Helping Students Struggling with Math - National Association of ...

RESEARCH REPORTHelping StudentsStruggling with MathElizabeth G. ShellardTeachers needto employ a widevariety of strategiesto developunderstanding ofmath concepts andencourage positiveattitudes.40Principal ■ November/December 2004

Their math homeworkincludes errors or isonly partially done—ifat all. They perform poorly onstandardized tests as well asclassroom math tests. Studentswho struggle with mathematicsmay do so because they areunable to “see” the largerpicture, make associations, orremember basic facts. Theyneed not only high-qualityIN BRIEFThis report focuses on strategiesteachers can use to help studentsstruggling with math. A critical instructionalcomponent is to make surethey understand a skill or concept beforebeing asked to practice it. Adaptinginstruction to a variety of learningstyles can be useful, as is encouragingstudents to “think aloud” about howthey approach math problems. Severalstrategies are suggested for studentswho have difficulty with basic mathoperations and word problems.teaching, but well-planned instruction explicitly structured todevelop a specific sequence of skills. In addition, providing amix of direct instruction of new skills and concepts, guidedpractice, opportunities for complex thinking and problemsolving,and time for discussion is even more important forthe struggling student than for students in general.BRITT ERLANSON/IMAGEBANKA critical component of mathinstruction—particularly crucial forstruggling students—is ensuring thatstudents understand a skill or conceptbefore being asked to practice it. Ashort in-class assignment can helpteachers check for this understanding.But assigning multiple problems to studentswho have only a tenuous understanding—orworse, a misunderstanding—of the skill can lead to confusion andfrustration. Teachers should take specialcare in assigning homework tothese students.Teachers can address some of theproblems presented by struggling learners,as well as normal differences in skilllevels and developmental levels, throughthe use of adaptations or accommodations(Ebeling et al. 1994), many ofwhich can be incorporated into regularclassroom instruction. Activities that provideopportunities for students to use avariety of learning styles increase thelikelihood that more students will understandthe new concept or skill beingpresented. Here are some approachesthat complement different strengths:Spatial: Using visual clues;Linguistic: Reading word problems;Logical-mathematical: Creating andsolving equations;Kinesthetic: Exploring tactile models;Musical: Creating auditory patterns;Interpersonal: Sharing strategies; andIntrapersonal: Journal writing (Kingand Parker 2001).Developing UnderstandingTeachers working with youngchildren know the importance ofinstruction directed toward students’developmental level. This conceptremains important to math instructionthrough all grade levels. It may requiremoving from the concrete to the pictorialto the abstract, with opportunitiesprovided for students to actively manipulateobjects or draw graph-like“pictures.” However, “Students do notdiscover or understand mathematicalconcepts simply by manipulating concretematerials.... [teachers] must helpstudents focus on underlying mathematicalideas...” (Sutton and Krueger2002)www.naesp.org Principal ■ November/December 2004 41

■ Provide an example of a correctlysolvedproblem at the beginning ofevery lesson;■ Have students verbally or visuallyexplain how to solve a problem;■ Introduce only one concept at atime and teach it to mastery;■ Teach in small chunks so that studentsget lots of practice, one step at atime;■ Provide learning aids, such ascalculators, to help students focus onconceptual understanding;■ Routinely model the use of estimationand have students estimate areasonable solution before starting anycomputation;■ Teach families of facts; and■ Demonstrate all concepts withmanipulatives.Word Problems. Many studentsexperience difficulty with word problems(Jarrett 1999). For some, theproblem lies with an inability to readand comprehend the problem (Bleyand Thornton 1995). Others have troubledistinguishing relevant from nonrelevantinformation, whereas somecannot translate the words into mathematicaloperations they understand.The following strategies may providestudents with different ways to “see”word problems and better grasp theconcepts of what is being asked andhow to work toward a solution:Work backward. Give students boththe problem and the answer, then helpthem to develop connections betweenthe words in the problem and their numericrepresentations.Draw and model. Draw a picture ormanipulate objects to form a modelto help students visualize a situation,verbalize abstract ideas, and explainrelationships.Make a table or a graph. Tables andgraphs provide visual means forstudents to organize and summarizenumerical and verbal data.Act it out. Some students learn bestwhen they act out a problem kinesthetically(Krulik and Rudnik 1996; Sorensonet al. 1996).Promoting a Positive AttitudeFinally, because many students whoexperience difficulty in math developnegative attitudes toward the subject,teachers must use good teaching practicesto encourage positive attitudes.Mercer and Miller (n.d.) suggest thefollowing:■ Involve students in setting challengingbut attainable instructional goals;■ Ensure that instruction builds onpreviously learned skills;■ Use progress charts to providestudents with feedback on how wellthey are doing;■ Discuss the relevance of a mathskill to real-life problems;■ Communicate positive expectationsfor student learning;■ Help students understand howtheir own effort affects achievementoutcomes; and■ Model an enthusiastic andpositive attitude toward math. PReferencesAllsopp, D. H. and Kyger, M. Math VIDSManual: Effective Instructional Strategiesfor Students Who Have Math LearningProblems, 1999. Retrieved from:http://coe.jmu.edu/mathvidsr/metacognitive.htmBley, N. S. and Thornton, C. A. TeachingMathematics to Students with LearningDisabilities, 3rd Edition. Austin, Tex.:Pro-Ed, 1995.Ebeling, D. G.; Deschenes, C.; and Sprague,J. Adapting Curriculum andInstruction in Inclusive Classrooms: StaffDevelopment Kit. Bloomington, Ind.:Institute for the Study of DevelopmentalDisabilities, 1994.Grouws, D. A. “Mathematics.” In G. Cawelti(Ed.), Handbook of Researchon Improving Student Achievement, 3rdEdition, 162–181. Arlington, Va.:Educational Research Service, 2004.Jarrett, D. The Inclusive Classroom: Mathematicsand Science Instruction for Students withLearning Disabilities. NorthwestRegional Laboratory, 1999. Retrievedfrom: www.nwrel/msec/book7.pdfKing, M. and Parker, C. A Galaxy of MathematicsStrategies and Accommodations. Universityof Florida InstructionalTechnology Resource Center, 2001.Retrieved from:www.itrc.ucf.edu/other/fdlrs2001/workshops/math/ppt/mathintro.pdfKline, K. “Early Childhood Teachers Discussthe Standards.” Teaching Children Mathematics,May 2000, 570.Krulik, S. and Rudnick, J. A. The New Sourcebookfor Teaching Reasoning and ProblemSolving in Junior and Senior High School.Boston: Allyn and Bacon, 1996.Mercer, C. D. and Miller, S. P. TeachingStudents with Learning Problems in Math toAcquire, Understand, and Apply Basic Facts,n.d. Retrieved from:www.enc.org/print/professional/learn/eq-uity/articles/document.shtm?input=ACQ-111397-1397_1Sorenson, J. S.; Busckmaster, L. R.; Francis,M. K.; and Knauf, K. M. The Power of Problem-solving:Practical Ideas and TeachingStrategies for Any K–8 Subject Area. Boston:Allyn and Bacon, 1996.Sutton, J. and Krueger, A. EDThoughts:What We Know About MathematicsTeaching and Learning. Aurora, Colo.:McREL, 2002.Elizabeth G. Shellard is senior researchspecialist for the Educational ResearchService. Her e-mail address iseshellard@ers.org.WEB RESOURCESMath Playground is an Internetsite that contains math games, logicpuzzles, and word problems designedto offer K–6 students entertainingways to practice math skills.www.mathplayground.com/index.htmlHelping Your Child Learn Math, developedby the U.S. Department ofEducation, is a guide for parentsthat discusses what it means to be aproblem solver, to communicatemathematically, and to demonstratereasoning ability.www.ed.gov/pubs/parents/Math/index.htmlThe executive summary of Principlesand Standards for School Mathematics,a document from the NationalCouncil of Teachers of Mathematicsthat outlines the essential qualitiesof an effective mathematics program,is available online.www.ntcm.org/standards/overview.htmwww.naesp.org Principal ■ November/December 2004 43