Mathematical text reading seems to require a different type of literacy than others since it heavily introduces abstractconcepts and require strict logical and literal reading. In this paper, we focus on grades 611 (elementary through highschool) students skill in reading math definitions, but not problem solving. Our experiment showed that their skills inreading and understanding math definitions improves as long as math is obligatory (through the 10th grade) but reachesa plateau very quickly after that. However, teaching a math definition and using it to solve exercise problems in theclassroom do not seem to improve students ability of reading that specific definition.

In this paper, we present a new information-processing modelof math problem solving in which representation change the-ory can be implemented. Specifically, we divided the problemrepresentation process into two. One is to straightforwardlytranslate problem texts into formulas in a conservative exten-sion of Zermelo-Fraenkel’s set theory, and the other is to in-terpret the translated formulas in local mathematical theories.A ZF formula has several interpretations, and representationchange is thus implementable as a choice of an appropriate in-terpretation. Adopting the theory of real closed fields as an ex-ample of local theory and its quantifier elimination algorithmsas an approximate process of searching for solutions, we de-velop a prototype system. We use more than 400 problemsfrom three sources as benchmarks: exercise books, univer-sity entrance examination, and the International MathematicalOlympiad problems. Our experimental results suggest that ourmodel can serve as a basis of a quantitative study on represen-tation change in the sense that the performance of our proto-type system reflects difficulties of the problems quite precisely.

Our team proposed a Reading Skills Test that assesses cognitive academic language skills from six perspectives: syntactic comprehension, referential resolution, paraphrasing, inference, matching textual and non-textual information, and reading and understanding definitions. Each test item consists of a 100-word description and a multiple-choice question that tests one of the abilities from the above six perspectives. Subjects solve the test items, which appear one after another on the browser based on item response theory. We have confirmed that this test meets the desirable properties of an assessment test and have demonstrated that the syntactic processing ability measured by this test has improved yearly from the fifth to the ninth grade. Furthermore, we found that the characteristics of the subjects as measured by this test reflect syntactic processing ability independent of vocabulary and academic knowledge.

We propose a computer-based testing environment, Reading Skill Test, to measure the effects of various types of systematic reading support systems. We prove its validity, reliability and one-dimensionality using 31,000 subjects. The effects of furigana system on the 5th to 8th grade students are analyzed using this environment. Furigana is a widely used Japanese reading support system that has been believed to be beneficial especially for pupils. Despite our expectation, we have to conclude that furigana failed to improve pupils’ reading significantly, and discuss why it did so.

A reading skill test to diagnose basic language skills is introduced. The test is designed to measure six component skills relevant to reading in comparison with those of state-of- the-art natural language processing technologies. The results of the first large-scale experiments using the test are reported. Surprisingly, almost half of Japanese junior high school students do no better than machines in dependency analysis. More than half of 7th grade students do no better than making random choices on questions involving inferences and definition understanding.