STRATEGIES FOR TEACHING MATHEMATICS Strategies for Building Number Sense and Computational Fluency

INCREMENTAL REHEARSAL INTERSPERSAL WORKSHEETS INDIVIDUALIZED SELF-CORRECTION CHECKLIST COVER-COPY-COMPARE ‘ERRORLESS LEARNING’ WORKSHEETS TIME DRILLS GAMES USE BOOKS TO ENGAGE STUDENTS WRITING ACTIVITIES SOCIO-DRAMATIC PLAY MNEMONICS MANIPULATIVES COOPERATIVE LEARNING MISCELLANEOUS IDEAS TIER II INSTRUCTIONAL PRINCIPLES

INCREMENTAL REHEARSAL Flash cards ( index cards with problems students are expected to knowhttp:// Student is given two seconds to answer problems – correct answers into “known” pile, incorrect answers into “unknown pile”. Nine cards are selected from “known” pile; rest discarded. A review deck is started by teacher reading and answering one problem from the unknown stack; student repeats problem and answer Teacher chooses one “known” card and uses with “unknown” card having student say problem and answer to both; two card sequence continues until each answer is given within two seconds Additional “known” problems are added to the deck until all nine known problems are used with “unknown problem” Review deck now has nine “known” and one “unknown” problem; when each is answered in two seconds or less, one original “known fact is discarded and another “unknown problem is added following the same procedure as above Jim Wright hp

INTERSPERSAL WORKSHEETS Teacher identifies challenging problems for a student Teacher identifies easy problems for a student Worksheet is prepared alternating two types of problems Worksheet Generator for Numbers at mult.php mult.php Jim Wright

INDIVIDUALIZED SELF- CORRECTION CHECKLIST Teacher meets with students to analyze mistakes Together develop way to avoid mistake Students use checklist when working independently Zrebiec Uberti, Mastropieri & Scruggs, 2004

COVER-COPY-COMPARE Jim Wright, enAcademic/ccc.php enAcademic/ccc.php Prepare worksheets with problems with answers on left, unsolved problems on right Student looks at worked problem Student covers correct problem, works problem on right and checks

‘ERRORLESS LEARNING’ WORKSHEETS Timed worksheets which include an answer key at the top of the page Student locates answer to problem they cannot work and write it in Caron, T. A. (2007). Learning multiplication the easy way. The Clearing House, 80, Jim Wright

TIME DRILLS TI-10/15

TIME DRILLS Textbook Worksheets Web Sources – athprobe/allmult.php athprobe/allmult.php – Extension Chart Progress Graph Progress

GAMES Mental Paper and Pencil Board Computer

MENTAL NUMBER GAMES A Minute or Less– start with a number and give students an operation and another number. Without telling them the answer, use that answer and give them another number and operation. Operations are performed in the order given. Make It More, Make It Less Number Sense and Operations Addenda Series Grades K-6, NCTM One-Out Navigating through Number and Operations in Prekindergarten-Grade 2, NCTM

PAPER AND PENCIL NUMBER GAMES Give students a number and have them come up with computational problems that fit that number. (The TI-10/TI-15 has a function that tells the students how many combinations there are and allows students to input their answers.) Give students a date and see how many problems they can write that uses all the digits in that date.

1/14/96 0 = – 9 – 1÷1 0r ÷1 - √9 1 = – 9 – = √9∙√4 – = √9 – (1+1) 4 = 5 = √9 – (1+1) 6 = 4√9 – etc

Board Games WWC Quick Review of the Article “Promoting Broad and Stable Improvements in Low-Income Children’s Numerical Knowledge Through Playing Number Board Games" 1 1 What is this study about? This study examined whether playing number board games improved numeracy skills of low- income preschoolers. It included 136 preschool children from 10 urban Head Start centers. The children ranged in age from four to five-and-a-half years old. Seventy-two children were randomly selected to play a number board game with a trained experimenter. The other 64 children played a different version of the game using colors instead of numbers. Numeracy skills were assessed at the end of a two-week period and again nine weeks later. What did the study authors report? Children who played the number game had better counting and number identification skills than children who played the color game. Children who played the number game were also better at picking the highest number from a pair of numbers and identifying positions on a number line. The effects persisted nine weeks after the game sessions ended. Estimated effect sizes at that point ranged from 0.55 to These effects did not differ by the age of the preschoolers. 1 “Promoting Broad and Stable Improvements in Low-Income Children’s Numerical Knowledge Through Playing Number Board Games.” Child Development, 79(2), Geetha B. Ramani and Robert S. Siegler. 1

Games Chart showing the possible applications/modifications of nine commercial board games for teaching early numeracy /intervention/Game_chart.pdf

BOOKS Remainder of One Annabelle Swift, Kindergartner Each Orange Had Eight Slices Two Ways to Count to Ten 12 Ways to get to 11 A Million Fish…More or Less How the Second Grade Got $8, to Visit the Statue of Liberty

WRITING ACTIVITIES Students write a letter to an absent student, parent, or student in another class to explain a process; include a problem to be worked using the process for the addressee to work Entrance/exit slips Media Campaign Middle School Mathematics Online Strategies for Teachers strategies/ strategies/

SOCIO-DRAMATIC PLAY Create Learning Stations Restaurant (menu, money, table numbers) Grocery (money, quantity, unit prices) Music (assign a number to instruments)

MNEMONICS FOR BASIC COMPUTATION (CAUTION) Don’t Miss Susie’s Boat Please Excuse My Dear Aunt Sally

MANIPULATIVES Base Ten Blocks Dominoes Number Lines Two sided chips, mat tiles, tile spacers Positive/Negative mats

COOPERATIVE LEARNING Homework Games I Have…Who Has… Activities Post-test checks Projects

MISCELLANEOUS IDEAS Position Paper Patterns in Math Color Coding Arithmetic Symbols Calculators Probes on Quantity Discrimination, Missing Number, Number Identification numberfly.php numberfly.php Jewell, Linda. (April 10, 2008). Early Number Strategies for Classroom Use.

Mathematics Intervention at the Secondary Prevention Level of a Multi-Tier Prevention System: Six Key Principles by Lynn S. Fuchs, Ph.D., Vanderbilt UniversityLynn S. Fuchs, Ph.D. “Mathematics interventions at the Tier 2 (secondary prevention) level of a multi-tier prevention system must incorporate six instructional principles: Instructional explicitness Instructional design that eases the learning challenge A strong conceptual basis for procedures that are taught An emphasis on drill and practice Cumulative review as part of drill and practice Motivators to help students regulate their attention and behavior and to work hard”