Christopher S. Hlas UW-Eau Claire

1. Literature review 2. Research questions 3. Methodology 4. Results 5. Discussion ◦ Interpret results ◦ Limitations of study ◦ Suggestions for future research 6. References / Appendix SoTL in Mathematics: Moving from Anecdotes to Analysis

 What data is relevant for answering the research questions?  What statistical analysis is needed to answer the research questions? (should be decided during planning)  How can data be organized to illustrate patterns? SoTL in Mathematics: Moving from Anecdotes to Analysis

DimensionPre-surveyPost-surveyMean difference Composition ** Structure * Status Doing Validating * Learning * Usefulness Paired t-test (N=22) SoTL in Mathematics: Moving from Anecdotes to Analysis * Significance at the 0.10 level ** Significance at the 0.05 level

DimensionPre-surveyPost-surveyMean difference Usefulness Structure * Doing Status Validating * Learning * Composition ** Results (table organization) Paired t-test (N=22) -- FINAL SoTL in Mathematics: Moving from Anecdotes to Analysis * Significance at the 0.10 level ** Significance at the 0.05 level SoTL in Mathematics: Moving from Anecdotes to Analysis

 Provide analysis only for conclusions you wish to draw  Assume your audience has a professional knowledge of statistics  Don’t repeat table/figure information in prose  Start with result then provide supporting details  Be succinct (patterns, not each little detail) SoTL in Mathematics: Moving from Anecdotes to Analysis Next >> Discussion

 How do the results impact the research questions?  How do the answers to research questions impact the field?  How else could the results be interpreted?  What does “significant” mean? SoTL in Mathematics: Moving from Anecdotes to Analysis

Likert scale: 1. Strongly agree 2. Agree 3. Slightly agree 4. Slightly disagree 5. Disagree 6. Strongly disagree Issues:  Comparing means of ordinal data  Can questions be combined into one dimension?  Is 3.26 functionally different than 3.03? SoTL in Mathematics: Moving from Anecdotes to Analysis DimensionPre-surveyPost-surveyMean difference Composition **

 Be careful to support claims well!  Do NOT include new data  Avoid words that do not allow that results may be misinterpreted, e.g. “proved” SoTL in Mathematics: Moving from Anecdotes to Analysis

Next >> Limitations

 What are areas of weakness in the study?  What rationalizations were used to compensate for these limitations?  What are possibilities for bias? (anything non- randomized)  What are possible lurking variables? What variables have not been controlled for? SoTL in Mathematics: Moving from Anecdotes to Analysis

Limitations (examples) Methodologies:  Case studies  Interviews  Observations  Pre/post assessment  Surveys Examples:  Small N  Lack of control group  Author was part of study  Volunteers  Lurking variables  Reliability  Validity SoTL in Mathematics: Moving from Anecdotes to Analysis

 Identify relevant limitations  Discuss alternate interpretations of the results  Validity? SoTL in Mathematics: Moving from Anecdotes to Analysis Next >> Suggestions

 What new questions arise as a result of this study?  How can the limitations be overcome? SoTL in Mathematics: Moving from Anecdotes to Analysis Next >> Causality

 Causility by philosopher John Stuart Mill 1.The cause is related to the effect 2.No plausible alternatives exist 3.The cause precedes the effect  Which came first? (chicken or egg)  Citations (would you use a result that you didn’t understand?)  Shark attacks & ice creams sales SoTL in Mathematics: Moving from Anecdotes to Analysis

 The general model tested in the present study has suggested ways in which school systems could be more “healthy” by providing more autonomy-supportive contexts, less pressure, and more frequent quality informal feedback. SoTL in Mathematics: Moving from Anecdotes to Analysis

 It is important to recognize that simply focusing on the correlation relationships of kindergarten performance and reading outcomes in subsequent grades is not adequate for deciding which variables are the best predictors. SoTL in Mathematics: Moving from Anecdotes to Analysis

 Our findings indicate that individual differences may be important in determining who is open to pedagogical approaches that involve change such as the teaching as persuasion metaphor, teaching for critical thinking, or conceptual change pedagogy. However … our results are preliminary, correlational, and further investigation is needed to more fully understand their implications. SoTL in Mathematics: Moving from Anecdotes to Analysis

 Findings from this study suggest the importance of early and continued intervention by educators all over the world to help all students maintain positive beliefs about themselves as mathematically and scientifically competent. SoTL in Mathematics: Moving from Anecdotes to Analysis

 The third way in which our results add to current canonical views about the word recognition processes of children with reading disabilities is by providing support for the hypothesis that a different balance of phonological and orthographical skills characterizes children with reading disabilities when they are compared with younger children without reading disabilities who are reading at the same level. SoTL in Mathematics: Moving from Anecdotes to Analysis

 Results of this study indicate that psychological dysfunction may justifiably be added to economic and cognitive consequences on the list of negative outcomes of not graduation from high school. Such results further testify to the importance of providing a nourishing learning environment for all children. SoTL in Mathematics: Moving from Anecdotes to Analysis

American Psychology Association. (2001). Publication manual of the American Psychological Association (5th ed.). Washington DC: Author. Fraenkel, J.R. & Wallen, N.E. (2000). How to design and evaluate research in education, (4th ed.). Boston: McGraw Hill. Klingner, J.K., Scanlon, D., & Pressley, M. (2005). How to publish in scholarly journals. Educational Researcher, 34, Locke, L.F., Spirduso, W.W., & Silverman, S.J. (2000). Proposals that work: A guide for planning dissertations and grant proposals (4th ed.). Thousand Oaks, CA: Sage Publications. Robinson, D.H., Levin, J.R., Thomas, G.D., Pituch, K.A., & Vaughn, S. (2007). The incidence of “causal” statements in teaching-and-learning research journals. American Educational Research Journal, 44, SoTL in Mathematics: Moving from Anecdotes to Analysis

“Mathematicians work with perfect data, whereas educators work with imperfect data.” -- Andrea Foster, math grad student SoTL in Mathematics: Moving from Anecdotes to Analysis