7 minute read
Meaningful and holistic integration of mathematics content in life
Stefanos Gialamas and Angeliki Stamati on a project that encompasses everything from athletics to psychology
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 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:
‘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 The rubric used to assess student proposals is as follows:
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.
Catergory
Mathematical Reasoning Mathematical Concepts
Mathematical Terminology and Notation
Strategy/ Procedures of the upcoming presentation
Creativity and authenticity of the project Neatness and Organization
4
Uses complex and refined mathematical reasoning.
Explanation shows complete understanding of the mathematical concepts used to describe the project.
Correct terminology and notation are always used, making it easy to understand what was done.
Uses an efficient and effective strategy for the upcoming presentation of the project. Transforms the authentic idea of the project into entirely new form.
The proposal is presented in a neat, clear, organized fashion that is easy to read.
3
Uses effective mathematical reasoning
Explanation shows substantial understanding of the mathematical concepts used to describe the project. Correct terminology and notation are usually used, making it fairly easy to understand what was done.
Uses an effective strategy for the upcoming presentation of the project.
Synthesizes the authentic idea of the project into a coherent whole.
The proposal is presented in a neat and organized fashion that is usually easy to read.
2
Some evidence of mathematical reasoning.
Explanation shows some understanding of the mathematical concepts needed to describe the project. Correct terminology and notation are used, but it is sometimes not easy to understand what was done.
Uses a not clearly defined strategy for the upcoming presentation of the project.
Connects authentic ideas in novel ways.
The proposal is presented in an organized fashion but may be hard to read at times.
1
Little evidence of mathematical reasoning.
Explanation shows very limited understanding of the underlying concepts needed to describe the project. There is little use, or a lot of inappropriate use, of terminology and notation.
Uses a non-effective strategy for the upcoming presentation of the project.
Recognizes existing connections among authentic ideas.
The proposal appears sloppy and unorganized. It is hard to know what information goes together.
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
Knowledge and understanding
Knowledge
Analysis
Reflection in mathematics
Communication in mathematics through mathematical calculations
Designing and Creating
10
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 develop and implement a simple procedure to demonstrate excellent conceptual understanding.
9-7
Able to find/ recognize/name/ show and organize examples to describe a mathematical concept when solving challenging problems. Able to develop and implement a simple procedure to demonstrate good conceptual understanding.
Able to recognize a variety of patterns and describe them as relationships. 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.
Shows excellent use of mathematical language and/or mathematical representation. Shows calculations clearly and accurately.
Creative model designed and created to demonstrate conceptual understanding. Able to recognize patterns and describe them as relationships. 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.
Shows good use of mathematical language and/ or mathematical representation. Shows calculations clearly. Interesting model designed and created to demonstrate conceptual understanding.
6-4
Able to find/ recognize/name/ show examples to describe a mathematical concept when solving more complex problems. Able to develop and implement a simple procedure to demonstrate satisfactory conceptual understanding. Able to recognize some patterns and suggest relationships. 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.
3-1
Able to find/ recognize/name examples to describe a mathematical concept when solving simple problems.
Able to develop and implement a simple procedure to demonstrate basic conceptual understanding.
Able to recognize some patterns.
Attempts to explain the reasonableness of results and their connection to real life.
0
Not able to find examples to describe a mathematical concept.
Not able to develop and implement a procedure.
Not able to recognize patterns.
Does not attempt to explain the reasonableness of results and their connection to real life.
Shows sufficient use of mathematical language and/ or mathematical representation. Shows calculations.
Satisfactory model designed and created to demonstrate conceptual understanding. Shows basic use of mathematical language and/ or mathematical representation. Shows some calculations.
Simple model designed and created to demonstrate conceptual understanding. Does not use any mathematical representation or calculations.
No model designed/ created 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 in multidimensional ways. Therefore, these self-inspired individuals are becoming mathematicians, musicians, philosophers, and so on.
