Maths Counts Insights into Lesson Study 1. Sharon Mack, Irene Stone and Gemma Fay 3 rd Years Problem Solving as a “Means” not an “End” Normally we teach.

Slides:



Advertisements
Similar presentations
Maths Counts Insights into Lesson Study 1. Jenny Moran, Celine McCarthy, Michael Murphy and Breda Fallon Transition year and Leaving Certificate classes.
Advertisements

Maths Counts Insights into Lesson Study
Lesson Study Lesson Study. Based on Japanese Lesson Study Introduced through TIMSS (1995) Based on Japanese Lesson Study Introduced.
Maths Counts Insights into Lesson Study 1. Jacqueline Normile, Norma Dowling and Elaine Hickey. Sixth Year. Associating derivatives with slopes of tangent.
Twitter Math Camp 2014 SPIRALING THROUGH THE CURRICULUM SLAMDUNKMATH.BLOGSPOT.COM
Maths Counts Insights into Lesson Study 1. Team: Kathleen Molloy & Breege Melley Topic: Introducing Integration Class: Sixth year Higher Level 2.
Maths Counts Insights into Lesson Study 1. Helen Mc Carthy & Eimear White Transformations of Functions in Second Year 2 2.
Maths Counts Insights into Lesson Study 1. Kathleen Molloy and Laura Craig 6 th yr HL GeoGebra and solving modulus inequalities 2.
Maths Counts Insights into Lesson Study 1. Moate Community School: Mathematics Department Target Group: Junior Cycle Topic: Introducing Patterns – Second.
Maths Counts Insights into Lesson Study
Maths Counts Insights into Lesson Study
FALs and MDC. Before the Collaborative Activity: Meet as a grade level to collaboratively plan in advance the administration of the pre- assessment As.
Fostering Algebraic Thinking October 26  December 2  6-hour Assignment after Session 2  January 20 Presented by: Janna Smith
Maths Counts Insights into Lesson Study 1. 2 Caitriona O Connell, Fiona Fahey, Helen Lambe 5 th Years Linking Patterns through the Strands.
DISCOVERING ALGEBRA GRAPHING LINEAR EQUATIONS by David A. Thomas and Rex A. Thomas.
Planning for Inquiry The Learning Cycle. What do I want the students to know and understand? Take a few minutes to observe the system to be studied. What.
Teach Equation Solving Kathy Hawes Discussion presented by Jessica Dow and Janice O’Donnell.
DED 101 Educational Psychology, Guidance And Counseling
Maths Counts Insights into Lesson Study 1. Teacher: Olivia Kelly SHS Maths department Class: First year Maths Ability:Mixed 2.
Maths Counts Insights into Lesson Study 1. Gemma O’Dwyer, Patricia Lewis, Jenny Donohoe Second Year Array model and quadratic factorisation 2.
Maths Counts Insights into Lesson Study
Maths Counts Insights into Lesson Study 1. Maths Department, Our Lady’s College Geometry in Context Transition Year and Ordinary Level Junior Cert 2.
Science Inquiry Minds-on Hands-on.
Maths Counts Insights into Lesson Study 1. Sandra Fay, Irene Stone, Sharon Mack First year Junior Cert An Introduction to Patterns 2.
Maths Counts Insights into Lesson Study 1. Mairead Murphy, Kevin Carey, Pat Brennan Second year Junior Certificate Taxation: Does your answer make sense?
M ATH C OMMITTEE Mathematical Shifts Mathematical Practices.
Big Ideas and Problem Solving in Junior Math Instruction
Welcome Welcome to “Getting Results” A National Science Foundation project developed by WGBH with the League for Innovation and 13 community colleges from.
Reflective practice Session 4 – Working together.
Maths Counts Insights into Lesson Study 1. Tim Page and Joanne McBreen Transition Year or Senior Cycle Introducing Tolerance and Error (Leaving cert.
Mathematics the Preschool Way
Mental Mathematics.
When we met back in October... Discussion took place: – issues that arise from doing group work – encouraging students to talk – spreading this practice.
1 Unit 4: One-Step Equations The Georgia Performance Standards Website.
Dates:Tuesdays, Jan 7 – Feb 11
Problem Solving as a “Means” not as an “End” Problem Solving as a “Means” not as an “End” 1.
Our Leadership Journey Cynthia Cuellar Astrid Fossum Janis Freckman Connie Laughlin.
© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Bridging the Gap Grades 6-9.
LinearRelationships Jonathan Naka Intro to Algebra Unit Portfolio Presentation.
Elizabeth Jean Bingham Central Elementary
Robert Kaplinsky Melissa Canham
GMU COMPLETE Center Candy Dilemma A VDOE SPONSORED MSP PROFESSIONAL DEVELOPMENT OPPORTUNITY THROUGH GEORGE MASON UNIVERSITY Cyndi Madden Mona SamahaPatricia.
Strategies that Address the Specific Learning Needs of English Language Learners in Mathematics Presented by ESL Department Pittsburgh Public Schools Dr.
Protocols for Mathematics Performance Tasks PD Protocol: Preparing for the Performance Task Classroom Protocol: Scaffolding Performance Tasks PD Protocol:
High Quality Math Instruction
Have you implemented “Number Talks” in your classroom? What are the pros? What are the cons? Any suggestions?????
Presenter’s Guide to Multiple Representations in the Teaching of Mathematics – Part 1 By Guillermo Mendieta Author of Pictorial Mathematics
Linear Algebra Unit Portfolio Presentation Stephanie Zub.
Maths Counts Insights into Lesson Study 1. Mairead Guiney Tomás Twomey 5 th Year Higher Level Carnival Games: Leaving Cert Probability 2.
Module 3 Preparing Students to Think Mathematically / Lesson Planning.
Financial education and the Secondary curriculum Equipping newly qualified teachers with the skills and confidence to teach financial education.
The Relationship between Elementary Teachers’ Beliefs and Teaching Mathematics through Problem Solving Misfer AlSalouli May 31, 2005.
Lecture # 19 SCIENCE 1 ASSOCIATE DEGREE IN EDUCATION Force and motion continue ………
How Students Learn College Teaching Institute Presenter: Monica McCrory The Graduate School.
Project Impact CURR 231 Curriculum and Instruction in Math Session 3 Chapters 3.
Math Assessments Math Journals When students write in journals, they examine, they express, and they keep track of their reasoning. Reading their journals.
Ryan Goodwin Essential Questions For All Grade Spans 1. What patterns or relationships do we see in each type of mathematics? 2. How do we use math in.
How to Teach Science using an Inquiry Approach (ESCI 215 – Chapter 1)
Plenary 1. What’s important about the Math we Teach? A Focus on Big Ideas Marian Small
Reflections on Practice Maths Counts Over to you The relationship between the volume of a cylinder and its height and radius.
Reflections on Practice Maths Counts Introduction to Linear Equations Laois Education Centre, Portlaoise.
Reflections on Practice Maths Counts Over to you Representing simultaneous equations graphically.
Using Linear Patterns to Foster Algebraic Reasoning Maths Counts 2016.
Mathshell in Practice Ready Made Quality Group Work 6-8
Maths Counts Insights into Lesson Study
Introduction. Conducting statistical investigations to develop learner statistical thinking.
Rethinking Junior Statistics
Big Ideas and Problem Solving
Workshop 6 Problem Solving
Maths No Problem! Parents Workshop
Presentation transcript:

Maths Counts Insights into Lesson Study 1

Sharon Mack, Irene Stone and Gemma Fay 3 rd Years Problem Solving as a “Means” not an “End” Normally we teach the skills of inequalities and then use these to solve problems. In this approach, we introduced the problem first, solved it, then used the problem to introduce inequalities and used our prior knowledge of equations to solve them. 2

Introduction: Focus of Lesson Student Learning : What we learned about students’ understanding based on data collected Teaching Strategies: What we noticed about our own teaching Strengths & Weaknesses of adopting the Lesson Study process 3

Topic investigated was Problem Solving as a “Means” not an “End” How we planned the lesson:  The idea and methodology was used in the Project Maths workshop 8.  Studied the lesson  Decided how we would approach it and the timing of the lesson  Photocopied the sheets 4

Topic investigated was Problem Solving as a “Means” not an “End” Resources used:  Photocopied sheets with graph paper on the reverse  PowerPoint  Whiteboard 5

6 John has 18 ten-cent coins in his wallet and Owen has 22 five-cent coins in his wallet. They each decide to take one coin per day from their wallets and put it into their money box, until one of them has no more coins left in their wallet. When does Owen have more money than John in his wallet? Our problem

Prior Knowledge:  Patterns  Tables, Graphs, words and formula  Slope (Change)  Variables and Constants  Equations 7

8

9 Development of the inequality

Learning Outcomes:  Practise their knowledge of patterns  More than one method to solve a problem  Concept of one expression being bigger or less than another expression  Relationship between equations and inequalities  How to solve inequalities  The necessity to bring all answers back to the context of the problem 10

Why did we choose to focus on this mathematical area?  Needed to introduce inequalities and saw this approach and wanted to try it. 11

Enduring understandings:  How patterns can be used to solve inequalities  The relationship between equations and inequalities  The ability to solve inequalities  More than one method to solve problems (List, Table, Graph and Formula) 12

13 More than one method to solve a problem

Student Learning : What we learned about students’ understanding based on data collected Teaching Strategies: What we noticed about our own teaching 14

Data Collected from the Lesson: 1.Academic e.g. samples of students’ work 2.Motivation 3.Social Behaviour 15

What we learned about the way different students understand the content of this topic?  Some students were:  Reluctant to show their work in case it was incorrect.  Reluctant to use Algebra in the first instance.  Did not read the question correctly. Money box vs. wallet. 16

17

Misconceptions/ Knowledge Gap:  Graph going up done from the money box point of view. Also did not treat axis as lines 18

Problem answered from wallet’s point of view rather than money box’s 19

Stopped at day 15 20

John has 1.80 on Day 1 instead of Day 0 21

Confused Algebra skills 22

Did not read the question properly; got days and weeks mixed up. 23

24 Did not label the axes

25 The need to let this student know they are correct, but not all problems can be solved this way; hence we use inequalities

Recommendations  Encouraged those who confused wallet and money box to re-read the problem during the class.  Have a money box and wallet in the class.  Encourage students to label axes 26

The understandings we gained regarding students’ learning as a result of being involved in the research lesson:  Students engaged with the problem and remained engaged when problem translated to algebra and the inequality.  Students also saw the difference between an equation and an inequality.  Some students used tables, others graphs and others formulas. 27

What did we learn about this content and approach to ensure we had a strong conceptual understanding of this topic?  How building on patterns can be used to introduce equations and inequalities.  Relationship between an equation and an inequality.  The need to encourage students to put the answer back into the context of question. 28

What did I notice about my own teaching? What was difficult?  Timing to complete the table  Not to intervene too soon  Some students’ lack of confidence to start the problem or discuss the problem 29

Was it difficult to facilitate and sustain communication and collaboration during the lesson?  As some students answered from the money box’s point of view, I put the two sets of solutions on the board. I re-read the question and asked the students, which one we could use to find the answer to the problem.  Put the formula as Owen > John rather than John < Owen. Why? 30

31

How did I engage and sustain students’ interest and attention during the lesson?  Students engaged with the context of the question because they could relate to it.  Spotted misconceptions during the class and gave direction when required. 32

How did I assess what students knew and understood during the lesson?  Students’ work showed their understanding of the problem.  Asked probing questions.  Students were working in groups and discussing the problem. 33

34

What understandings have I developed regarding teaching strategies for this topic as a result of my involvement in Lesson Study?  I never would have thought of using patterns as an introduction to inequalities, but now see it is a brilliant approach.  A slow lead-up to inequalities did not scare the students and they were still engaged at the end of the lesson. 35

What changes would I make in the future, based on what I have learned in my teaching, to address students’ misconceptions?  Use a context-based question to introduce equations.  Encourage the students to spot patterns, where possible. 36

37 In future relate the change in the diagram, to the slope of the graph

Strengths & Weaknesses As a mathematics team how has Lesson Study impacted on the way we work with other colleagues?  Learned from my colleagues.  Liked feedback from my colleagues. Do not spot everything yourself. Good or Bad. 38

Strengths & Weaknesses Personally, how has Lesson Study supported my growth as a teacher?  Confidence to be able to discuss ideas with my colleagues.  Easier to see the learning as an observer.  Privilege to see other teaching styles. Learning from each other. Recommendations as to how Lesson Study could be integrated into a school context.  More timetabled time needed for department meetings. 39