Previous studies have shown that diagram use is effective in mathematical word problem solving. However, they have also revealed that students manifest many problems in using diagrams for such purposes. A possible reason is an inadequacy in students’ understanding of variations in types of problems and the corresponding kinds of diagrams appropriate to use. In the present study, a preliminary investigation was undertaken of how such correspondences between problem types and kinds of diagrams are represented in textbooks. One government-approved textbook series for elementary school level in Japan was examined for the types of mathematical word problems, and the kinds of diagrams presented with those problems. The analyses revealed significant differences in association between kinds of diagrams and types of problems. More concrete diagrams were included with problems involving change, combination, variation, and visualization of quantities; while number lines were more often used with comparison and variation problems. Tables and graphs corresponded to problems requiring organization of quantities; and more concrete diagrams and graphs to problems involving quantity visualization. These findings are considered in relation to the crucial role of textbooks and other teaching materials in facilitating strategy knowledge acquisition in students.

ABSTRACT. We have developed a rapid and efficient genotyping method for detection of the mouse leptin obese mutation (Lep ob ) using tetra-primer amplification refractory mutation system-polymerase chain reaction (tetra-primer ARMS-PCR). In this method, whole blood collected onto gamma-ray sterilized Flinders Technology Associates (FTA) filter paper is used as PCR template without a DNA purification step. Three genotypes (Lep ob /Lep ob , Lep ob /+ and +/+) differentiated by single-tube PCR and electrophoresis were perfectly consistent with those determined by PCR-restriction fragment length polymorphism (PCR-RFLP). This method can save material costs and operation time, because it does not require restriction enzyme digestion and could be set up in most specific pathogen-free (SPF) barrier facilities. Because of their short generation times and high breeding efficiency, rodents are extremely useful for researching disorders [2,12]. Point mutation-carrying strains, such as mice with an obese mutation in the leptin gene (Lep ob ) [16] and rats with a fatty mutation in the leptin receptor gene (Lepr fa ), [13] are included in representative rodent disease models [6]. For authentic research and for maintaining strains, it is important to verify the existence of point mutations.Tetra-primer amplification refractory mutation systempolymerase chain reaction (tetra-primer ARMS-PCR) employs 2 primer pairs to amplify, respectively, the 2 different alleles of a single nucleotide polymorphism (SNP) in a single PCR [15]. Moreover, the primers can be designed to amplify fragments of differing sizes for each allele [15]. Therefore, tetra-primer ARMS-PCR does not require restriction enzyme digestion and allows genotyping of a point mutation solely by inspection of PCR products with agarose gel electrophoresis. Combining Flinders Technology Associates (FTA) filter paper and appropriate PCR buffer allows for direct PCR amplification of DNA from unpurified blood on FTA filter paper [7]. To use FTA filter paper in our specific pathogenfree (SPF) barrier facility, we have so far used ethylene oxide gas (EOG) sterilization. However, ethylene oxide is a directly acting alkylating agent which is associated with an increase in chromosomal aberrations and sister chromatid exchange [1,5]. On the other hand, radiation leaves no toxic residues on treated medical items [10]. Here, we describe a rapid and efficient point mutation genotyping of the mouse leptin gene using tetra-primer ARMS-PCR and gamma-ray sterilized FTA filter paper in SPF barrier facilities.All procedures involving the use of mice were approved by the animal welfare committee of CHARLES RIVER LABORATORIES JAPAN. FTA filter paper (GE Healthcare Japan, Tokyo, Japan) was sterilized with EOG or with gamma-ray irradiation and carried into our in-house vivarium. Future breeders of the SPF B6.Cg-Lep ob /J strain (CHARLES RIVER LABORATORIES JAPAN, Yokohama, Japan), housed in the in-house vivarium, were used when weaning age. A small drop of whole blood, exuded by cutting the mice ...

The use of diagrams can be effective in solving mathematical word problems solving. However, students worldwide do not construct diagrams unprompted or have trouble using them. In the present study, the effects of problem-appropriate diagram use instruction were investigated with an adaptation of the multiple baseline design method. The instruction for using line diagrams, tables, and graphs was provided to 67 junior high school students in a staggered manner and the effects on problem solving of three different types of problems was examined. The results showed that use of problem-appropriate diagrams increased and persisted over time. More importantly, the instruction led to increases in problem solving performance and to decreases in perceived cognitive load. These findings support the argument that effective diagram use depends on the acquisition not only of declarative knowledge, but also sufficient procedural and conditional knowledge.

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