International School Aut | 2019 | Volume 21 | Issue 3
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The magazine for international educators
A model for differentiation techniques Education in Silicon Valley | Focus on mental health and wellbeing | Balancing sport with school
Curriculum, learning and teaching
Meaningful and holistic integration of mathematics content in life Stefanos Gialamas and Angeliki Stamati on a project that encompasses everything from athletics to psychology
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in a way that is relevant to individual needs and interests, and above all is exciting. The range of selection of topics on mathematical projects is very broad. Students choose to focus on sports such as basketball, taekwondo, tennis, or soccer. Other students opt for Arts having drawn a face, or a flower through equations. Designing a house through linear equations, or the mathematical interpretation of psychology researches have been very popular student choices. On the first day of the class, students discuss with the instructor(s) the creative year-long projects. Expectations are made clear to them, together with the due date proposal, the assessment criteria and the settings of the final presentation. Students need to answer two questions:
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As educators we are constantly trying to evolve and enhance our teaching practices, to inspire our students and to convey to them our passion for the content we are teaching. Creating an inspiring environment in a mathematics classroom has always been a struggle to many mathematics instructors, as students regard their discipline with skepticism and many times with aversion. At ACS Athens, the delivery of mathematics is defined in harmonious and holistic terms. In particular, high school students of Algebra 2 and Trigonometry are exposed to an authentic, relevant real world application of mathematics through year-long creative projects. Students explore a specific mathematical concept using their individual skills creatively
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Curriculum, learning and teaching
‘What do I like doing most in my personal time?’ and ‘How can I relate this to the Algebra 2 and Trigonometry curriculum?’ The instructor(s) of the course assist(s) the student in making the connection between those two questions. Once the proposal is finalized each student is assigned a project supervisor who will guide him/her through the year-long process. The proposal must be submitted before the end of the first quarter, and students must submit a written proposal based on a mathematics topic that is part of the Algebra 2 and Trigonometry curriculum. In their proposal, students must briefly describe what this mathematics concept is and
how creatively they plan on presenting the final day of the exhibition. In addition, students need to clearly identify the real-life application of their chosen topic. The year-long creative math project is a continuous learning process embarked upon at the beginning of the academic year and climaxing at the end of the year. In between times, students have a close communication with their individual supervisors. The instructor(s) fine-tune the process with quarterly checkups that assess not only the level of commitment but also the quantity and the quality of the progress demonstrated.
The rubric used to assess student proposals is as follows: Catergory
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3
2
1
Mathematical Reasoning
Uses complex and refined mathematical reasoning.
Uses effective mathematical reasoning
Some evidence of mathematical reasoning.
Little evidence of mathematical reasoning.
Mathematical Concepts
Explanation shows complete understanding of the mathematical concepts used to describe the project.
Explanation shows substantial understanding of the mathematical concepts used to describe the project.
Explanation shows some understanding of the mathematical concepts needed to describe the project.
Explanation shows very limited understanding of the underlying concepts needed to describe the project.
Mathematical Terminology and Notation
Correct terminology and notation are always used, making it easy to understand what was done.
Correct terminology and notation are usually used, making it fairly easy to understand what was done.
Correct terminology and notation are used, but it is sometimes not easy to understand what was done.
There is little use, or a lot of inappropriate use, of terminology and notation.
Strategy/ Procedures of the upcoming presentation
Uses an efficient and effective strategy for the upcoming presentation of the project.
Uses an effective strategy for the upcoming presentation of the project.
Uses a not clearly defined strategy for the upcoming presentation of the project.
Uses a non-effective strategy for the upcoming presentation of the project.
Creativity and authenticity of the project
Transforms the authentic idea of the project into entirely new form.
Synthesizes the authentic idea of the project into a coherent whole.
Connects authentic ideas in novel ways.
Recognizes existing connections among authentic ideas.
Neatness and Organization
The proposal is presented in a neat, clear, organized fashion that is easy to read.
The proposal is presented in a neat and organized fashion that is usually easy to read.
The proposal is presented in an organized fashion but may be hard to read at times.
The proposal appears sloppy and unorganized. It is hard to know what information goes together.
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Curriculum, learning and teaching The final project is evaluated on the basis of: • the degree of difficulty of the mathematical topic • the degree of creativity of the presentation • the project’s connection to a real-life application while the rubric used in assessing the final presentation is as follows Criteria
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9-7
6-4
3-1
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Knowledge and understanding
Able to find/recognize/ name/show and organize examples to describe a mathematical concept when solving challenging problems in a variety of situations.
Able to find/ recognize/name/ show and organize examples to describe a mathematical concept when solving challenging problems.
Able to find/ recognize/name/ show examples to describe a mathematical concept when solving more complex problems.
Able to find/ recognize/name examples to describe a mathematical concept when solving simple problems.
Not able to find examples to describe a mathematical concept.
Knowledge
Able to develop and implement a simple procedure to demonstrate excellent conceptual understanding.
Able to develop and implement a simple procedure to demonstrate good conceptual understanding.
Able to develop and implement a simple procedure to demonstrate satisfactory conceptual understanding.
Able to develop and implement a simple procedure to demonstrate basic conceptual understanding.
Not able to develop and implement a procedure.
Analysis
Able to recognize a variety of patterns and describe them as relationships.
Able to recognize patterns and describe them as relationships.
Able to recognize some patterns and suggest relationships.
Able to recognize some patterns.
Not able to recognize patterns.
Reflection in mathematics
Critically explains the reasonableness of results. Assesses and describes in detail the importance of the results and their connection to real life. Justifies the accuracy of the results and suggests improvements of the method used.
Explains the reasonableness of results. Describes the importance of results and their connection to real life. Justifies the accuracy of the results and suggests improvements of the method used.
Briefly explains the reasonableness of results. Describes the importance of results and their connection to real life. Attempts to justify the accuracy of the results.
Attempts to explain the reasonableness of results and their connection to real life.
Does not attempt to explain the reasonableness of results and their connection to real life.
Communication in mathematics through
Shows excellent use of mathematical language and/or mathematical representation. Shows calculations clearly and accurately.
Shows good use of mathematical language and/ or mathematical representation. Shows calculations clearly.
Shows sufficient use of mathematical language and/ or mathematical representation. Shows calculations.
Shows basic use of mathematical language and/ or mathematical representation. Shows some calculations.
Does not use any mathematical representation or calculations.
Satisfactory model designed and created to demonstrate conceptual understanding.
Simple model designed and created to demonstrate conceptual understanding.
No model designed/ created to demonstrate conceptual understanding.
Designing and Creating
Creative model designed Interesting model and created to demonstrate designed and created conceptual understanding. to demonstrate conceptual understanding.
The philosophy behind this project is to encourage student choice and to promote students to investigate aspects of a subject in which they are genuinely interested, using their own discretion in terms of approach and medium. In doing so, their curiosity guides them into the real world of mathematics. This freedom is meant to foster life-long interest in mathematics. It is well documented that when human beings are interested in a particular concept or idea, they become self-inspired to learn more, by mastering the concept, and exploring opportunities to utilize their knowledge of the concept. Additionally, they research the implementation of their ideas
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in multidimensional ways. Therefore, these self-inspired individuals are becoming mathematicians, musicians, philosophers, and so on. Dr Stefanos Gialamas is President of the American Community Schools (ACS) of Athens, Greece, and holds a BS, MA and PhD in Mathematics. Dr Angeliki Stamati is a faculty member of the Mathematics department at ACS Athens and holds a BS, MA and PhD in Applied Mathematics and Studies of Science. Email: stamatia@acs.gr
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mathematical calculations
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