SOCIAL J MATH M MONTHLY

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Office

80 Sheppard Avenue East 416 222 8282 (general) 416 222 229 5364 (fax)

MIreya Martin X2545

Superintendents C&A - Dan Koenig

Early Years - Cristina Fernandes Special Services - Frank Piddisi Student Success - Patrick Keyes

Program Coordinator

Kathy Kubota-Zarivnij X2533 or 647 227 3584 (cell)

K to 6 Math Resource Miranda Kus (1,2) X6020 Adrian Pope (3,4) X2723 Bart Vanslack (5,6) X2724

Wilma Simmons (7,8) X2703

9 to 12 Math Resource Grace Mlodianowski X2728

Varvara Nika X2722 Stefana Penelea (sec. coach) "Life is good for two things, learning mathematics and teaching mathematics." -

Simeon Poisson

TCDSB MATH MONTHLY January 2014

Issue 1 No. 1 FROM THE MATH DEPT Finally, our inaugural issue of TCDSB Math Monthly is available! This system-wide, monthly mathematics newsletter is intended to be a vehicle for system-wide communication, as well as a resource for TCDSB mathematics education leaders to use to support: • educators’ knowledge and knowing of

mathematics for teaching • classroom implementation of

mathematics instructional strategies • observation and study of students’

mathematics learning in classrooms • co-teaching • student work sample analysis • professional conversations • staff newsletters • whole staff and divisional meetings • school newsletters All issues focus on the mathematical work from the math study groups and after school sessions, as well as requests and ideas put forth by teachers, principals/ vice-principals and superintendents across our system. January’s issue focuses on Addition Mental Math Strategies. Currently, most of the math study groups have been working on these ideas in their classroom. As well, particular structures, processes and strategies used for mathematics learning and teaching are outlined, as they are the basis for mathematics instructional practices in classrooms, as well as our mathematics professional learning (e.g., math study groups, after-school sessions, principal LSA sessions). February’s issue will be available the week of January 27 … just in time for your February school newsletter.

KKZ Program Coordinator Mathematics (K to 12) and Business Studies

SOCIAL JUSTICE AND MATHEMATICS Aguirre & Anhalt (2006) and Gustein (2003) identify these goals for teaching social justice using mathematics. 1) Read the World with Mathematics to: • understand relations of power,

resource inequities, and disparate opportunities between different social groups

• understand discrimination based on race, class, gender, language and other differences

• analyse and deconstruct media and other forms of representation to examine phenomena, both in one’s immediate life and in the broader social world in order to identify relationships and make connections between them.

2) Write the World with Mathematics to: • change the world • see oneself as capable of

making change and developing a sense of social agency.

Read the World With Mathematics -> Survey the students about the ways that they want to be treated and how they are actually treated by others. Write the World with Mathematics -> Represent the survey results to show the range and frequency of ways students want to be treated and how they are actually treated (e.g., tally chart, pictograph, bar graph) How could this use of mathematics give the students courage to make change in their classroom?

TCDSB MATHEMATICS DEPARTMENT

Let’s use our virtues as a site for reading and writing the world with mathematics

COURAGE - We know that followers of Christ remember the Golden Rule and treat others the way they would like to be treated.

TCDSB Math Monthly, January 2014 Page

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IDEAS TO CONSIDER … Teaching Mathematics is Specialized Knowledge (Davis & Renert, 2014) Mathematics for teaching (MfT) is a sort of knowing that is most real in action, in inheres in flexible in-the-moment responsiveness. It is a way of being with mathematics knowledge that enables a teacher to structure learning situations interpret student actions mindfully and respond flexibly in ways that enable learners to extend understandings and expand the range of the learners’ interpretive possibilities (Davis & Renert, 2014). Who Knows Mathematics Well Enough to Teach Grade 3? (Ball, Hill & Bass, 2005; Glaser & Chi, 1988) Ball, Hill and Bass (2005, p. 19) report that “knowing mathematics for teaching demands a kind of depth and detail that goes well beyond what is needed to carry out the algorithm reliably … there are predictable and re-current tasks that teachers face that are deeply entwined with mathematics and mathematical reasoning.” For example, figuring out where and why a student has made errors or using mathematical representations (e.g., number line, area grid) to develop conceptual understanding. These and other tasks of teaching involve both mathematical reasoning and pedagogical thinking. Developing precision in learning and teaching mathematics suggests the notion of developing expertise. Glaser and Chi (1988) explain that when experts are compared to novices, experts: • perceive large and meaningful patterns • work quickly and solve problems with little error • posses remarkably large short-term memories • see and represent problems at a deeper or principles

level, whereas novices focus on superficial aspects • spend relatively more time analyzing problems

carefully and qualitatively • have strong skills in self-monitoring

LET’S DO MATH! DEVELOPING OUR KNOWLEDGE AND KNOWING OF MATHEMATICS FOR TEACHING What is Mental Math? Calculators and computers are only useful when people know what information must be entered and if they know the answer is reasonable. Reasonableness necessitates the use of some sort of mental math Mental math is often used as a way to calculate, estimate and or visualize using mathematical relationships and strategies that were previously learned conceptually with and without the use of pencil/paper, calculators or math tools. For example: • composing numbers to 5s and 10s makes

calculations easier 23+16+44 = 20+10+40+6+4+3 = 50+10+3 = 63

• rotating a right angle triangle 1800 CW by focusing on the rotation of the line segment of the right angle.

What Instructional Strategies Develop Students’ Mental Math Strategies? From a learning trajectory perspective, mental math strategies are derived from students’ understanding of mathematical concepts and meaningful use of different algorithms and strategies. Let’s start with a mini-lesson. Mini Mental Math Lesson Framework (15 min) • Post 1 or 2 questions on a mental math bulletin

board or square grid chart paper by the class door for the students to work on throughout the day

• Discuss and record 3 students’ different solutions in the afternoon, using equations and number line.

• Label the mental math strategies used. • Record strategy in Highlights/Summary (add to it

after every mini-lesson). Mental Math Addition Strategies Start with 1-digit numbers with 2 to 6 addends. Break Up the Numbers Strategy Use when regrouping is required. One of the addends is broken up into its expanded form and added in parts to the other addend. 57+37 -> 57+30=87 and 7 more is 94 87+8=87+3+4=90+4=94 Front-End (left to right) Strategy Adding the front-end digits (adding larger place value digits first) and towards the right (or smaller place value digits) keeping a running total in your head. 124+234 ->1+2 hundreds + 2+3 tens + 4+4 ones -> 3 hundreds+5 tens +49 ones -> 300+50+8 = 358

Discussion Prompts: • What ways can we prepare ourselves

mathematically to be flexible in-the-moment responsive to students’ mathematical thinking?

• How can educators be prepared to understand and leverage the range of learners’ interpretive possibilities of mathematics in order to co-construct success criteria during the lesson?

Discussion Prompts: What experiences do educators need to develop their expertise in: • responding to students’ mathematical thinking by

coordinating conversation to make connections, clarify and elaborate?

• next step instruction in relation to error analysis?

start 00 900 CW 1800CW rotation rotation


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MATHEMATICS CURRICULUM AND PROGRAMMING Several key instructional concepts and strategies for mathematics that TCDSB educators are studying and learning to implement in their classrooms this year are described briefly below. These will be elaborated with grade specific math examples in subsequent newsletters. Three-Part Problem Solving Lesson Design • 1- Before (Getting Started) - 5 to 10 minutes –

students revisiting mathematical ideas and strategies from a previous lesson that relates to the learning goal of the lesson

• 2- During (Working On It) - 15 to 20 minutes - students are solving the lesson problem in pairs, small groups, or individually

• 3a- After (Consolidation) - 20 to 25 minutes -> teacher coordination of whole class discussion/analysis of student solutions; co-construction of success criteria

• 3b- After (Highlights/Summary) - 5 minutes -> students are recounting key mathematical ideas and strategies related to the learning goal of the lesson; summarizing the lesson learning goal in relation to co-constructed success criteria

• 3c -After (Practice) - 5 to 10 minutes – students solving a problem that is similar to the lesson problem in order to practise applying new ideas and strategies.

Mathematics Learning Trajectory imagine a network that shows mathematical connections between clusters of mathematical concepts, skills, strategies and generalizations. More specifically, Clements and Sarama (2009), describe a mathematics learning trajectory as comprised of: • mathematics learning goal - clusters of concepts and

skills that are mathematically central and coherent, consistent with children's thinking, and generative of future learning

• developmental progressions or paths of learning - describes a typical path children follow in developing understanding and skill about that mathematical topic through levels of mathematical thinking; each more sophisticated than the last, which lead to achieving the mathematical goal.

• instructional tasks or paths of teaching - are matched to each of the levels of mathematical thinking in the developmental progression and are designed to promote children’s growth from one level to the next; that is to learn the ideas and skills needed to achieve mathematics learning goal

Mathematics Lesson Learning Goal A lesson learning goal is derived from grade specific curriculum expectations. A lesson learning goal is derived

from grade specific curriculum expectations. Mathematical interpretation of the grade specific curriculum expectations is needed in order to discern the key mathematical ideas, properties, generalizations and strategies. Though the teacher has lesson learning goals mapped out for a unit of study, during lessons, it is student and teacher co-constructed during the After (Consolidation) and recounted by students during the After (Highlights/ Summary). Co-Constructed Success Criteria for Mathematics Success criteria are what students need to know and/or do mathematically to achieve the lesson learning goal. Such mathematical details include: math concepts, strategies, models of representation, mathematical approaches and mathematical generalizations. Success criteria are co-constructed by students and the teacher throughout the three-part problem-solving lesson, especially during After (Consolidation). Mathematical annotations are carefully chosen in order to elaborate on the mathematical thinking of the students' solutions. These elaborations comprise the details of the success criteria. Organizing the student solutions as a mathematical learning trajectory (i.e., a mathematical scaffold from the students’ mathematical thinking towards to the lesson learning goal) provokes mathematical connections between students’ thinking and aspects of the lesson learning goal (i.e., co-constructed success criteria). The co-constructed, success criteria are summarized by the students in the After (Highlights/Summary) part of the 3 part problem solving lesson. The structure of the Highlights/Summary is as follows: • math concept - sets the context for the learning goal

(if not the learning goal) • learning goal (as a stem statement) • success criteria - specific details the learning goal

(e.g., concept, different strategies/mathematical approaches are explained briefly, followed by a math example (student solutions analysed in After (Consolidation))

Descriptive Feedback for Mathematics Mathematical descriptive feedback includes mathematical details that provide specific directions for improvement and gives students opportunity for input for their own and others' mathematics learning. More specifically, mathematics descriptive feedback is focused on students' collective co-construction of success criteria related to the mathematics lesson learning goal

Students and the teacher provide descriptive feedback to students to improve the precision, mathematical reasoning and explanatory detail of their mathematical thinking, in relation to the lesson learning goal by: • asking questions about the precision, clarity and

applicability of a mathematical approach/method,


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calculations, labeled diagrams • providing comments to elaborate on a math idea

presented by students or on the board • requesting additional proof and reasoning in a

solution • describing mathematical relationships between

solutions • providing additional examples to test the reliability of

solutions. Bansho (Board-Writing) and Mathematical Annotations Bansho (board-writing) is the systematic and strategic recording of the students' mathematical discussion throughout all parts of the 3 part problem solving lesson. Bansho (Board-Writing) is recorded by the teacher in relation to the students' and teacher's collective co-construction of mathematics success criteria. Bansho (Board-Writing) is comprised of mathematical annotations, which are: • mathematical details that are recorded on and

around student solutions (e.g., math terms, symbols, labeled diagrams, calculations)

• used to make visible students’ mathematical thinking in their solutions; are often elaborations by adding mathematical detail

• describes mathematical relationships between students’ solutions (e.g., How is solution 1 and solution 2 similar, mathematically? How are the solutions different mathematically?)

• provides mathematical details for co-constructing success criteria related to the lesson learning goal

STRATEGIES FOR SCHOOL IMPROVEMENT IN MATHEMATICS Using the EQAO IIRs Throughout the Year Your schools EQAO IIRs are full of information that could inform teacher’s mathematics curriculum lesson and unit planning, as well as next steps instruction. This year’s IIRs for mathematics include only half of the assessment items. Consider using last year’s IIRs and this year’s IIRs for the following purposes: • identifying the range and frequency of responses to

multiple choice items to anticipate this year’s students’ mathematical thinking

• examining student errors to multiple choice questions to discern the mathematical thinking (or misconceptions) of students for math concepts

• using student errors to anticipate possible mathematical responses to questions

• developing mathematics strategies that provoke students to rethink these errors and consider other ideas.

MATHEMATICS PROFESSIONAL LEARNING Additional Qualifications Courses TCDSB and York University Partnership These Additional Qualifications courses are face-to-face courses that are aligned with TCDSB board improvement plan and school improvement plans. For these courses only, the first 50 TCDSB permanent teachers who successfully complete the course will receive a $400 reimbursement. Math resources (books and a manipulatives kit) are also provided. Register at York U, Faculty of Ed, Field Development Phone: 416-736-5003 Email: [email protected] Website: http://www.raiseyouraq.ca ABQ Intermediate Mathematics (Register by Jan 9) Course code – TW14INMT Date – Wednesdays (Jan 23, Time – 6:00pm to 9:30pm Location – Epiphany of Our Lord CA AQ Primary-Junior Mathematics, Part 1 (Register by Course Code – TS14MA1T Date – Wednesdays April 2 to 18 plus Saturdays - April 12 and 26, May 10 and 31) Time – 6:00pm to 9:30pm Location – Epiphany of Our Lord CA After School Sessions (4:00pm – 6:00pm) These sessions are hosted by schools, which are interested in studying a particular math topic. These schools welcome other schools to study with them. Register by calling the school. A light dinner is provided. • Jan 27 – Proportional Reasoning – St Marcellus • Jan 28 – Leaps and Bounds – St Martha • Feb 3 – Mental Math Strategies – St Benedict • Feb tbd – Bansho (Board-Writing) – St Florence • Feb tbd – Leaps and Bounds – Christ the King Schools who have at least 6 to 8 teachers interested in studying a particular math topic for an after school session should contact the Math Dept (KKZ) to organize monthly or bi-monthly after school sessions. The Math Dept will reimburse costs for refreshments. Elementary Math Study Group Schedule Areas 1 and 2 • Jan 8 – at St Roch -> Junior – St Andrew, St Roch, St

Stephen, St Marcellus • Jan 15 – at St Andrew -> Primary - St Andrew, St

Roch, St Stephen, St Marcellus


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• Jan 22 – at St John E -> Primary – Holy Child, OL of • Victory, Santa Maria, St Angela, St John E, St Maurice • Jan 29 – at St John Vianney -> Junior – St Angela,

St Benedict, St Dorothy, St John Vianney, VJM Areas 3 and 4 • Jan 8 – at St Philip Neri-> Primary – St Augustine, St

Francis de Sales, St Philip Neri • Jan 15 – at St Augustine -> Junior - St Augustine, St • Charles Garnier, St Philip Neri, St Gerard Majella • Jan 22 – Blessed Margherita -> Junior - Blessed

Margherita, St Jane Frances, St Martha, St Jerome • Jan 29 – at Blessed Trinity -> Junior – Blessed Trinity,

D’Arcy McGee, St Charles, St Francis X, St Margaret, St Raphael

Areas 5 and 6 • Jan 17 – at St Rita -> Primary – Blessed John XXIII, St

Bruno, St Luke, St Mary, St Rita • Jan 22 – at Bl John XXIII -> Junior – Bl John XXIII, St

Bruno, St. Helen, St Luke, St Rita Areas 7 and 8 • Jan 8 – at Holy Spirit> Primary - EOOL, Holy Spirit,

St Kateri, St Robert, St Theresa Shrine • Jan 15 – at OL of Fatima -> Junior – Imm Heart of

Mary, Our Lady of Fatima St Barbara, St Bede, St Boniface St Dunstan, St Florence

• Jan 17 – at St Nicholas -> Primary – St Agatha, St Barnabas, St Joseph, St Nicholas, St Paul

• Jan 22 – at?? -> Primary FI – OL Peace, OL Wisdom, St Agatha, St Cecelia, St Cyril

• Jan 29 – at Holy Spirit -> Bl P Georgio Fr, EOOL, Holy Spirit, OLof Guadalupe, Precious Blood, St Aidan, St Bartholomew, St Cyril, St Nicholas, St Theresa Shrine, The Divine Infant

Public Research Lesson – Open House • Jan 16 (am) – St Andrew (grade 5) Secondary Math Study Group Schedule • Jan 16 – at Don Bosco -> Gr10 – Father Henry Carr,

Don Bosco Special Education and Mathematics • Jan 17 – at EOOL – DMI Session 4 • Jan 31 – at Msgr Fraser and BLGF SPA3 Session 4

Special Interest Study Groups • Jan 20 - at St Andrew - M4YC Session 2 • Jan 29 – at St Roch – SS Coaches Session 5

MATHEMATICS RESOURCES

Geometer’s Sketchpad 5.0 Sketchpad Version 5 The Geometer's Sketchpad is a dynamic construction, demonstration, and exploration tool that can build and investigate mathematical models, objects, figures, diagrams, and graphs.

Download Geometer’s Sketchpad at: http://www.keycurriculum.com/gsp/download. License Name: ONTARIO TORONCDSB STUDENT 2012-2013 Authorization Code: EZK7CY-CT79TX-ETM865-0XUX4X Gizmos ExploreLearning.com offers the world's largest library of interactive online simulations (or gizmos) for math and science education for students. The provincial license is for students in grades 7 to 8 only. Gizmos help students develop a deep understanding of challenging concepts through inquiry and exploration. Register at www.explorelearning.com/register . TCDSB Registration Key : XV5B-KTJM Your Gizmos password will be personalized, as you set it at the time of registration. Homework Help For students in grades 7 to 10 Students can get help with math homework with live, online math tutoring from an Ontario teacher. It's free. Students Register At: https://homeworkhelp.ilc.org/secure/login.php with their OEN (Ontario Education Number) found on their report cards and their date of birth to register. Registration is free. Homework Help is offered in English and is only available to students at publicly funded schools. Live Online Tutoring - You can log in between 5:30 p.m. to 9:30 p.m. ET from Sunday to Thursday for one-on-one tutoring. Students can join your grade's tutor room to see what questions other students are asking and then watch teachers walk through problems on the group whiteboard.

Nelson Mathematics On-Line Resources The Nelson Mathematics (for grades 3 to 8) username and password for the next 2 years is as follows: Nelson Site: http://mathk8.nelson.com/ Username: torontocatholic2013 Password: tcdsb2013 Grades 1 and 2 teacher resources have no password. The Nelson username and password provided is for TCDSB teaching staff only. It should not be shared with students, parents or non-TCDSB educators. OAME Gazette and Abacus Journals For elementary and secondary schools that sent a teacher and/or principal to OAME conference in May 2013, you have a two year electronic paid subscription to these resources. Use the login and password set up then to access resources at http://www.oame.on.ca


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UPDATED and NEW! TCDSB SharePoint Site for Numeracy Professional Learning

A. Internet SharePoint (www.tcdsb.org as "Home") This site is for public access, with a focus on parent/guardian engagement. Follow this path: Home -> Programs And Services -> School Programs K12 -> Numeracy B. Intranet SharePoint (intranet as "Home") This site has TCDSB educator professional learning resources such as readings, schedules and math curriculum planning tools. Follow this path Home > Departments -> C and A -> A>Numeracy

THINKMATH@HOME

For Your School Ideas, resources and information for parent/ guardian engagement with their children’s mathematics learning are sprinkled throughout this monthly newsletter. Here a different ways that you could use these ideas over the month. • Cut and paste these ideas into your monthly

school newsletter, a school or classroom-based school math flyer, and/or school webpage.

• Create a school math bulletin board. o Have students from different grades do the

mathematics. o Post their solutions on the bulletin board. o Annotate the students’ work so that their

mathematical thinking is made explicit. Do this by labelling the mathematics evident in their solutions.

• Consider including any of these mathematics items on your CSAC agenda. CSAC meetings could be a place for mathematics information sharing and learning as well.

Use Your Students’ Mathematical Work • Use one page of your newsletter to send samples of

students’ mathematical thinking to a lesson problem • Here’s a possible structure:

o Learning Goal o Lesson Problem o Pics of 3 solutions … followed by the question,

What’s the students’ mathematical thinking? NEW! Parent Engagement Site for Mathematics on TCDSB SharePoint Site Follow this path to thinkMATH@home at the Internet site, www.tcdsb.org. Get to the site using this path: Home > Programs And Services > School Programs K-12 > Numeracy > thinkMATH@home NEW! Monthly thinkMATH@home Posters • Monthly posters for families to use at home for

mathematics learning accompany the TCDSB Math Monthly newsletter.

• Please make enough copies for each family in your school and send out each month.

Developing Students’ Mathematical Understanding, Reasoning and Communication Strategy #1 - Have your child solve math problems in different ways, such as using different numbers, different sets of operations in calculations or different models of representation like the number line, set of objects, or square grid. Strategy #2 - Ask your child to explain their solutions to math problems that they solved during class lessons or are working on for practice at home. As they explain their thinking, they are developing reasoning, proving, and communication. Get a classroom to provide student work samples as examples for each strategy.

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SOCIAL J MATH M MONTHLY