People’s fear and anxiety about doing math – over and above actual math ability – can be an impediment to their math achievement. We show that when the math anxious individuals are female elementary school teachers, their math anxiety carries negative consequences for the math achievement of their female students. Early elementary school teachers in the U.S. are almost exclusively female (> 90%...

We have been developing an end-to-end math problem solving system that accepts natural language input. The current paper focuses on how we analyze the problem sentences to produce logical forms. We chose a hybrid approach combining a shallow syntactic analyzer and a manuallydeveloped lexicalized grammar. A feature of the grammar is that it is extensively typed on the basis of a formal ontology ...

In this chapter we present a thread-based approach for analyzing synchronous collaborative math problem-solving activities. Threading information is shown to be an important resource for analyzing collaborative activities, especially for conducting sequential analysis of interaction among participants of a small group. We propose a computational model based on thread information, which allows u...

Spatial thinking skills positively relate to Science, Technology, Engineering, and Math (STEM) outcomes, but spatial training is largely absent in elementary school. Elementary school is a time when children develop foundational cognitive skills that will support STEM learning throughout their education. Spatial thinking should be considered a foundational cognitive skill. The present research ...

Children's anxiety for situations requiring mathematical problem solving, a concept referred to as math anxiety, has a unique and detrimental impact on concurrent and long-term mathematics achievement and life success. Little is known about the factors that contribute to the emergence of math anxiety. The current study builds on the hypothesis that math anxiety might reflect a maladaptive affec...

In this paper, we present a dual representation for the multiple stopping problem, hence multiple exercise options. As such, it is a natural generalization of the method in Rogers (Math. Finance 12:271–286, 2002) and Haugh and Kogan (Oper. Res. 52:258–270, 2004) for the standard stopping problem for American options. We term this representation a ‘pure martingale’ dual as it is solely expressed...

This paper presents a tag-based statistical math word problem solver with understanding, reasoning, and explanation. It analyzes the text and transforms both body and question parts into their tag-based logic forms, and then performs inference on them. The proposed tag-based approach provides the flexibility for annotating an extracted math quantity with its associated syntactic and semantic in...

We compute the asymptotics of the eigenvalues of the classical Sturm–Liouville problem with a piecewise smooth coefficient q. This means that q and/or its derivatives can have jump discontinuities. The boundary conditions are arbitrary. Our results extend the classical work of H. Hochstadt (see [Comm. Pure Appl. Math., 14 (1961), pp. 749–764]) and some related formulas discovered by G. Borg (se...

We reported a study that analyzes collaborative information behavior of small groups in an online math discourse community. Taking group as the unit of analysis, we analyzed the social interactions of participants engaged in collaborative math problem solving and examined how they seek for information in such context. Participants look for information oriented to the procedure, problem, context...

During the summer of 2007, I participated in a Research Experience for Undergraduates (REU) at Illinois State University. I was one of eight undergraduates, all of whom were mathematics education majors. During my eight week experience, we worked with four in-service teachers from the Normal-Bloomington area, as well as math and math education professors from Illinois State and surrounding univ...