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4434Can Automated Scoring Surpass Hand Grading of Students' Constructed Responses and Error Patterns in Mathematics?
http://www.merlot.org/merlot/viewMaterial.htm?id=875493
A unique online parsing system that produces partial-credit scoring of students' constructed responses to mathematical questions is presented. The parser is the core of a free college readiness website in mathematics. The software generates immediate error analysis for each student response. The response is scored on a continuous scale, based on its overall correctness and the fraction of correct elements. The parser scoring was validated against human scoring of 207 real-world student responses (r = 0.91). Moreover, the software generates more consistent scores than teachers in some cases. The parser analysis of students' errors on 124 additional responses showed that the errors were factored into two groups: structural (possibly conceptual), and computational (could result from typographical errors). The two error groups explained 55% of students' scores variance (structural errors: 36%; computational errors: 19%). In contrast, these groups explained only 33% of the teacher score variance (structural: 18%; computational: 15%). There was a low agreement among teachers on error classification, and their classification was weakly correlated to the parser's error groups. Overall, the parser's total scoring closely matched human scoring, but the machine was found to surpass humans in systematically distinguishing between students' error patterns.Effective Online Office Hours in the Mathematical Sciences
http://www.merlot.org/merlot/viewMaterial.htm?id=860782
In this paper, we describe our introduction of anonymous online office hour sessions for mathematics courses and outline a number of ways in which these sessions are more effective than traditional office hours. Our study is based on our experience with conducting the sessions as well as on data from student surveys. Our sessions make use of the enVision communication software (freeware), which permits easy, real-time communication of complex mathematical ideas.Online Resources for Non-Statisticians Teaching Statistics
http://www.merlot.org/merlot/viewMaterial.htm?id=860731
Many teachers whose backgrounds are not in statistics must teach statistical concepts. Non-statisticians face extra challenges in preparing for a statistics class, including uncertainty about content and pedagogy. This article addresses this challenge by suggesting the use of CAUSEweb, an online repository of statistics education resources. Methods are described to incorporate this resource into the planning and teaching of several difficult statistical concepts, including time series and hypothesis testing, using resources tailored to different application areas, such as biology, engineering, and chemistry.Algebra Help
http://www.merlot.org/merlot/viewMaterial.htm?id=200182
Algebra practice problemsFREE: Federal Resources for Educational Excellence
http://www.merlot.org/merlot/viewMaterial.htm?id=284186
FREE makes it easier to find teaching and learning resources from the federal government.Hippocampus
http://www.merlot.org/merlot/viewMaterial.htm?id=284195
The goal of HippoCampus is to provide high-quality, multimedia content on general education subjects to high school and college students free of charge. HippoCampus was designed as part of Open Education Resources (OER), a worldwide effort to improve access to quality education for everyone.6.006 Introduction to Algorithms
http://www.merlot.org/merlot/viewMaterial.htm?id=680817
This course provides an introduction to mathematical modeling of computational problems. It covers the common algorithms, algorithmic paradigms, and data structures used to solve these problems. The course emphasizes the relationship between algorithms and programming, and introduces basic performance measures and analysis techniques for these problems.6.041 Probabilistic Systems Analysis and Applied Probability
http://www.merlot.org/merlot/viewMaterial.htm?id=680897
This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.6.042J / 18.062J Mathematics for Computer Science
http://www.merlot.org/merlot/viewMaterial.htm?id=680828
This is an introductory course in Discrete Mathematics oriented toward Computer Science and Engineering. The course divides roughly into thirds: Fundamental Concepts of Mathematics: Definitions, Proofs, Sets, Functions, Relations Discrete Structures: Modular Arithmetic, Graphs, State Machines, Counting Discrete Probability Theory A version of this course from a previous term was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5512 (Mathematics for Computer Science).6.042J / 18.062J Mathematics for Computer Science
http://www.merlot.org/merlot/viewMaterial.htm?id=680883
This course is offered to undergraduates and is an elementary discrete mathematics course oriented towards applications in computer science and engineering. Topics covered include: formal logic notation, induction, sets and relations, permutations and combinations, counting principles, and discrete probability.