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In recent years, international comparisons have revealed wide differences in mathematical performance around the world, generating a general concern for improving mathematics teaching and learning. Yet, while teachers strive to improve performances on tests, there is a growing realization that in many cases this leads to the teaching of procedures...
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Through our experience in teaching mathematics to engineering undergraduates, we found that students had numerous difficulties with the mathematics learned. Although our students have demonstrated the ability to answer standard or routine questions, there were still some inconsistencies between their ability to answer questions and their understand...
Mathematics teaching and learning with emphasis on connecting mathematical knowledge is necessary for fostering student’s mathematical competence to explore the unknown world and create a new value. Students should have experiences of solving problems by using various mathematical tools such as the way of mathematical thinking and the mathematical...
Citations
... in several reports of Lesson Study experiments (Fernandez & Chokshi, 2002;Fernandez, Cannon, & Chokshi, 2003;Murata et al., 2004;Zilliox & Fernandez, 2004;Cerbin & Kopp, 2006;Isoda, 2006;Roback, Chance, Legler, & Moore, 2006;Tall, & Isoda, 2007;Kratzer & Teplin, 2007;Bergenske, 2008;Suh & Fulginiti, 2012;Adams, 2013;Tatang & Kuno, 2013;Hj Suhaili & Shahrill, 2015;Ngang;Sam, 2015;Elliott, 2016;Griffiths, 2016;Bae, Hayes, Seitz, O'Connor, & DiStefano, 2016;C. Lewis, 2016;J. ...
The Japanese methodology, known in the West as Lesson Study, has been exploited in teacher education programs in various parts of the world, including the Brazilian Amazon where two pioneering studies have been carried out recently. This paper is a reflection on potential challenges to the implementation of this methodology in the Amazon. An inference that is drawn from it is that the current circumstances of the teaching culture and other cultural characteristics obtaining in this region only admit the implementation of a vague version of the Japanese Lesson Study.
... In a time of technological change and economic globalization, we need to use every resource in our power to improve the ways we organize our lives. Lesson study viewed within a framework of long-term growth of mathematical thinking is a powerful tool to improve how we learn to think mathematically (Isoda & Tall, 2007). ...
GeoGebra mathematical software is the best alternative way of teaching and learning calculus in 21st century by exploration and visualization. This software opposes the traditional teaching and learning method, or solution only approaches and make the teaching and learning process more active in the classroom which goes with the constructive approach of teaching and learning methods. The study aims to implement the GeoGebra mathematical software/technological tool/ oriented lesson plan in the classroom using some developed steps and list out some criteria that the teacher may need to know to implement this dynamic software in his or her classroom. Finally, the study also put the recommendations of the study.
... This article presented example the compression procedures in problem solving to thinkable concept under context using Lesson Study and Open Approach, with the four of first graders a project school supported by CRME. In this study based on the framework that purposed by Tall and Isoda (2007) and Poynter (2004). ...
... Idea is consistent with the way in finding answers or results obtained by considering what dually of symbols in the calculation is the process of using different procedures to solve problems and conceptualize that created apply the refined concept of calculating symbolic (Gray & Tall, 1994) and Tall (2004) suggest that as of now, the change of the process to the concept can not be built obvious, or can not be observed easily. So the idea that seen as a substantial and consistent is the concept of Tall and Isoda (2007) describes the classes that implement Lesson Study caused students an idea or concept of the stages through implementation compression to thinkable concept of the 4 sequences of procedures used in the solution to the outcome. Such an idea is based on the idea of Tall (2006) discusses the compression into thinkable concept through the implementation of the 5 sequence steps. ...
... That students use to solve problems. At this stage of analysis based on the concept of Tall and Isoda (2007) and Poynter (2004) discusses the process of refining the concept into a concept that can think for themselves in the context of education classes and methods open. Which does not restrict students to use a single method to solve the problem, but beneficial to students using a variety of methods to solve problems and push to the concept or notion of students to solve problems. ...
The distinction between procedural and conceptual learning has long been a topic of discussion in mathematics education and the idea of compression into thinkable concepts that enable the individual make links between them (Tall, 2007). In addition to, the compression to thinkable concept was to be thinking mechanism arising naturally and important thinking tool in developing concepts (Gray & Tall, 2002). The major act of compression to thinkable concept shifts attention from the sharing procedure as a sequence of steps to the effect of that procedure (Gray & Tall, 2007). So, the compression to thinkable concept is one important way in order to understand in development from procedures to concept.
This article presented example the compression procedures in problem solving to thinkable concept under context using Lesson Study and Open Approach, with the four of first graders a project school supported by CRME. In this study based on the framework that purposed by Tall and Isoda (2007) and Poynter (2004).
Under context using Lesson Study and Open Approach provide to students manipulated with designed materials for supporting and checking their various symbolic thinking before into same effect through parallel compression 5 steps into thinkable concept in blending embodiment and symbolism. In embodiment from step-by-step action, to the possible choice of several different action, to seen the overall effect as same effect that can be carried out in various ways, to compressing it as effect as prototype, to awareness and appreciation of effect used later. In symbolism from step-by-step procedure, to the possible choice of several different procedures, to seen the overall effect as a general process that can be carried out in various ways, to compressing it as thinkable concept, to awareness and appreciation of thinkable concept in extending mathematical structure. Consequently, the students used considering the way of thinking and refined the ideas in order to develop a major idea from different procedures in problem solving.
... esim. Laine, A. & Huhtala, S., 2003;Isoda, M & Tall, D. 2007). Mielekkäät oppimiskokemukset voivat liittyä esimerkiksi symbolisen ja ilmenevän maailman kokonaisvaltaiseen yhdistämiseen (ks. ...
The three worlds of mathematics by David Tall provide a framework for studying mathematical thinking and its development. Extending the framework of three worlds by Tall with Juha Oikkonen’s ”two faces of mathematics” develops a new, broader framework in which certain aspects to research on learning mathematics (such as mini-theories) are included to form a larger entity. The framework, previously drafted by Oikkonen and more thoroughly analyzed in this article, has the power to explain, for example, the learning processes of individual mathematical concepts.
... There are many barriers to overcome in relation to the Japanese situation. In Europe as well as in the United States there is no widespread history of a changing process from individualized instruction to whole classroom instruction (Isoda and Tall 2007). Moreover, the barrier in Europe is its focus on renewing instead of improving teaching and learning approaches. ...
... In a time of technological change and economic globalization, we need to use every resource in our power to improve the ways we organize our lives. Lesson study viewed within a framework of long-term growth of mathematical thinking is a powerful tool to improve how we learn to think mathematically (Isoda and Tall 2007). ...
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... In deze studie wordt in de theorievorming over sensible mathematics aangesloten bij de drie door Bruner (1966) (Isoda & Tall, 2007;Isoda, 2011). ...
Deze studie gaat in op kenmerken van sensible mathematics - het gevoelig maken voor wiskundige begrippen en bewerkingen - in de context van het begrip afgeleide in 4vwo wiskunde B. Zes wiskundedocenten van verschillende scholen onderzochten samen hun lespraktijken aan de hand van lesson study. Concreet werden onderzoekslessen samen voorbereid, waarbij de uitvoering gezamenlijk werd geobserveerd. Op basis van discussie en reflectie werden de onderzoekslessen herzien en opnieuw uitgevoerd op een andere locatie. De resultaten van het onderzoek laten zien dat het gevoelig maken voor wiskunde begint met het activeren van het denken van leerlingen, inspelend op de intuïtie. Het gaat erom dat leerlingen gaan redeneren en communiceren in een eigen taal. Daarna ontstaat de fase waarin behoefte is aan visualisaties (iconen) om situaties te beschrijven die vervolgens overvloeien in getallen en bewerkingen daarmee (symbolen). In de fase waarin getallen een rol spelen is onderscheid gemaakt tussen het werken met getallen en het redeneren over de bewerkingen met getallen.
... Tall (2004) explained that the changing process from procedures to thinkable concept cannot be seen easily. So, this is a point of view important of Tall and Isoda (2007) said that for classroom developed through Lesson Study provided to compression through four steps based on Tall (2006b) to be five steps of compression to thinkable concept. ...
... The purpose of analyzing teaching scenes was to study the students' abstraction process through compression to thinkable concept under classroom using Lesson Study and Open Approach. The data was analyzed under the framework that proposed by Tall and Isoda (2007). The analysis were divided into three parts: 1) analyzing students' way of thinking in solving problem; 2) Analyzing of compression into thinkable concept in students' abstraction process from calculation symbolic and interaction designed material; 3) Analyzing the students' abstraction process based on compression into thinkable concept from blending embodiment and symbolism under context using Lesson Study and Open Approach. ...
... Students background knowledge was construct 10 from decomposing and composing, using diagram as thinking tool. This situation focused on writing symbols addition and subtraction using diagram and base 10 based on analyzing data under the theory of Tall and Isoda (2007). ...
The objective of mathematics learning and teaching was to develop students' concept in content so that the persons as teachers, educators, and researchers would try to search for instruments, and know for comprehending the students' existing concepts. The study abstraction process based on compression into thinkable concept was to be a major guideline in considering and findings answer in order to understand the students' concept (Gray & Tall, 2007). In Thai classroom using Lesson Study and Open Approach produced the students' mathematical thinking by using open-ended problems with designed material for supporting interaction of students and their problem solving arithmetic (Inprasitha, 1997). According to view of Tall (2007a) suggested a parallel construction of compression in the symbolism and embodiment to thinkable concept. This paper aim to analyze the students' abstraction process based on compression into thinkable concept from blending embodiment and symbolism. The four first grader as targeted group at Kookham Pittayasan School, a project school with supported by CRME, Faculty of Education, Khon Kaen University, Thailand. For research design used ethnographic study and teaching experiment. The collected data were used video analysis, interviewing, and students' task analysis. The research revealed that, the students' thinking shift steadily from performing sequence of parallel compression from actions being linked together in increasingly sophisticated ways to thinkable concept in embodiment and symbol-ism. This research revealed that Lesson Study incorporated Open Approach as teaching approach pro-vided to students' abstraction process from considering that they manipulated with designed materials for supporting and checking their various symbolic thinking before into same effect on arithmetic operation.
... Tall (2004) suggested that the changing process from procedures to thinkable concept cannot be seen easily. Tall and Isoda (2007) described in classroom using Lesson Study caused to the student's abstraction process for concept formation from considering compression to thinkable concept through 4 steps of procedures in problem solving to effect based on Tall (2006) five steps of thinkable concept. ...
... These various underlying frameworks have a general development of increasing flexibility and compression, which is introduced in an overall problem-solving way in Lesson Study. Tall and Isoda (2007) suggested that a c rough Lesson Study does not limit students to think, it helps the students to think and act differently in solving problem to same effect through four steps of compression to thinkable concept as follows: ...
... The purpose of analyzing teaching scenes was to study "how to" as a tool in the students' abstraction process through compression to thinkable concept under classroom using Lesson Study and Open Approach. The data was analyzed based on the framework that proposed by Tall and Isoda (2007). The analyzing was divided into three parts: 1) Analyzing students' way of thinking in solving problem 2) Analyzing students' abstraction process through compression to thinkable co 3) Analyzing "how to" in the students' abstraction process through compression to thinkable concept under cl ing Lesson Study and Open Approach. ...
This study focuses on mathematics teachers’ professional development through
elements of Japanese lesson study. The teachers designed a research lesson with
regard to sense-making of the derivative using the integration of GeoGebra. In
the second year of the four-year lesson study project, seven secondary school
teachers – from different Dutch schools – worked cooperatively, building on the
first-year experiences with the introduction of the derivative. The teachers
designed a lesson that focused on encapsulation of the conceptual understanding
of the derivative before solving problems with operational symbolism later in the
course. They tried to make sense of the calculus using GeoGebra as a tool to
realize surprise in which conceptual embodiment and operational symbolism
blend together. The teachers integrated GeoGebra to consolidate the derivative
using the visual idea of zooming in on the graph to see its local behavior (where
a differentiable function looks ‘locally straight’). The teachers reported that they
have learned to use visualizations and experienced the importance of student
interaction. The teachers realized that this approach of the derivative – integrating
GeoGebra – encouraged them to reflect on how the students made sense of
learning activities in general.
