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Inquiry and Communication in Maths and Stats:

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## Inquiry and Communication in Maths and Stats:

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**Inquiry and Communication in Maths and Stats:**Training students to be self-starters who persevere and communicate their thinking. Presented by Jeremy Brocklehurst**Goals of workshop today:**• “Open-ended holistic task” : - What are they exactly? - What makes them good vs a waste of time? - Why ?? - Does this lead to bigger questions about what Mathematics is ? - How to help all students with them. Warning: I have some ideas but more questions than answers! This is where you come in!**How many coins could we fit on the floor of this classroom?**How could we get the greatest possible money value using a single layer of coins?**What’s the minimum length of fencing needed to enclose a**paddock holding 50 cows if each cow requires 25m2 to graze?**The quadrilateral ABCD has vertices A (0, 0), B (1, 4), C**(5, 3), and D (7, 1). P, Q, R, and S are the midpoints of the sides of the quadrilateral. If the points P, Q, R, and S are joined, a new quadrilateral is formed. What type of quadrilateral is PQRS? You must show the co-ordinate geometry methods you used to get your answer.**The following graphs are distributions of ages in two**populations. The United States of America (based on US census data) and Facebook users: Describe features of the distributions comparatively. Aim to make at least three statements. Support your statements with statistical evidence.**Questions to discuss:**• Whygive students open-ended ‘holistic’ tasks? Is there any research around this or is it just a “fad”?**Questions to discuss:**• What do students find most challenging about open-ended Maths or Stats tasks?**Questions to discuss:**• What is required for a person to become engaged and engrossed in them?**Questions to discuss:**• What about students who insist on being “spoon fed” ?**Questions to discuss:**• Other issues?**What the OSEM writing frame means:**O stands for Obvious observations Write down one thing you notice, then leave a gap, and write down something else you notice. Try to get 3 obvious things. S is for Specific Under each obvious observation, explain what you mean so that another person would get it. E is for Evidence Support each observation with numbers or calculations. M is for Meaning: So what? Write down what each of your points tells you about the original problem/situation. What else could we find out?**What the OSEM writing frame means:**O stands for Obvious observations: Write down one thing you notice, then leave a gap, and write down something else you notice. Try to get 3 obvious things. S is for Specific: Under each obvious observation, explain what you mean so that another person would get it. E is for Evidence: Support each observation with numbers or calculations. M is for Meaning: So what? Write down what each of your points tells you about the original problem/situation. What else could we find out?**What the OSEM writing frame means:**O stands for Obvious observations: Write down one thing you notice, then leave a gap, and write down something else you notice. Try to get 3 obvious things. S is for Specific: Under each obvious observation, explain what you mean so that another person would get it. E is for Evidence: Support each observation with numbers or calculations. M is for Meaning: So what? Write down what each of your points tells you about the original problem/situation. What else could we find out?**What the OSEM writing frame means:**O stands for Obvious observations: Write down one thing you notice, then leave a gap, and write down something else you notice. Try to get 3 obvious things. S is for Specific: Under each obvious observation, explain what you mean so that another person would get it. E is for Evidence: Support each observation with numbers or calculations. M is for Meaning: So what? Write down what each of your points tells you about the original problem/situation. What else could we find out?**What the OSEMwriting frame means:**O stands for Obvious observations: Write down one thing you notice, then leave a gap, and write down something else you notice. Try to get 3 obvious things. S is for Specific: Under each obvious observation, explain what you mean so that another person would get it. E is for Evidence: Support each observation with numbers or calculations. M is for Meaning: Make sense of it. So what?**What the OSEMwriting frame means:**O stands for Obvious observations: Write down one thing you notice, then leave a gap, and write down something else you notice. Try to get 3 obvious things. S is for Specific: Under each obvious observation, explain what you mean so that another person would get it. E is for Evidence: Support each observation with numbers or calculations. M is for Meaning: Make sense of it. So what? Write down what each of your points tells you about the problem/situation.**What the OSEMwriting frame means:**O stands for Obvious observations: Write down one thing you notice, then leave a gap, and write down something else you notice. Try to get 3 obvious things. S is for Specific: Under each obvious observation, explain what you mean so that another person would get it. E is for Evidence: Support each observation with numbers or calculations. M is for Meaning: Make sense of it. So what? Write down what each of your points tells you about the problem/situation. Why is this relevant?**What the OSEMwriting frame means:**O stands for Obvious observations: Write down one thing you notice, then leave a gap, and write down something else you notice. Try to get 3 obvious things. S is for Specific: Under each obvious observation, explain what you mean so that another person would get it. E is for Evidence: Support each observation with numbers or calculations. M is for Meaning: Make sense of it. So what? Write down what each of your points tells you about the problem/situation. Why is this relevant? What else could we find out?**What the OSEMwriting frame means:**O stands for Obvious observations: Write down one thing you notice, then leave a gap, and write down something else you notice. Try to get 3 obvious things. S is for Specific: Under each obvious observation, explain what you mean so that another person would get it. E is for Evidence: Support each observation with numbers or calculations. M is for Meaning: Make sense of it. So what? Write down what each of your points tells you about the problem/situation. Why is this relevant? What else could we find out? Towards Excellence Towards Merit**%**Meaning:**%**Meaning: So what?**%**Meaning: So what? What does this tell us about the situation?**In the Level 1 Multivariate Data standard (1.10), my**students found OSEM a useful guide when writing their conclusions:**1.10 Multivariate – Conclusion**Obvious**1.10 Multivariate – Conclusion**Obvious (Make call: Yes/No)**1.10 Multivariate – Conclusion**Obvious Specific**1.10 Multivariate – Conclusion**Obvious Specific (about what? – popns / variable)**1.10 Multivariate – Conclusion**Obvious Specific Evidence**1.10 Multivariate – Conclusion**Obvious Specific Evidence (justify, support with stats) Meaning**1.10 Multivariate – Conclusion**Obvious Specific Evidence (justify, support with stats) • Meaning (so what?) • Context (does it make sense etc.? • Sampling variability**1.10 Multivariate – Conclusion**Obvious Specific Evidence Meaning**1.10 Multivariate – Conclusion**Obvious (Make call: Yes/No) Specific (about what? – popns / variable) Evidence (justify, support with stats) • Meaning (so what?) • Context (does it make sense etc.?) • Sampling variability**And even in Level 2 Coordinate Geometry**Obvious observations Specific (labelling) Evidence (calculations) Meaning (so what?) (Relate back to problem)**2013 Level 2 Probability external**Compare and contrast the two distributions. You should discuss shape, centre and spread in relation to the context.**Reference for SOLO Taxonomy symbols: Pam Hook:**http://hooked-on-thinking.com**Algebra in Years 9 and 10**Key ideas in teaching it: Start with meaningful problems that involve either: • The students themselves and can be acted out. • Something that might interest them (saving money for something, get to know common interests of class members). Students creating their own problems is a powerful tool to engage and motivate learning.