Improving Mathematics Achievement of Students in the Junior Division TDSB and LNS Junior Math Strategy (CIL-M and GCS) Fri, Mar 25, 2011

Wanda De Castro Jung Choi-Perkins MaryLou Kestell your co-learners

Learning Goals Articulate strategies to improve student achievement Practise teaching 3-part problem solving lessons in Math Talk learning communities Understand how to use Gap Closing materials to help students struggling in grade 6 mathematics Practise using Differentiated Instruction during instruction Build teacher pedagogical / math content knowledge

Norms Start and end on time 9:00 – 3:30 Comfort breaks and “crack”berry breaks will be provided Active participation is required and suffering is optional Respectful listening

Agenda 9:00 - 9:15 Welcome and introductions 9: :30 Do math together 10: :45 Break 10: :00 Overview of project and GAP Closing pre-test 12:00 – 12:45 Lunch 12:45 – 1:15 Goal setting 1:15 – 2:45 Split up gr 4 & 5 and gr 6 2:45 – 3:30 Wrap up and wish lists

6 Let’s Start by Doing Math Together:

Getting Started In our project, there will be 24 people altogether. There will be about: –15% admin and math facilitators –50% Spec Ed and ESL teachers –35% classroom teachers How many of each kind of educator will work with us?

8 90 students in a school have visited at least two other provinces. If this represents 24% of the students in the school, how many students are in the school? Student Travellers Working On It

9 Possible strategies - Estimation 24 % ≈ 25 % or ¼ 90 Whole school Which is approximately 360. Hence the whole school is 360?

10 Diagram 24% 90 students 96 % 360 students 4% 15 students 100% 375 students 4x24 4x90 24/6 90/

11 Diagram Let 25 square represent 100% 24% = 24/100 = 6/25 (1 colour group) 4 colour groups fit in a 5x5 square each colour group represents 90 students coloured sq’s: 4x90 = 360 students but 1 square is uncoloured each square is 1/6 of 90 = 15 students So, total is 360(coloured) + 15(uncloured) = 375 students

12 Number Line 24 % 4 % %

13 Friendly Numbers 24% = 90 students 12% = 45 students 4% = 15 students 100% = 375 students ÷2 ÷3 X 25

14 Double Number Line 4% % 100% 375 ÷6 x25

15 Ratio Tables % ÷ 2 ÷ 3 x %100% 375 4% 15

16 Elastic Meter Manipulative x 90 = Elastic Meter Manipulatives

Consolidation Parts 2 and 3 Part 2 The notes we make about our mathematical thinking during this lesson (to meet the learning goal) Part 3 Independent practice (what students can do alone – after they have learned collaboratively in their zone of proximal development)

BREAK 15 min

What will our work look like?

Consolidation Part 1 Consolidation Part 2

Today’s 3-part Problem Solving Lesson

3-part Problem-Solving Lesson Design BEFORE Activating prior knowledge; discussing previous days’ methods to solve a current day problem DURING Presenting and understanding the lesson problem Students working individually or in groups to solve a problem Students discussing solution methods AFTER Teacher coordinating discussion of the methods (accuracy, efficiency, generalizability) teacher highlighting and summarizing key points Individual student practice (Stigler & Hiebert, 1999)

Sample Bansho Plan 11” 8-1/2” AFTER Highlights/ Summary -3 or so key ideas From the discussion AFTER Practice -Problem -2 solutions Knowledge Package Gr 7 to 10 -codes and description -lesson learning goals highlighted Math Vocabulary list BEFORE Activation -Task or Problem -2 solutions DURING -Lesson Problem -What information will WE use to solve the problem? List info AFTER Consolidation Gr7 Gr8 Gr9 Gr10 4 different solutions exemplifying mathematics from specific grades labels for each solution that capture the mathematical approach -Math annotations on and around the solutions (words, mathematical details to make explicit the mathematics in the solutions -Mathematical relationship between the solutions

Dates by School Legend: Red text Full-day CIL-M studies Black text in white box GCS days Blue text in shaded boxes

TDSB Mobile Computing Strategy Within TDSB Mobile Computing Strategy, intervention for students is based on identifying in particular students who are at and below level 2 in mathematics as well as below their grade level. In this intervention, Grade 6 teachers and the special education resource teacher (SERT) or the Methods Resource teacher (MART) will engage in a collaborative inquiry focussed on the big ideas of student learning of mathematics and incorporating technology and its intervention possibilities for students with special needs.

Junior Math Strategy (JMS) Intentional emphasis and focus will be to connect JMS with the TDSB Mobile Computing Strategy to address learning mathematics in a digital environment, specifically in building teachers’ capacity and optimising teachers’ expertise in using technology in a thoughtful and powerful way in creating customised conditions for learning that support differentiated learning.

Gap Closing Resource The Gap Closing resources is for Grade 6 students who are struggling in mathematics but not in other subjects. This resource is intended to target specific gaps in number sense and provide appropriate remediation to close the gap. This research based resource is for small groups, provides appropriate remediation to close the gap and is designed with open questions. GCS Gr 6

Gap Closing Resources GCS Gr 6 What is it? It is only a new resource – an aid for differentiating instruction – consequently useful for teachers of grades 4 and 5 too

Pre-test and Post-test To be administered to ALL students in grade 6 –Lynnwood Heights and Pauline Johnson March 28 or 29 if possible –Highland Heights March 28, 29, 30 if possible To be marked by Ministry appointed markers – results returned within 3 weeks Will confirm your choice of Marker Students but will we start with students identified by you GCS Gr 6

LUNCH 45 min

Flexibility and In-flexibility Within CIL-M Teaching through problem solving using the 3-part lesson framework Role of learners Asset model Classroom component with co- teaching Use of professional resources CIL – M

Some aspects include: Valuing curiosity, wonder and risk- taking Honouring diversity of ideas, thoughts and actions Fostering rich opportunities to question and test ideas Accessing resources including high-quality professional resources and research literature

Collaborative Inquiry for Learning – Mathematics for Teaching A collaborative model of work used by teachers, coaches, administrators to build knowledge of mathematics for teaching Inquiry means we focus on your needs of providing effective instruction to ALL students in your classes Occurs in a 3-part lesson format and includes co-planning, co-teaching, and co- debriefing Focuses on students: student thinking, student demonstrations of understanding and active construction of math knowledge CIL – M

Collaborative Inquiry for Learning – Instructional Model CIL-M is –focused on formalizing student-generated, informal, mathematical thought –begins with students’ mathematical thinking –is centred on making sense of the thinking everybody shows (evidenced) –and is concluded and consolidated by summarizing the collective thinking of the class –meant to include the introduction and formalization of the mathematical notation, vocabulary and conventions of representation CIL – M

Collaborative Inquiry for Learning – Instructional Model CIL-M, of course includes… –the formalized mathematical knowledge is applied, connected, argued, proved, discussed and practised after consolidation –the shared knowledge is continually reviewed, adapted, refined, represented, described and communicated and used to make decisions when solving problems throughout the rest of the unit of study, the day, the month, the year CIL – M Ideally, the strategies, vocabulary, number fluency, organizational senses, analysis, and logical thought learned in math class are used in the lives of the students again and again, throughout the day, the month, the year, and FOREVER.

Setting Goals and Articulating Success Criteria What are your goals for our 9 weeks of working together? How will you know you have been successful?

Goals and Success Criteria Think – Alone –brainstorm your own queries and learning goals and write a few words to represent your idea on a post-it (5 min) –paste them on sheet of chart paper In your school group… –group stickies with similar statements –label the groups –write 2-3 shared learning goals

What are the learning goals at your school? Using post its Identify your needs to best serve your students you want us to address during this PLC What is it that I professionally need out of this experience? Sort circle label/ name Write learning goals Learning goals for each school…

Grade 4/5 Wanda and Jung

Gr 6 - MLK

GCS Gr 6 Gap Closing Strategy A Frayer model

Student Surveys We will give you the student surveys today along with the GCS materials The surveys are to be completed at the beginning and then again at the end of the project. It will take students about minutes to complete.

In-between days We will define the actions for these days as we go. Please make suggestions, for learning activities that you would benefit from and we will try to accommodate them. JMS

Pre-test and Post-test GCS Gr 6 Let’s see what’s in the test…

Reflection

Wish Lists

Remember Dates pm

Collaborative Inquiry for Learning – Instructional Model CIL-M is focused on formalizing student- generated (even though rather informal) mathematical thinking. The lesson begins with students' (N.B. plural) mathematical thinking, is centred on making sense of the thinking everybody showed (based on evidence not on anyone's judgment of the validity of that thinking) and is concluded and consolidated by summarizing the collective thinking of the class including the introduction of vocabulary and formalization of the mathematical notation and vocabulary. Of course, this formalization is applied, connected, argued, proved, discussed and practised after consolidation. The shared knowledge is continually reviewed, adapted, refined, represented, described and communicated and used to make decisions when solving problems throughout the rest of the unit of study, the day, the month, the year. Ideally, the strategies, vocabulary, number fluency, organizational senses, analysis, and logical thought (their own) are used in the lives of the students again, throughout the day, the month, the year, FOREVER. CIL – M