# GES3 Solve problems using quantitative reasoning.

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1 GES3 Solve problems using quantitative reasoning. MATH1010 Foundations of Math Semester: FALL 2013 REPORT DATE: 1/13/2014 Foundations of Math is an introductory level mathematics course that serves non- stem/business majors such as liberal arts, education, or fine arts. QR assessment was composed of selected questions given on the third (and final) common exam scored by one instructor using the AAC&U Quantitative Literacy Value Rubric. Number of students: 314 enrolled 248 completed assessment (test 3) Number of sections: 11 registered 11 assessed Distribution of Scores Analysis 0 Benchmark 1 Benchmark 2 Milestone 3

2 Mean scores overall: Distribution of Scores: Criteria Analysis Mean Benchmark Benchmark Milestone Total Analysis Percentages of Score Application Analysis Final Score 0* 11% 24% 10% 10% 98% 5% 1 71% 67% 4% 27% 2% 40% 2 4% 4% 65% 49% 0% 40% 3 15% 5% 21% 15% 0% 15% *0: no response

3 Discussion/Action/Closing the Loop: Background Math1010 is a terminal course developed for non- STEM majors (nor other programs such as business, economics, psychology, that require pre- calculus or higher level math.) Quantitative Reasoning in the context of this course we have defined as Proportional Reasoning. Our goal for our students is for them to be able to make reasonable proportional judgments within their fields of study (for example be able to compare the age of Egyptian or Chinese cultures with that of the US proportionally and have that comparison inform judgments about History, Politics, economic development, human rights, etc.) or in the context of their own economic and political lives (for example be able to judge the size of the US national debt, or compare proportionally local property tax rates to those of other states, etc.) To this end we focus Math1010 mathematical content on sets, number and numeral (especially rational numbers), linear equations, variation, geometrical (and other) formulas, percents, and probability. We then are in the process of embedding this content within realistic contexts that relate to a wide range liberal arts programs. The Fall 2013 assessment was the first analysis of Math1010 students' learning based on the AAC&U Literacy Value Rubric applied to open- ended quantitative reasoning questions designed using data from 2 semesters of smaller pilot studies within Math1010 of proportional reasoning and open- ended problem solving. Results 1. Students show weakness in interpretation (15% met level 3) and representation (5% met level 3). This weakness is not surprising as students (in particular freshmen) may have had little experience with such problems and in answering such without typical categorical clues (test is on probability so interpret everything as probability etc.) Additionally, students may have had little experience explaining their thinking, conclusions, analysis 1 and must be given many more opportunities to practice these skills. To this end we must begin to revise the course curriculum and pedagogy as follows: All assignments (Mathlab homework, quizzes, and tests) must be expanded/enriched with instructor designed open- ended authentic problems (at least one per assignment) that require students to go beyond calculation to explain their solution processes and reflect upon and evaluate their answers. Class time must include additional practice with open- ended authentic problems and the analysis there of. To that end all quizzes will include open ended problems that will be reviewed and analyzed in class. 2. Students were successful with calculations on familiar problems but less so on problems with unfamiliar or not previously seen contexts. For example, 146 students reached Milestone 3 on a pay- cut pay raise question, while only 25 students reached Milestone 3 on the interpret the size of the National Debt question. In particular it is difficult to trigger students' multiplicative, and 1 Majority of our student may not have experienced the Common Core Curriculum throughout their secondary education as the Common Core State Standards were adopted in NJ in 2010 (

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