Teacher Created •10- minute Math •Hands on Activities assess Games •Problem of the •Problems to solve •Computational •Commercially Week •Games Fluency Games prepared games •“Good Question”Examples •Activity sheets •First in Math of the Day •Computer Activities •Greg Tang Math •Menus •Differentiated Learning Tasks
Investigations Math Journals Computer Use Math Related toComponent Other Subject Areas •Similar to problem- •Enhance •Supports the •Help students solving practice, but mathematical process understanding of realize the requires the gathering skills math concepts interrelatedness of of data or other •Resource for the disciplinesObjectives information by investigation and for •Focus on the real- students creation of life applications of presentation of math findings •Real-life, relevant •Mathematical •Math games •math activities investigations observations •Math fluency tied to current provided by the •Definitions of math- practice (First in events teacher or generated specific vocab Math) •Science projects by students •Recording of •Compass Learning •Math connections •Test out conjectures conjectures •Smart Tech from social studies, •Discovery Questions •Log of prob. Solving •Blogs language arts, andExamples •I have, who has steps or strategies •Wikis science text books •Concept Maps •Explanation of •Matrix mathematical understandings
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
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)
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)
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
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
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
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
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
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
Teacher Facilitated/Student Directed 30-40 minutesWhole GroupMath Learning Centers 20-30 minutesClosure/Sharing 10 minutes ORWhole Group Lesson 4 days a week 45-60 minutesMath Learning Center 1 day a week 45-60 minutes
TimeActivityMath Fluency Practice 5-10 minutesProblem Solving Review and Focus (A.M. Math) 5-10 minutesSm. Group Instruction & Problem Solving 30-45 minutesLearning CentersIndependent Practice and Assessments (Exit Tickets, 10-20 minutescommon formative and summative assessments)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 activationof prior knowledge.
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.
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.