Research Mathematics education

robust, useful theories of classroom teaching not yet exist . however, there useful theories on how children learn mathematics , research has been conducted in recent decades explore how these theories can applied teaching. following results examples of of current findings in field of mathematics education:

important results
one of strongest results in recent research important feature in effective teaching giving students opportunity learn . teachers can set expectations, time, kinds of tasks, questions, acceptable answers, , type of discussions influence students opportunity learn. must involve both skill efficiency , conceptual understanding.


conceptual understanding
two of important features of teaching in promotion of conceptual understanding attending explicitly concepts , allowing students struggle important mathematics. both of these features have been confirmed through wide variety of studies. explicit attention concepts involves making connections between facts, procedures , ideas. (this seen 1 of strong points in mathematics teaching in east asian countries, teachers typically devote half of time making connections. @ other extreme u.s.a., no connections made in school classrooms.) these connections can made through explanation of meaning of procedure, questions comparing strategies , solutions of problems, noticing how 1 problem special case of another, reminding students of main point, discussing how lessons connect, , on.


deliberate, productive struggle mathematical ideas refers fact when students exert effort important mathematical ideas, if struggle involves confusion , errors, end result greater learning. has been shown true whether struggle due challenging, well-implemented teaching, or due faulty teaching students must struggle make sense of.


formative assessment
formative assessment both best , cheapest way boost student achievement, student engagement , teacher professional satisfaction. results surpass of reducing class size or increasing teachers content knowledge. effective assessment based on clarifying students should know, creating appropriate activities obtain evidence needed, giving feedback, encouraging students take control of learning , letting students resources 1 another.


homework
homework leads students practice past lessons or prepare future lessons more effective going on today s lesson. students benefit feedback. students learning disabilities or low motivation may profit rewards. younger children, homework helps simple skills, not broader measures of achievement.


students difficulties
students genuine difficulties (unrelated motivation or past instruction) struggle basic facts, answer impulsively, struggle mental representations, have poor number sense , have poor short-term memory. techniques have been found productive helping such students include peer-assisted learning, explicit teaching visual aids, instruction informed formative assessment , encouraging students think aloud.


algebraic reasoning
it important elementary school children spend long time learning express algebraic properties without symbols before learning algebraic notation. when learning symbols, many students believe letters represent unknowns , struggle concept of variable. prefer arithmetic reasoning algebraic equations solving word problems. takes time move arithmetic algebraic generalizations describe patterns. students have trouble minus sign , understand equals sign mean answer is....

methodology

as other educational research (and social sciences in general), mathematics education research depends on both quantitative , qualitative studies. quantitative research includes studies use inferential statistics answer specific questions, such whether teaching method gives better results status quo. best quantitative studies involve randomized trials students or classes randomly assigned different methods in order test effects. depend on large samples obtain statistically significant results.

qualitative research, such case studies, action research, discourse analysis, , clinical interviews, depend on small focused samples in attempt understand student learning , @ how , why given method gives results does. such studies cannot conclusively establish 1 method better another, randomized trials can, unless understood why treatment x better treatment y, application of results of quantitative studies lead lethal mutations of finding in actual classrooms. exploratory qualitative research useful suggesting new hypotheses, can tested randomized experiments. both qualitative , quantitative studies therefore considered essential in education—just in other social sciences. many studies “mixed”, simultaneously combining aspects of both quantitative , qualitative research, appropriate.

randomized trials

there has been controversy on relative strengths of different types of research. because randomized trials provide clear, objective evidence on “what works”, policy makers take studies consideration. scholars have pushed more random experiments in teaching methods randomly assigned classes. in other disciplines concerned human subjects, biomedicine, psychology, , policy evaluation, controlled, randomized experiments remain preferred method of evaluating treatments. educational statisticians , mathematics educators have been working increase use of randomized experiments evaluate teaching methods. on other hand, many scholars in educational schools have argued against increasing number of randomized experiments, because of philosophical objections, such ethical difficulty of randomly assigning students various treatments when effects of such treatments not yet known effective, or difficulty of assuring rigid control of independent variable in fluid, real school settings.

in united states, national mathematics advisory panel (nmap) published report in 2008 based on studies, of used randomized assignment of treatments experimental units, such classrooms or students. nmap report s preference randomized experiments received criticism scholars. in 2010, works clearinghouse (essentially research arm department of education) responded ongoing controversy extending research base include non-experimental studies, including regression discontinuity designs , single-case studies.