• Math

    K-12 Math
    Tier 1 & 2 Intervention Menu
    www.interventioncentral.org 
     
    Students who can be trusted to work independently and need extra drill and practice with math computational problems, spelling, or vocabulary words will benefit from Cover-Copy-Compare.
     
    Students can improve both their accuracy and fluency on math computation worksheets by independently self-monitoring their computation speed, charting their daily progress, and earning rewards for improved performance.
     
    Teachers can improve accuracy and positively influence the attitude of students when completing math-fact worksheets by intermixing 'easy' problems among the 'challenging' problems. Research shows that students are more motivated to complete computation worksheets when they contain some very easy problems interspersed among the more challenging items.
     
    Students can consistently perform better on applied math problems if they follow an efficient 4-step plan of understanding the problem, devising a plan, carrying out the plan, and looking back.
     
    This intervention employs students as reciprocal peer tutors to target acquisition of basic math facts (math computation) using constant time delay (Menesses & Gresham, 2009; Telecsan, Slaton, & Stevens, 1999). Each tutoring ‘session’ is brief and includes its own progress-monitoring component--making this a convenient and time-efficient math intervention for busy classrooms.
     
     The student monitors and records her or his work production on math computation worksheets during time-drills—with a goal of improving overall fluency (Maag, Reid, R., & DiGangi, 1993). This intervention can be used with a single student, a small group, or an entire class. 

    Students can consistently perform better on applied math problems if they follow an efficient 4-step plan of understanding the problem, devising a plan, carrying out the plan, and looking back. 

    8. Balanced Massed & Distributed Practice
    Teachers can best promote students acquisition and fluency in a newly taught math skill by transitioning from massed to distributed practice. When students have just acquired a math skill but are not yet fluent in its use, they need lots of opportunities to try out the skill under teacher supervision – a technique referred to as ‘massed practice’. Once students have developed facility and independence with that new math skill, it is essential that they then be required periodically to use the skill in order to embed and retain it – a strategy also known as ‘distributed practice’.

    Students can effectively clarify their knowledge of math concepts, and problem-solving strategies through regular use of class ‘math journals’. Journaling is a valuable channel of communication about math issues for students who are unsure of their skills and reluctant to contribute orally in class. Regular math journaling can prod students to move beyond simple ‘rote’ mastery of the steps for completing various math problems toward a deeper grasp of the math concepts that underlie and explain a particular problem-solving approach. Teachers will find that journal entries are a concrete method for monitoring student understanding of more abstract math concepts. To promote the quality of journal entries, the teacher might also assign them an effort grade that will be calculated into quarterly math report card grades.
     
    Making a drawing of an applied or “word”, problem is one tool that students can use to help them find the solution. An additional benefit is that it can reveal to the teacher any student misunderstandings about how to set up or solve the word problem.
     
    Reluctant students can be motivated to practice number problems to build computational fluency when given worksheet that include an answer key (number problems with correct answers) displayed at the top of the page. Such speed drills build computational fluency while promoting student’s ability to visualize and to use a mental number line.
     
    Explicit time-drills are a method to boost students’ rate of responding on math-fact worksheets. Explicit time-drills work best on ‘simple’ math facts requiring few computation steps. They are less effective on more complex math facts. Also, a less intrusive and more flexible version of this intervention is to use time-prompts while students are working independently on math facts to speed their rate of responding. For example, at the end of every minute of seat work, the teacher can call the time and have students draw a line under the item that they are working on when the minute expires.
     
    Improve students’ rate of homework completion and quality by using reinforcers, motivating ‘real-life’ assignments, a homework planner, and student self-monitoring.
     
    Research shows that when teachers use specific techniques to motivate their classes to engage in higher rates of active and accurate academic responding, student learning rates are likely to go up.
     
    15. Math Talk 
    Teachers can promote greater student ‘risk-taking’ in mathematical learning when they cultivate a positive classroom atmosphere for math discussions while preventing peers from putting each other down.
     
    During large-group math lectures, teachers can help students to retain more instructional content by incorporating brief Peer-Guided Pause sessions into lectures.
     
    Response cards can increase student active engagement in group math activities while reducing disruptive behavior.
     
    When teachers instruct students in more complex math cognitive strategies they must support struggling learners with a ‘wrap-around’ instructional plan. The plan incorporates several elements: assessment of the student’s problem-solving skills, explicit instruction, process modeling, performance feedback and review of mastered skills or material.
     
    Solving an advanced math problem independently requires the coordination of a number of complex skills. The student must have the capacity to reliably implement the specific steps of a particular problem-solving process, or cognitive strategy. At least as important, though, is that the student must also possess the necessary metacognitive skills to analyze the problem, select an appropriate strategy to solve that problem from an array of possible alternatives, and monitor the problem-solving process to ensure that it is carried out correctly.
     
     The student is taught explicit number counting strategies for basic addition and subtraction. Those skills are then practiced with a tutor (adapted from Fuchs et al., 2009).
     
    The student plays a number-based board game to build skills related to 'number sense', including number identification, counting, estimation skills, and ability to visualize and access specific number values using an internal number-line (Siegler, 2009) 
     
    22. Self- Monitoring: Customized Math Self-Correction Checklists
    The teacher analyzes a particular student's pattern of errors commonly made when solving a math algorithm (on either computation or word problems) and develops a brief error self-correction checklist unique to that student. The student then uses this checklist to self-monitor—and when necessary correct—his or her performance on math worksheets before turning them in (Dunlap & Dunlap, 1989; Uberti et al., 2004).
     
    The student plays a number-based board game to build skills related to 'number sense', including number identification, counting, estimation skills, and ability to visualize and access specific number values using an internal number-line (Siegler, 2009). 
     
     Students should develop automatic recall of basic math-facts in the elementary grades. Math-fact mastery permits students to shift valuable cognitive capacity away from simple calculations toward higher-level problem-solving (Gersten, Jordan, & Flojo, 2005; National Mathematics Advisory Panel, 2008). An important goal for schools, then, is to ensure that students are proficient in math-facts by the end of grade 5 (Kroesbergen & Van Luit, 2003) to better prepare them for the demanding middle-school math curriculum. 
     
    Teachers need an instructional strategy to encourage students to be more savvy interpreters of graphics in applied math problems. One idea is to have them apply a reading comprehension strategy, Question-Answer Relationships (QARs) as a tool for analyzing math graphics. 
     
    The teacher analyzes a particular student's pattern of errors commonly made when solving a math algorithm (on either computation or word problems) and develops a brief error self-correction checklist unique to that student. The student then uses this checklist to self-monitor—and when necessary correct—his or her performance on math worksheets before turning them in (Dunlap & Dunlap, 1989; Uberti et al., 2004).