Mathematics at roxy
- 1. Creating Rich and Balanced Maths Programs to fit the National Curriculum and AUSVELS Part One PD @ RPPS 1st May 2013
- 5. PD Learning Intentions: • To establish compelling reasons for investigating and implementing change in the teaching and learning of Maths at RPPS • To introduce the ‘Mathematician’s Model’ • To explore ‘Rich Tasks’ within the context of Mathematics
- 6. Mathematics @ RPPS • State of Maths at RPPS:What does the student data tell us?
- 7. Mathematics @ RPPS • State of Maths at RPPS • What does the staff data tell us?
- 8. Mathematics @ RPPS So where to now? Change in strategy : ‘Mathematician’s Model’ Not 4 ‘number’ 2 ‘other’ but 4 ‘Toolbox’ and 2 ‘Be a Mathematician’ lessons
- 10. Who is in the photo in the middle? http://en.wikipedia.org/wiki/Terence_Tao We celebrate our pop stars, sports stars... Let’s celebrate our mathematicians too! Let’s provide our students with positive academic role models.
- 12. The Mathematician’s Model The school has six sessions a week (50 minutes a day). (FYI: ‘Key Characteristics of Effective Numeracy Teaching’ advocates for 5 x 1hr sessions per week). For four sessions a week, teachers run ‘toolbox lessons’. ‘You cannot solve any problems if you don’t have the tools’.
- 13. Toolbox Lessons Toolbox lessons focus on: Mathematical content knowledge Developing a range of problem solving strategies Developing student’s mental arithmetic capacity
- 14. Toolbox Lessons: What do they look like? BEFORE TEACHING: • Students prior knowledge assessed via Pre Unit Test. • Toolbox lessons build skills based on progression of skills according to maths continuum. Students grouped and placed on continuum according to need (based off test findings). Planning completed after pre unit test and based on student need. TEACHING: • Lessons progressive, building upon prior learning. • Learning intentions communicated with students at the start of the lesson. • Strong emphasis placed on collaboration and discussion between students. • Strong emphasis placed upon development of mental arithmetic strategies. • Learning wrapped up with a reflection on learning: http://www.magicalmaths.org/top-50-maths-mini-plenaries-ideas-to-use-in-an- outstanding-maths-lesson/ ASSESSMENT: Observation, Questioning, Rich Tasks (Portfolio), Post Unit, Post Semester (OnDemand)
- 15. ‘Be A Mathematician’ Lesson A carpenter is called upon to fix a door which has come off it’s hinges. The carpenter does not turn up empty handed – what are they carrying? Answer: a toolbox – they take one look at the problem and go rummaging around in their tool box for the right tool – in this case, a screwdriver. Importantly, if the tool is not there, the problem cannot be fixed, but equally, the only reason for carrying the tool us to use it in problem situations.
- 17. ‘Be A Mathematician’ Lesson In these sessions students get to ‘be a mathematician’. Teachers use a range of Rich open-ended investigative challenges. The investigation is the mathematics. The ‘toolbox’ skills are activated to solve a worthwhile problem. Work completed can be collected and submitted into a Maths Portfolio, to be used as part of our assessment schedule.
- 20. What is a “Rich Task”? A rich task involves both process and product, following an inquiry-based model of learning. Students learn large amounts of new content, develop important skills and develop in interdisciplinary learning. This includes personal- management, interpersonal development, communication, ICT and particularly in thinking.
- 21. How to create a ‘Rich Task’? • Open Ended • Problem Based • Inquiry Based • Wide/Narrow Curriculum • Process Product • Collaboration • Experiential • Engaging and Relevant
- 22. Open Ended? In an open-ended task there are multiple possible outcomes for success. This assists in catering for different levels of ability amongst the students. It also allows for student ownership of the task, as they are able to choose their own directions and work on their own solutions. Student choice is important! It allows for student ownership, self-direction, and engagement. This means students are genuinely thinking for themselves, rather than simply trying to crack the code to predict an answer/solution that has been predetermined as being correct by the teacher. Make sure that the task is genuinely open-ended, and not just that it is possible for some minor differences in answers, with only one main solution being possible. It is also a good idea to aim to be open-ended in allowing for various modes of presenting the final product (ie: speech, ICT, visuals, movie, drama, print-based text, etc.).
- 23. Problem Based? Having a task where students have to respond by solving a problem ensures that there will be the need for both creative and critical thinking (ie: brainstorming ideas, critiquing suggestions, evaluating, etc.). Solving an open-ended problem, where students have the power of task- ownership and self-direction provides a context for deep thinking and engagement. In order to solve a problem, students have to engage in thinking and not merely rely on the pre- established ideas of others.
- 24. Inquiry Based? In short you could say this means that a task follows the pattern of Bloom’s Taxonomy: “gathering information, processing information for comprehension, applying information to solve a problem and evaluating the results“. Following this model ensures that students build skills and content knowledge in a lot of disciplines. It also helps to develop interdisciplinary learning, such as group-work, personal-management, thinking and communication. You don’t want a rich task just to be all about gathering information and presenting it – there need to be tasks that require students to apply their new-found knowledge by thinking creatively and critically in order to solve an open- ended problem with opportunities for self-assessment and reflection throughout.
- 25. Wide/Narrow Curriculum? A rich task should provide opportunities for wide study and learning of content from a wide selection of areas. There should also be opportunities for narrow inspection of important details that are crucial to the outcomes of the study. Students need opportunities to learn broad concepts, with broad examples from the broader world, while also having opportunities to ensure that they comprehend important details and key skills and concepts through targeted teaching and learning.
- 26. Process Product Process comes before product and that the process in itself is a bigger aspect of learning than just the end product by itself. A rich task should have a significant process of learning and discovery as well as difficult challenges in the tasks themselves. When assessing a student’s work on a rich task, it is important that a teacher includes some process-related indicators as part of the assessment. For instance, a student may have displayed excellent thinking, group-work and personal-management throughout the task, but their product may have failed for some particular reason. It is valuable for the student to receive feedback about both the process and product so that they understand their strengths and areas for improvement as a learner. It is important to realise that the rich task is both the process and the product.
- 27. Collaboration? Collaboration is important for developing interpersonal skills as well as personal-management. It is also important for developing the ability to think creatively and critically and to engage in discussion and work in ways that are respectful to others. If a student simply works by themselves, then they are less likely to be challenged in their thinking. Working in a group means that students are more likely practice important mathematical vocabulary to justify their answers and ask clarifying questions of others and develop the ability to learn from others and accept differences in thinking. Collaboration provides a good context for group discussion and exploratory talk using key mathematical vocabulary. Collaboration also provides many challenges and supports for students as individuals, in that they are challenged to improve in certain areas, whilst also being supported by the variation of skills and abilities of their peers throughout the learning process.
- 28. Experiential? Not all students have the life experience and knowledge required to tackle a open-ended, problem-based task. Not all students have the same degree of skill with print-based texts or receptiveness to “chalk and talk” teaching to rely on these methods for gaining new knowledge. So, the learning experiences that go with the rich task should be ones that offer students different ways to learn new content. For instance, excursions, interactive activities, experiments, discussions, hands-on activities, movies, documentaries, ICT, games, software, websites, audio, guest-speakers, books, drama, etc. Do not discount the value of print-based texts, but certainly don’t limit resources and texts just to print-based versions.
- 29. Engaging and Relevant? Ask yourself these questions; Is the task relevant for students as individuals? Is the task relevant to the wide curriculum? Is the task relevant in relation to the broader world (both local and global)? What is it about the task that is going to engage students as learners? A rich task may not necessary tick all of these boxes initially, but it should tick most of them.
- 30. “I have a challenge for you today: Take six squares and try to construct a cube in as many different ways that you can...”
- 31. There are 11 different possibilities. These are referred to as ‘hexominoes’. What would you do next to extend this activity?
- 32. Mathematics @ RPPS Paul Halmos: • “It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.” • “The only way to learn mathematics is to do mathematics.” • “Mathematics is not a deductive science – that’s a cliché. When you try to prove a theorem, you don’t just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.” Paul Halmos:March 3, 1916 – October 2, 2006) was a Hungarian born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis .
Editor's Notes
- #19: Dan Meyer talks about how Mathematics lessons/curriculum need to be reorganised to put problem solving at the heart of all learning.