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## Metacognition and Cooperative Learning in the Mathematics ClassroomKhalid S. Alzahrani
pp.
Based on theoretical notions of metacognition in light of the reality of mathematics learning and teaching in Saudi Arabia, this study aimed to explore a teacher’s and students’ perceptions of the nature of the relationship between cooperative learning and an improvement in metacognition. Consequently, a case study design was favoured in order to suit the research agenda and meet its aims. The participants consisted of one case study class from a secondary school in Saudi Arabia. Semi-structured interviews and classroom observation were used for data collection. The findings of the data analysis asserts that metacognition can be assisted through the creation of a suitable socio-cultural context to encourage the social interaction represented in cooperative learning. This has a role in motivating the establishment of metacognition, as the absence of this social interaction would impede this type of learning. The importance of the student’s role in learning through metacognition was asserted by this study.
Adey, P., Robertson, A., & Venville, G. (2001). Artz, A. F., & Armour-Thomas, E. (1992). Development of a cognitive-metacognitive framework for protocol analysis of mathematical problem solving in small groups. Artzt, A. F., & Newman, C. M. (1997). Azevedo, R., & Aleven, V. (2013). Metacognition and learning technologies: an overview of current interdisciplinary research Bernard, M., & Bachu, E. (2015). Enhancing the Metacognitive Skill of Novice Programmers Through Collaborative Learning Blatchford, P., Kutnick, P., Baines, E., & Galton, M. (2003). Toward a social pedagogy of classroom group work. Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Brown, A. (1987). Metacognition, Executive Control, Self Regulation and Mysterious Mechanisms. In R. K. Franz E. Weinert (Ed.), Buratti, S., & Allwood, C. M. (2015). Regulating Metacognitive Processes—Support for a Meta-metacognitive Ability Chinn, C. (2010). Collaborative and cooperative learning Coles, A. (2013). Desoete, A. (2007). Evaluating and improving the mathematics teaching-learning process through metacognition. Flavell, J. H. (1979). Metacognition and cognitive monitoring. Goos, M., & Galbraith, P. (1996). Do it this way! Metacognitive strategies in collaborative mathematical problem solving. Hartman, H. (2015). Engaging Adolescent Students’ Metacognition Through WebQuests: A Case Study of Embedded Metacognition Hinsz, V. B. (2004). Hogan, M. J., Dwyer, C. P., Harney, O. M., Noone, C., & Conway, R. J. (2015). Metacognitive skill development and applied systems science: A framework of metacognitive skills, self-regulatory functions and real-world applications Hurme, T.-R., Järvelä, S., Merenluoto, K., & Salonen, P. (2015). What Makes Metacognition as Socially Shared in Mathematical Problem Solving? Kluwe, R. H. (1982). Cognitive knowledge and executive control: Metacognition Kramarski, B., & Mevarech, Z. R. (2003). Enhancing mathematical reasoning in the classroom: The effects of cooperative learning and metacognitive training. Larkin, S. (2006). Collaborative group work and individual development of metacognition in the early years. Merriam, S. B. (1998). Mevarech, Z., & Kramarski, B. (1997). IMPROVE: A multidimensional method for teaching mathematics in heterogeneous classrooms. Moga, A. (2012). Mokos, E., & Kafoussi, S. (2013). Elementary Student'Spontaneous Metacognitive Functions in Different Types of Mathematical Problems. Panitz, T. (1999). Collaborative versus Cooperative Learning: A Comparison of the Two Concepts Which Will Help Us Understand the Underlying Nature of Interactive Learning. Retrieved from ERIC website: http://eric.ed.gov/?id=ED448443 Pannitz, R. (1996). A definition of collaborative vs. cooperative learning. Rockwood, R. (1995). Sandi-Urena, S., Cooper, M., & Stevens, R. (2012). Effect of cooperative problem-based lab instruction on metacognition and problem-solving skills. Stake, R. E. (1995). |
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## Vocational High School Students’ Perceptions of Success in MathematicsHuseyin Ozdemir & Neslihan Onder-Ozdemir
pp.
Knowledge of mathematics is significant for each society because mathematics “acts as a ‘gatekeeper’ to social progress” (Gates & Vistro-Yu, 2003, p. 32) and also a gateway for a good profession. The Programme for International Student Assessment (PISA) 2015 was completed by approximately 540,000 15-year-old students and published in 2016 PISA report. The 2016 PISA report showed that among 72 countries and economies, Turkey lagged behind most of the countries, i.e., 49th in mathematics, 52nd in science and 50th in reading. Given the state of Turkey, the problems in education should be scrutinised across subjects, including maths. To address this apparent proven problem, we conducted research on vocational high school students (i.e., mostly disadvantaged students). To the best of our knowledge, Turkish students’ perceptions of success in mathematics who are studying in a vocational high school are under-researched. In light of this gap, the present longitudinal study sets out to investigate Turkish Vocational and Technical High School students’ perceptions as learners of mathematics to contribute to the literature (n=165). Open-ended questions were asked whether students believe that they are successful or unsuccessful and the underlying reasons why. The data were collected through a face-to-face structured interview and classroom observation. Among 165 vocational high school students, 61 of them believed that they were successful, 93 believed that they were unsuccessful and 11 students were hesitant. Reasons why students believed they are successful or unsuccessful were collected under five salient themes as follows: (i) reasons arising from students themselves; (ii) reasons arising from students’ perceptions of maths course//their maths abilities, (iii) reasons arising from maths teacher, (iv) reasons arising from students’ educational background, (v) reasons arising from the milieu.
Aytaş, A., Panal, A., Türker, H. & Oğulcu, F. (2000). Bandura, A. (1993). Perceived self-efficacy in cognitive development and functioning. Berelson, B. (1952). Content analysis in communication research Birgin, O., Baloğlu, M., Çatlıoğlu, H. & Gürbüz, R. (2010). An investigation of mathematics anxiety among sixth through eighth grade students in Turkey. Borisovaa, O. V., Vasbievaa, D. G., Malykhb, N. I., Vasnevc, S. A. & Vasnevad, N. N. (2017). Trends and Challenges in Development of Continuing Vocational Education and Training in Russia. Bulut, M. (2007). Curriculum reform in Turkey: A case of primary school mathematics curriculum. Carlson, M. P. (1999). The mathematical behavior of six successful mathematics graduate students: Influences leading to mathematical success. Das J. P. & Janzen, C. (2004). Learning Math: Basic concepts, math difficulties and suggestions for intervention. Garofalo, J. (1989). Beliefs, responses, and mathematics education: Observations from the back of the classroom. Gates, P. & Vistro-Yu, C. P. (2003). Hannover, B. & Kessels, U. (2004). Self-to-prototype matching as a strategy for making academic choices. Why high school students do not like math and science. Hannula, M. S. (2002). Attitude towards mathematics: Emotions, expectations and values. Kaufman, R. A., & English, F. W. (1979). Needs assessment: Concept and application. Kiryakova, A. V., Tretiakovb, A. N., Kolgac, V. V., Piralovad, O. F. & Dzhamalovae, B. B. (2016). Experimental Study of the Effectiveness of College Students’ Vocational Training in Conditions of Social Partnership. Kloosterman, P. & Stage, F. K. (1992). Measuring beliefs about mathematical problem solving. Kutueva, R. A., Mashkinb, N. A., Yevgrafovac, O. G., Morozovd, A. V., Zakharovae, A. N. & Parkhaevf, V. T. (2017). Practical Recommendations on the Organization of Pedagogical Monitoring in Institutions of Vocational Education. Leder, G. C., Pehkonen, E. & Törner, G. (2006). Longo, G. (1999). Mathematical intelligence, infinity and machines: beyond Godelitis. Lubienski, S. T. (2000). Problem solving as a means toward mathematics for all: An exploratory look through a class lens. Mane, F. (1999). Trends in the payoff to academic and occupation-specific skills: the short and medium run returns to academic and vocational high school courses for non-college-bound students. Mohr, C. (2008). Aligning classroom instruction with workplace skills: Equipping CTE students with the math skills necessary for entry-level carpentry. Nicholls, J. G., Cobb, P., Wood, T., Yackel, E. & Patashnick, M. (1990). Assessing students' theories of success in mathematics: Individual and classroom differences. Nogay, S. (2007). Odell, P. & Schumacher, P. (1998). Attitudes toward mathematics and predictors of college mathematics grades: Gender differences in a 4-Year business college. OECD. (2004). Learning for tomorrow’s world – first results from PISA 2003. Paris: PISA OECD Publishing OECD. (2016). Ozgen, K., & Bindak, R. (2011). Determination of Self-Efficacy Beliefs of High School Students towards Math Literacy. Rudduck, J. & Flutter, J. (2000) Pupil Participation and Pupil Perspective: ‘carving a new order of experience'’. Saunders, J. (2005). Schoenfeld, A. H. (1989). Explorations of students' mathematical beliefs and behavior. Stanic, G. M. & Hart, L. E. (1995). Attitudes, persistence, and mathematics achievement: Qualifying race and sex differences. Usul, H., Eroğlu, H. & Akın, O. (2007). Meslek liseleri ve meslek yüksek okullarındaki eğitim süreçleri arasındaki uyum sorununun analizi ve ticaret lisesi örneği. Weber, R. P. (1990). Basic content analysis (No. 49). Sage. Weinstein, G. & Fantini, M. D. (1970). Williams, P. (2008). Wolf, A. (2011). Review of vocational education: The Wolf report. Woods, P. (1990). |
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## Assessment for Learning in the Calculus Classroom: A Proactive Approach to Engage Students in Active LearningReem Jaafar & Yan Lin
pp.
There is a variety of classroom assessment techniques we can use in the college classroom (Angelo and Cross, 1993). In an effort to diagnose and identify gaps between students’ learning and classroom teaching, we implemented weekly short assessments in a calculus I classroom at an urban community college in the United States. The goals of these assessments were to identify misconceptions, and address them using an appropriate intervention. In this paper, we share these assessments, how they can be used to cement students’ conceptual learning, and how it can help the instructor develop insights into students’ misunderstandings. We also share students’ feedback, challenges and implications for practitioners.
Angelo, T. A., & Cross, K. P. (1993). Attorps, I., Björk, K., Radic, M., & Tossavainen, T. (2013). Varied Ways to Teach the Definite Integral Concept. Bailey, T., Jeong, D. W., & Cho, S. (2010). Referral, enrollment, and completion in developmental education sequences in community colleges. Bean, J. C. (2011). Bonwell, C. C., &Eison, J. A. (1991). Bolte, L. A. (1999). Using Concept Maps and Interpretive Essays for Assessment in Mathematics. Cross, K. P. (2003). Cullinane, M. J. (2011). Helping Mathematics Students Survive the Post-Calculus Transition. Dawkins, P. C., & Epperson, J. A. (2014). The development and nature of problem-solving among first-semester calculus students. Güçler, B. (2013). Examining the discourse on the limit concept in a beginning-level calculus classroom. Idris, N. 2009. Enhancing Students' Understanding in Calculus Through Writing. Iannone, P., & Simpson, A. (2015). Students' preferences in undergraduate mathematics assessment. Jaafar, R. (2016). Writing-to-Learn Activities to Provoke Deeper Learning in Calculus. Kinley, (2016). Grade Twelve Students Establishing the Relationship Between Differentiation and Integration in Calculus Using graphs. Maharaj, A., & Wagh, V. (2014). An outline of possible pre-course diagnostics for differential calculus. Meyers, C., & Jones, T. B. (1993). National Research Council, & Bass, H. (1993). Porter, M. K., & Masingila, J. O. (2000). Examining the effects of writing on conceptual and procedural knowledge in calculus. Pugalee, D. K. (2001). Writing, Mathematics, and Metacognition: Looking for Connections Through Students' Work in Mathematical Problem Solving. Robert, A., & Speer, N. (2001). Research on the teaching and learning of calculus/elementary analysis. In D. Holton (Ed.), Rybolt, W., & Recck, G. (2012). Conceptual versus Computational Formulae in Calculus and Statistics Courses. Scheja, M., & Pettersson, K. (2009). Transformation and contextualization: conceptualizing students’ conceptual understandings of threshold concepts in calculus. Thompson, P. W. (1994). Images of rate and operational understanding of the fundamental theorem of calculus. Vincent, B., LaRue, R., Sealey, V., & Engelke, N. (2015). Calculus students' early concept images of tangent lines. Yoder, J., & Hochevar, C. (2005). Encouraging Active Learning Can Improve Students' Performance on Examinations. |
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## Metacognition and Its Role in Mathematics Learning: an Exploration of the Perceptions of a Teacher and Students in a Secondary SchoolKhalid S. Alzahrani
pp.
The study aims to explore teachers’ and students’ perspectives regarding metacognition and its role in mathematics learning. The use of case study was a methodical means to achieve elaborate data and to shed light on issues facing the study. The participants consisted of a case study class from a secondary school in Saudi Arabia. The instruments used for data collection were semi-structured interviews and classroom observation. The data produced essential finding based on thematic analysis techniques, regarding study’s aim. Firstly, the traditional method can hinder mathematics teaching and learning through metacognition. Secondly, although metacognitive mathematics instruction should be planned, the strategy that is introduced should be directly targeted at improving the monitoring and regulation of students’ thought when dealing with mathematics problems.
Almeqdad, Q. I. (2008). Azevedo, R., & Aleven, V. (2013). Metacognition and learning technologies: an overview of current interdisciplinary research Bernard, M., & Bachu, E. (2015). Enhancing the Metacognitive Skill of Novice Programmers Through Collaborative Learning Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Brown, A. (1987). Metacognition, Executive Control, Self Regulation and Mysterious Mechanisms. In R. K. Franz E. Weinert (Ed.), Buratti, S., & Allwood, C. M. (2015). Regulating Metacognitive Processes—Support for a Meta-metacognitive Ability Cardelle-Elawar, M. (1992). Effects of teaching metacognitive skills to students with low mathematics ability. Cetin, I., Sendurur, E., & Sendurur, P. (2014). Assessing the Impact of Meta-Cognitive Training on Students' Understanding of Introductory Programming Concepts. Coles, A. (2013). Desoete, A. (2007). Evaluating and improving the mathematics teaching-learning process through metacognition. Desoete, A. (2009). Metacognitive prediction and evaluation skills and mathematical learning in third-grade students. Efklides, A., & Misailidi, P. (2010). Introduction: The present and the future in metacognition Eldar, O., & Miedijensky, S. (2015). Designing a Metacognitive Approach to the Professional Development of Experienced Science Teachers Fortunato, I., Hecht, D., Tittle, C., & Alvarez, L. (1991). Metacognition and problem solving. Gillies, R. W., & Richard Bailey, M. (1995). Goos, M. (1993). Grant, G. (2014). Grizzle-Martin, T. (2014). Hartman, H. J. (2001). Developing students’ metacognitive knowledge and skills Hurme, T.-R., Järvelä, S., Merenluoto, K., & Salonen, P. (2015). What Makes Metacognition as Socially Shared in Mathematical Problem Solving? Kapa, E. (2001). A metacognitive support during the process of problem solving in a computerized environment. Kluwe, R. H. (1982). Cognitive knowledge and executive control: Metacognition Kramarski, B., & Mevarech, Z. R. (2003). Enhancing mathematical reasoning in the classroom: The effects of cooperative learning and metacognitive training. Kramarski, B., & Michalsky, T. (2013). Student and teacher perspectives on IMPROVE self-regulation prompts in web-based learning Kuhn, D. (2000). Theory of mind, metacognition, and reasoning: A life-span perspective. In P. R. Mitchell, Kevin John (Ed.), la Barra, D., León, M. B., la Barra, D., León, G. E., Urbina, A. M., la Barra, D., & León, B. A. (1998). Larkin, S. (2000). Larkin, S. (2006). Collaborative group work and individual development of metacognition in the early years. Larkin, S. (2010). Lester, F., Garofalo, J. & Kroll, D.L. . (1989). Bloomington, IN. USA Patent No. Eric Document Reproduction Service No. ED 314 255: M. E. D. Indiana University & Centre. Merriam, S. B. (1998). Mevarech, Z., & Fridkin, S. (2006). The effects of IMPROVE on mathematical knowledge, mathematical reasoning and meta-cognition. Mevarech, Z., & Kramarski, B. (1997). IMPROVE: A multidimensional method for teaching mathematics in heterogeneous classrooms. Mevarech, Z. R., & Amrany, C. (2008). Immediate and delayed effects of meta-cognitive instruction on regulation of cognition and mathematics achievement. Moga, A. (2012). Mohini, M., & Nai, T. T. (2005). The use of metacognitive process in learning mathematics. Mutekwe, E. (2014). Unpacking Student Feedback as a Basis for Metacognition and Mediated Learning Experiences: A Socio-cultural perspective. Naglieri, J. A., & Johnson, D. (2000). Effectiveness of a cognitive strategy intervention in improving arithmetic computation based on the PASS theory. Panaoura, A., & Philippou, G. (2005). Peña-Ayala, A., & Cárdenas, L. (2015). A Conceptual Model of the Metacognitive Activity Raoofi, S., Chan, S. H., Mukundan, J., & Rashid, S. M. (2013). Metacognition and Second/Foreign Language Learning. Robson, C. (2002). Sahin, S. M., & Kendir, F. (2013). The effect of using metacognitive strategies for solving geometry problems on students’ achievement and attitude. Schoenfeld, A. H. (1987). What’s All the Fuss About Metacognitlon. In A. H. Schoenfeld (Ed.), Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. Schraw, G., & Gutierrez, A. P. (2015). Metacognitive Strategy Instruction that Highlights the Role of Monitoring and Control Processes Simons, P. R. (1996). Metacognitive strategies: Teaching and assessing. In E. DeCorte, Weinert, F.E. (Ed.), Thomas, G. (2012). Metacognition in science education: Past, present and future considerations. In B. Fraser, Tobin, Kenneth, McRobbie, Campbell J. (Ed.), Tok, Ş. (2013). Effects of the know-want-learn strategy on students’ mathematics achievement, anxiety and metacognitive skills. Wolf, S. E., Brush, T., & Saye, J. (2003). Using an information problem-solving model as a metacognitive scaffold for multimedia-supported information-based problems. Yimer, A. (2004). Yin, R. K. (2014). Zohar, A., & Barzilai, S. (2013). A review of research on metacognition in science education: current and future directions. |
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## Triangular law of students’ Mathematics Interest in Ghana: A Model with motivation and perception as predictorSamuel Asiedu -Addo, Charles K. Assuah, Yarhands Dissou Arthur
pp.
The main purpose of this study was to verify by means of structural equation modelling (SEM) how students’ interest in mathematics (SIM) is affected by students’ perception and students’ motivation to learn mathematics. The study further investigated the effect of students’ perception (SP) on students’ motivation (SM) to learn mathematics. The study adopted a simple random sampling technique to administer 150 questionnaires to 10 public Senior High Schools in Ghana. In all, a total number of 1,500 students were given the questionnaire to indicate their responses. However, 1,263 questionnaires were properly administered, representing 84.3% response rate. The constructs reliability for SIM, SP, and SM were 0.71, 0.82, and 0.68 respectively. The further explored how the goodness-of-fit influences the measurement model, structural model and the overall model. The findings indicated that when Ghanaian high school students’ have good perception about mathematics and have the motivation to learn mathematics, their interest in mathematics would improve significantly.
Arthur, Y., Asiedu-Addo, S., & Assuah, C. (2017). Students’ Perception and Its Impact on Ghanaian Students’ Interest in Mathematics: Multivariate Statistical Analytical Approach. Arthur, Y. D., Oduro, F. T., & Boadi, R. K. (2014). Statistical Analysis of Ghanaian Students Attitude and Interest Towards Learning Mathematics . Bong, M. (2004). Academic Motivation in Self-Efficacy, Task Value, Achievement Goal Orientations, and Attributional Beliefs. Fornell, C., & Larcker, D. (1981). Evaluating structural equation models with unobservable variables and measurement error. Githua, B. N., & Mwangi, J. G. (2003). Students ’ mathematics self-concept and motivation to learn mathematics : relationship and gender differences among Kenya ’ s secondary-school students in Nairobi and Rift Valley provinces. Hair, J. F., Black, B., Babin, B., TathamR.L, & R.E, A. (2005). Hair, J., Sarstedt, M., & Ringle, C. (2012). An assessment of the use of partial least squares structural equation modeling in marketing research. Henseler, J., Ringle, C., & Sinkovics, R. (2009). The use of partial least squares path modeling in international marketing. Ignacio, N., Nieto, L., & Barona, E. (2006). The affective domain in mathematics learning. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.495.3040 Köǧce, D., Yildiz, C., Aydin, M., & Altindaǧ, R. (2009). Examining elementary school students’ attitudes towards mathematics in terms of some variables. Linnenbrink-Garcia, L., Durik, A. M., Conley, A. M., Barron, K. E., Tauer, J. M., Karabenick, S. A., & Harackiewicz, J. M. (2010). Measuring Situational Interest in Academic Domains. Martin, A. J. (2006). The relationship between teachers’ perceptions of student motivation and engagement and teachers’ enjoyment of and confidence in teaching. Matic, L. J. (2014). Mathematical knowledge of non-mathematics students and their beliefs about mathematics. Meece, J. L., Wigfield, A., & Eccles, J. S. (1990). Predictors of math anxiety and its influence on young adolescents’ course enrollment intentions and performance in mathematics. Mensah, J. K., Okyere, M., & Kuranchie, A. (2013). Student attitude towards Mathematics and performance : Does the teacher attitude matter ? Mutodi, P., & Ngirande, H. (2014a). Exploring Mathematics Anxiety: Mathematics Students’ Experiences. Mutodi, P., & Ngirande, H. (2014b). The Influence of Students ` Perceptions on Mathematics Performance . A Case of a Selected High School in South Africa. Pantziara, M., & Philippou, G. (2007). Students ’ motivation and achievement and teachers ’ practices in the classroom, Proceedings of 31th PME Conference Singh, K., Granville, M., & Dika, S. (2002a). Mathematics and science achievement: effects of motivation, interest, and academic engagement. Singh, K., Granville, M., & Dika, S. (2002b). Mathematics and Science Achievement: Effects of Motivation, Interest, and Academic Engagement. Skaalvik, E. M., & Skaalvik, S. (2008). Self-concept and self-efficacy in mathematics: Relation with mathematics motivation and achievement. Tooke, D. J., & Lindstrom, L. C. (1998). Effectiveness of mathematics methods course in reducing math anxiety of preserves elementary teacher. |
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## A Topic Revisited: Students in the Republic of the Maldives Writing Contextual Word ProblemsJason Johnson
pp.
Students dislike for solving word problems is not new for mathematics teachers. Most word problems have no cultural significance or relate to the student. A student dislike for solving word problems could be contributed to the lack of reference to the lived experience of the student (i.e., social class, race, ethnicity, mother language, gender, sexual orientation, and any other demographic characteristics). А study was designed to explore a group of students, on the island of Kuda Hudaa in the Republic of the Maldives, ability to write contextual word problems. Contextual word problems are word problems that relate to a student population in a classroom. The results indicate that all students were able to create contextual word problems for both multiplication and division. Most student written multiplication and division word problems met Marks (1994) three considerations when developing word problems. The intent is to encourage students to write contextual word problems that make learning mathematics more meaningful for students.
Amit, M. & Klass-Tsirulnikov, B. (2005). Paving a way to algebraic word problems using a nonalgebra route. Mathematics Teaching in the Middle School, 10, 271 – 276. Basurto, I. (1999). Conditions of reading comprehension which facilitate word problems for second language learners. Reading Improvement, 36(3), 143 – 148. Brown, N. M. (1993). Writing mathematics. Arithmetic Teacher, 41(1), 20 – 21. Burton, M. B. (1991). Grammatical translation-inhibitors in two classic word problem sentences. For the Learning of Mathematics, 11(1), 43 – 46. D'Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the Learning of Mathematics, 5, 44-8. D’Ambrosio, U. (2001). What is Ethnomathematics and how can it help children in schools? Teaching Children Mathematics, 7(6), 308-310. D’Ambrosio, U. (2009). The program Ethnomathematics: A theoretical basis of the dynamics of intra cultural encounters. Journal of Mathematics and Culture. 1, (1), 1 – 7. Darby, L. (2008). Marking mathematics and science relevant through story. Australian Mathematics Teacher, 64(1), 6 – 11. DiPillo, M. L., Sovich, R., & Moss, B. (1997). Exploring middle graders' mathematical thinking through journals. Mathematics Teaching in the Middle School, 2 (5), 308 – 314. Edie, R. (2009). Making sense of word problems (Master’s Thesis). University of Nebraska – Lincoln. Retrieved from: http://digitalcommons.unl.edu/mathmidactionresearch/42/ Foley, T. E., Parmar, R. S., & Cawley, J. F. (2004). Explanding the agenda in mathematics problem solving for students with mild disabilities: alternative representations. Learning Disabilities, 13(1), 7 – 16. François, K. (2009). The role of Ethnomathematics within mathematics education. Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (CERME). January 28 – February 1, 2009, Lyon France. <www.inrp.fr/editions/cerme6> Heinze, K. (2005). The language of math. Presentation handouts from TESOL conference. Retrieved from http://www.rtmsd.org/cms/lib/PA01000204/Centricity/Domain/594/Language_of_Math.doc. Hoz, R. & Harel, G. (1990). Higher order knowledge involved in the solution of algebra speed word problems. Journal of Structural Learning, 10(4), 305 – 328. Langeness, J. (2011). Methods to improve student ability in solving math word problems (Master’s Thesis). Hamline University. Retrieved from: http://www.hamline.edu/WorkArea/DownloadAsset.aspx?id=2147514388. LeGere, A. (1991). Collaboration and writing in the mathematics classroom. Mathematics Teacher. 84(3), 166 – 171. Marks, D. (1994). A guide to more sensible word problems. The Mathematics Teacher, 87(8), 610 – 611. Mangan, C. (1989). Choice of operation in multiplication and division word problems: A developmental study. Journal of Structural Learning, 10, 73 – 77. Martinez, J. G. R. (2001). Thinking and writing mathematically: Achilles and the tortoise as an algebraic word problem. Mathematics Teacher, 94(4), 248 – 252. Miller, L. D. (1991). Constructing pedagogical content knowledge from students’ writing in secondary mathematics. Mathematics Education Research Journal, 3(1), 30 – 44. Miller, L. D. (1992). Teacher benefits from using impromptu writing prompts in algebra classes. Journal for Research in Mathematics Education, 23(4), 329 – 340. Patton, M. Q. (2002). Qualitative research and evaluation methods (3rd Ed.). London: Sage Publications. Powell, A.B., & Lopez, J.A. (1989). Writing as a vehicle to learn mathematics: A case study. In P. Connolly & T. Vilardi (Eds.), Presmeg, N. (1998). Ethnomathematics in teacher education. Journal of Mathematics Teacher Education, 1, 317 – 339. Puchalska, E. & Semadeni, Z. (1987). Children’s reactions to verbal arithmetical problems with missing, surplus or contradictory data. For the Learning of Mathematics, 7(3), 9 – 16. Rubenstein, R. N. & Thoompson, D. R. (2002). Understanding and supporting children’s mathematical vocabulary development. Teaching Children Mathematics, 9(2), 107 – 112. Rudnitsky, A., Etheredge, S., Freeman, S. J. M., and Gilbert, T. G. (1995). Learning to solve addition and subtraction word problems througha structure-plus-writing approach. Journal for Research in Mathematics Education, 26(5), 467 – 486. Stix, A. (1994). Pic-jour math: Pictorial journal writing in mathematics. Arithmetic Teacher, 41(5), 264 – 269. Wedege, T. (2010). Ethnomathematics and mathematical literacy: People knowing mathematics in society. C. Bergsten, E. Jablonka, and T. Wedege (eds). Mathematics and mathe-matics education: Cultural and social dimensions. 31 – 46. Winograd, K., & Higgins, K. (1994). Reading, writing and talking mathematics: One interdisciplinary possibility. The Reading Teacher, 48, 310 – 319. Xin, Y. P. (2007). Word problem solving tasks in textbooks and their relation to student performance. The Journal of Educational Research, 100(6), 347 – 359. |
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## A review of methods for highway-railway crossings safety management processBehzad Dezhkam ,Seyed Mehrdad Eslami
pp.
This paper reviews the literature concerning the risks associated with Highway- Railway Crossings (HRC). The aim of this study is to evaluate and validate previous investigations conducted in the United States and Canada. The main issues addressed in this paper are: a) Identify HRC with potential the average collision frequency or collision severity as black spots, tests that are used to identifying hazardous location and compare the methods, b)Identify the contributing factors to safety problems at an identified HRC location, c)Identification of countermeasures to address the contributing factors. This research has thrown up many questions in need of further investigations on risks associated with HRC to mitigate the accident frequency and injury severity.
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