Validity of translation tests as a measure of reading comprehension

Identifying the main idea of an expository text is one of the most important skills in reading comprehension (Tomitch, 1996; 2000). In English entrance examinations of many Japanese national universities, expository texts are commonly used to measure reading comprehension. However, a translation-into-Japanese test method (TIJ-T) is still employed as a measure of reading comprehension despite being a target of criticism. This study attempts to examine to what extent this method can measure main idea reading comprehension. Two experiments have revealed that a TIJ-T is not valid as a means for measuring main idea comprehension of an expository text.Additionally, the findings have also indicated that some test takers can identify a main idea but cannot translate it into Japanese, while others who cannot identify a main idea (do not comprehend the text) are still able to provide a literal translation

Demotivation of English Language Learners in Highly Competitive University Preparatory High Schools in Japan : Based on Interviews of University Students

本研究は，日本の進学校の高校生にとって，英語学習への動機を減退させる要因は何か，また，それらの要因や動機減退経験を進学校出身の大学生はどのように認識しているかを探索的に捉え，多様な動機減退経験の過程をモデル化することが目的である。進学校出身の国立大学生3名にインタビュー調査を実施し，高校での動機減退経験の詳しい状況や認識を質的な研究で分析した。分析方法はM-GTA（木下，2003）を採用し，事例数や具体数を研究目的と相関的に決定するためにSCQRM（西條，2007，2008）をメタ理論として用い，概念モデルを作成した。研究結果から，「上位層に合わせた授業」「教師の態度」「文法訳読式の指導」「難解なテスト」「難易度の高い大量の課題」が動機減退の要因であることが明らかとなった。高校1年時から「上位層に合わせた授業」についていけない生徒は，学習内容や課題の量と難易度が難しくなるにつれて無力感を抱くこと，さらに状況が改善されない場合は長期的に英語学習への動機を失うことが明らかとなった

Random Variables and Product of Probability Spaces

We have been working on the formalization of the probability and the randomness. In [15] and [16], we formalized some theorems concerning the real-valued random variables and the product of two probability spaces. In this article, we present the generalized formalization of [15] and [16]. First, we formalize the random variables of arbitrary set and prove the equivalence between random variable on Σ, Borel sets and a real-valued random variable on Σ. Next, we formalize the product of countably infinite probability spaces.The 1st author was supported by JSPS KAKENHI 21240001, and the 2nd author was supported by JSPS KAKENHI 22300285Okazaki Hiroyuki - Shinshu University Nagano, JapanShidama Yasunari - Shinshu University Nagano, JapanGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Józef Białas. The σ-additive measure theory. Formalized Mathematics, 2(2):263-270, 1991.Józef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173-183, 1991.Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Peter Jaeger. Elementary introduction to stochastic finance in discrete time. Formalized Mathematics, 20(1):1-5, 2012. doi:10.2478/v10037-012-0001-5.Andrzej Nedzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.Hiroyuki Okazaki. Probability on finite and discrete set and uniform distribution. Formalized Mathematics, 17(2):173-178, 2009. doi:10.2478/v10037-009-0020-z.Hiroyuki Okazaki and Yasunari Shidama. Probability on finite set and real-valued random variables. Formalized Mathematics, 17(2):129-136, 2009. doi:10.2478/v10037-009-0014-x.Hiroyuki Okazaki and Yasunari Shidama. Probability measure on discrete spaces and algebra of real-valued random variables. Formalized Mathematics, 18(4):213-217, 2010. doi:10.2478/v10037-010-0026-6.Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1 (1):187-190, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Bo Zhang, Hiroshi Yamazaki, and Yatsuka Nakamura. The relevance of measure and probability, and definition of completeness of probability. Formalized Mathematics, 14 (4):225-229, 2006. doi:10.2478/v10037-006-0026-8

Effective motivational strategies for English classes in Japan (1) : Based on questionnaires to teachers and students

Although most teachers would agree that motivation has avery important role in determining successor failure in English language learning, research on motivational strategies has infrequently been conducted until now in Japanese contexts. The complete study consists of two related investigations aimed at exploring effective motivational strategies for Japanese junior and senior high school students, with the following article presenting the results of an empirical survey on motivational strategies from the perspectives of English teachers. Eightysix Japanese teachers of English from junior high and senior high schools were asked how important they considered a selection of 50 teaching strategies (Dörnyei and Csizér, 1998). Based on their responses, a concise set of ten motivational macrostrategies called the \u27Ten commandments for motivating Japanese students\u27 were compiled, and then compared with those proposed by Dörnyei and Csizér(1998)

Formalization of the Data Encryption Standard

In this article we formalize DES (the Data Encryption Standard), that was the most widely used symmetric cryptosystem in the world. DES is a block cipher which was selected by the National Bureau of Standards as an official Federal Information Processing Standard for the United States in 1976 [15].This work was supported by JSPS KAKENHI 21240001Okazaki Hiroyuki - Shinshu University, Nagano, JapanShidama Yasunari - Shinshu University, Nagano, JapanGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Czesław Bylinski. Some properties of restrictions of finite sequences. Formalized Mathematics, 5(2):241-245, 1996.Shunichi Kobayashi and Kui Jia. A theory of Boolean valued functions and partitions. Formalized Mathematics, 7(2):249-254, 1998.Jarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275-278, 1992.Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83-86, 1993.U.S. Department of Commerce/National Institute of Standards and Technology. Fips pub 46-3, data encryption standard (DES). http://csrc.nist.gov/publications/fips/-fips46-3/fips46-3.pdf. Federal Information Processing Standars Publication, 1999.Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Many argument relations. Formalized Mathematics, 1(4):733-737, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990

Effective motivational strategies for English classes in Japan (2) : based on questionnaires to teachers and students

The present article aims at exploring effective motivational strategies through investigating how junior high and senior high school students are motivated by the strategies. The questionnaire titled "Research on attitudes toward English classes and English learning" with the same 50 items utilized in the questionnaire for teachers in the previous article (1) (Narikawa and Okazaki, 2011) was administered to 223 junior high school and 492 senior high school students. Two remarkable findings were discovered: one is that both junior and senior high school students hope for more opportunities in which they can use English than they presently have and the other is that strategies for promoting extrinsic motivation can be effective for students who seem not to have high motivation for learning English. The pedagogical implications suggest Japanese English teachers can motivate their students if they increase the opportunities inside and outside classes in which students can actually use English, and that teachers can utilize extrinsic motivation more effectively

Properties of Primes and Multiplicative Group of a Field

In the [16] has been proven that the multiplicative group Z/pZ* is a cyclic group. Likewise, finite subgroup of the multiplicative group of a field is a cyclic group. However, finite subgroup of the multiplicative group of a field being a cyclic group has not yet been proven. Therefore, it is of importance to prove that finite subgroup of the multiplicative group of a field is a cyclic group. Meanwhile, in cryptographic system like RSA, in which security basis depends upon the difficulty of factorization of given numbers into prime factors, it is important to employ integers that are difficult to be factorized into prime factors. If both p and 2p + 1 are prime numbers, we call p as Sophie Germain prime, and 2p + 1 as safe prime. It is known that the product of two safe primes is a composite number that is difficult for some factoring algorithms to factorize into prime factors. In addition, safe primes are also important in cryptography system because of their use in discrete logarithm based techniques like Diffie-Hellman key exchange. If p is a safe prime, the multiplicative group of numbers modulo p has a subgroup of large prime order. However, no definitions have not been established yet with the safe prime and Sophie Germain prime. So it is important to give definitions of the Sophie Germain prime and safe prime. In this article, we prove finite subgroup of the multiplicative group of a field is a cyclic group, and, further, define the safe prime and Sophie Germain prime, and prove several facts about them. In addition, we define Mersenne number (Mn), and some facts about Mersenne numbers and prime numbers are proven.Arai Kenichi - Shinshu University, Nagano, JapanOkazaki Hiroyuki - Shinshu University, Nagano, JapanBroderick Arneson and Piotr Rudnicki. Primitive roots of unity and cyclotomic polynomials. Formalized Mathematics, 12(1):59-67, 2004.Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485-492, 1996.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Yoshinori Fujisawa and Yasushi Fuwa. The Euler's function. Formalized Mathematics, 6(4):549-551, 1997.Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relative primes. Formalized Mathematics, 1(5):829-832, 1990.Michał Muzalewski and Lesław W. Szczerba. Construction of finite sequences over ring and left-, right-, and bi-modules over a ring. Formalized Mathematics, 2(1):97-104, 1991.Hiroyuki Okazaki and Yasunari Shidama. Uniqueness of factoring an integer and multiplicative group R/pZ*. Formalized Mathematics, 16(2):103-107, 2008, doi:10.2478/v10037-008-0015-1.Christoph Schwarzweller. The ring of integers, euclidean rings and modulo integers. Formalized Mathematics, 8(1):29-34, 1999.Dariusz Surowik. Cyclic groups and some of their properties - part I. Formalized Mathematics, 2(5):623-627, 1991.Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.Wojciech A. Trybulec. Subgroup and cosets of subgroups. Formalized Mathematics, 1(5):855-864, 1990.Wojciech A. Trybulec. Lattice of subgroups of a group. Frattini subgroup. Formalized Mathematics, 2(1):41-47, 1991.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990

Probability on Finite Set and Real-Valued Random Variables

In the various branches of science, probability and randomness provide us with useful theoretical frameworks. The Formalized Mathematics has already published some articles concerning the probability: [23], [24], [25], and [30]. In order to apply those articles, we shall give some theorems concerning the probability and the real-valued random variables to prepare for further studies.Okazaki Hiroyuki - Shinshu University, Nagano, JapanShidama Yasunari - Shinshu University, Nagano, JapanGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Józef Białas. Infimum and supremum of the set of real numbers. Measure theory. Formalized Mathematics, 2(1):163-171, 1991.Józef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173-183, 1991.Józef Białas. The σ-additive measure theory. Formalized Mathematics, 2(2):263-270, 1991.Józef Białas. Some properties of the intervals. Formalized Mathematics, 5(1):21-26, 1996.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Noboru Endou and Yasunari Shidama. Integral of measurable function. Formalized Mathematics, 14(2):53-70, 2006, doi:10.2478/v10037-006-0008-x.Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Basic properties of extended real numbers. Formalized Mathematics, 9(3):491-494, 2001.Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions. Formalized Mathematics, 9(3):495-500, 2001.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.Grigory E. Ivanov. Definition of convex function and Jensen's inequality. Formalized Mathematics, 11(4):349-354, 2003.Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.Jarosław Kotowicz and Yuji Sakai. Properties of partial functions from a domain to the set of real numbers. Formalized Mathematics, 3(2):279-288, 1992.Keiko Narita, Noboru Endou, and Yasunari Shidama. Integral of complex-valued measurable function. Formalized Mathematics, 16(4):319-324, 2008, doi:10.2478/v10037-008-0039-6.Andrzej Nędzusiak. Probability. Formalized Mathematics, 1(4):745-749, 1990.Andrzej Nędzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.Jan Popiołek. Introduction to probability. Formalized Mathematics, 1(4):755-760, 1990.Yasunari Shidama and Noboru Endou. Integral of real-valued measurable function. Formalized Mathematics, 14(4):143-152, 2006, doi:10.2478/v10037-006-0018-8.Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Bo Zhang, Hiroshi Yamazaki, and Yatsuka Nakamura. The relevance of measure and probability, and definition of completeness of probability. Formalized Mathematics, 14(4):225-229, 2006, doi:10.2478/v10037-006-0026-8

Formalization of the Advanced Encryption Standard. Part I

In this article, we formalize the Advanced Encryption Standard (AES). AES, which is the most widely used symmetric cryptosystem in the world, is a block cipher that was selected by the National Institute of Standards and Technology (NIST) as an official Federal Information Processing Standard for the United States in 2001 [12]. AES is the successor to DES [13], which was formerly the most widely used symmetric cryptosystem in the world. We formalize the AES algorithm according to [12]. We then verify the correctness of the formalized algorithm that the ciphertext encoded by the AES algorithm can be decoded uniquely by the same key. Please note the following points about this formalization: the AES round process is composed of the SubBytes, ShiftRows, MixColumns, and AddRoundKey transformations (see [12]). In this formalization, the SubBytes and MixColumns transformations are given as permutations, because it is necessary to treat the finite field GF(28) for those transformations. The formalization of AES that considers the finite field GF(28) is formalized by the future article.Arai Kenichi - Tokyo University of Science Chiba, JapanOkazaki Hiroyuki - Shinshu University Nagano, JapanGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.U.S. Department of Commerce/National Institute of Standards and Technology. FIPS PUB 197, Advanced Encryption Standard (AES). Federal Information Processing Standars Publication, 2001.Hiroyuki Okazaki and Yasunari Shidama. Formalization of the data encryption standard. Formalized Mathematics, 20(2):125-146, 2012. doi:10.2478/v10037-012-0016-y.Andrzej Trybulec. On the decomposition of finite sequences. Formalized Mathematics, 5 (3):317-322, 1996.Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Many argument relations. Formalized Mathematics, 1(4):733-737, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990

Researching English Classes Based on “CAN-DO” Statements : Focusing on the Processes of the Self-Evaluation through Language Learning

本研究の目的は，タスク型の英語授業におけるCAN-DO形式の学習到達目標に沿って自己評価をすることによる英語学習への効果を確かめるものである。本研究では，通常の中学の英語授業のためにCAN-DOリストを作成し，生徒にCAN-DOリストに沿って自己評価させることで自己肯定感が高まり，英語学習に効果をもたらすのかについて検証した。質問紙に対する回答についてt検定を行なったところ，CAN-DOリストの形式で自己評価を繰り返し行うことで，学習者自身が「できた」「できなかった」を明確に評価できるようになり，学習の計画を立てる能力が身に付き，英語学習に対する動機づけを高めた。また，学習者と指導者がCAN-DOリストの形式で学習到達目標を共有し，学習者に目標を意識させたことで，英語授業に対する意識が向上し，授業内容の理解の向上につながったと思われる。CAN-DOリストの形式で自己評価をさせるためには，授業をタスク化し，「何ができて」「何ができなかったのか」を学習者が判断できるようにすることが重要である