Creating, Collaborating and Computing in Math

Enhancing the teaching and learning of mathematics using

technology

Riverside School Board and McGill University- March 26, 2014

9:00 - 9:45 Review of CCCM Project Goals

9:45 - 10:15 Formative Assessment

10:15- 10:30 Break 10:30-12:00 Formative

Assessment 12:00- 1:00 Lunch 1:00 - 3:00 Small Focus Groups 3:00 - 3:30 Wrap up

Plan for the Day

1. Student success in mathematics

2. Digital literacy

3. Focus on the transition from elementary to secondary

4. Professional learning network

5. Use of data to monitor and orient practice, inquiry, and learning

Key Themes of CCC-M project

1. Foster a community of practice in mathematics teaching and digital tools

2. Develop collective understandings of the situation

3. Develop practice in terms of using digital tools for ourselves and for students

4. Sharing, reflection, and inquiry

Objectives for Year 1

Technological Pedagogical Content Knowledge (TPACK)

http://www.tpack.org/

Teacher beliefs and practices

• Assessing beliefs on

1) Mathematics as a subject (M)

2) Mathematics learning (L), and

3) Mathematics teaching (T)

• Three orientations in beliefs and practices

Three orientations in teacher’s beliefs

• Transmission (T) views Mathematics as a series of “rules and truths” that must be conveyed to students and teaching as “chalk and talk” followed by individual practice until fluency is attained.

• Discovery (D) views Mathematics as a human creation and encourages students to learn through individual exploration and reflection, while the teacher adopts a reflective, facilitating role.

• Connectionist (C) views mathematics as a network of ideas that teacher and student must construct together through collaborative discussion.

Survey results (1/4): Mathematics as a subject

1

2

3

4

5

6

78

9

10

11

12

13

0

50

100

MT 

 MD

 MC

Survey results (2/4):Mathematics learning

1

2

3

4

5

6

78

9

10

11

12

13

0

50

100

 LT

 LD

 LC

Survey results (3/4):Mathematics teaching

1

2

3

4

5

6

78

9

10

11

12

13

0

50

100

 TT

 TD

 TC

Survey results (4/4):Teacher beliefs

Transmission Discovery Connectionist0

5

10

15

20

25

30

35

40

45

50

ElementarySecondary

Reflection happens in different ways Fluid, informal Deliberate, recorded, traceable

Individual and collective

What is Reflection?

Teacher reflection

Reflective practitioners (Schön, 1983)

a) Reflection in action: Developing an awareness if decisions in practices

b) Reflection on action: Developing an interpretive critique of practice

Reflective teachers identify problems, generate and evaluate solutions, thereby build a professional knowledge base constructed through experience and a consciousness of professional action.

A multilayer model for reflection

Layer 1: Technical• Critique of Lesson Development &

Delivery

Layer 2: Deliberative• Interactive journal writing• Video-based lesson analysis

Layer 3: Inquiry• Topical Seminar discussions

* Reference: Etscheidt, Curran, & Sawyer (2014)

Various approaches for reflection

Case-study / Autobiographical / Action research

Self-reflection / Collaborative reflection (e.g., support group; critical friends; peer reflection)

Verbal reflection (e.g., audio recording) / Written reflection (e.g., teacher diary or journal; reflection blog)

Answer the Teacher Self-Assessment

Time to reflect

According to Hattie (Hattie Ranking: Influences And Effect Sizes Related To Student Achievement)

Formative Assessment ranks as the third greatest influence on student achievement and Micro Teaching ranks fourth.

What research says

Using data day to day to:

Formative Classroom Assessment Cycle

Plan

Teach

Reflect

Summative Assessment

Data about people, practices and perceptions

Benchmark Common Assessments

Formative Common Assessment(1-4 times per month)

Formative Classroom Assessments (daily or weekly)

The Data Pyramid

e.g. student self-assessments, descriptive feedback, use of

rubrics/criteria, student products that check for understanding

(checklists), Gizmos

Math problems of the week, video of understanding

Before Instruction

During Instruction

After Instruction

Find out what student knows• Pre-assess• Anticipate

confusions and misconceptions

To monitor and adjust teaching and learning• Check for

understanding• Make student

thinking visible• Give students

specific, description non-evaluative feedback

• Regroup and reteach (differentiate)

To reflect and plan next steps• Establish quickly

who exceeds, meets and no yet

• Analyze student work according to rubric

• Identify misconceptions, errors and confusion

• Plan to re-group, re-teach or extend

The Cycle in Action

Formative assessment means simply using an assessment to inform instructional adjustments

Formative assessments is used to inform the next step needed for students to succeed

It is assessment FOR learning

Continuous Assessment

Types of Formative Assessment

Pre-Assessment or during the learning cycle Reflections or self-assessments Response systems (or paddles) Ticket-in or Ticket-out Engineered discussions Tasks Activities Quiz Peer checking (correcting)

• Differentiated Math PracticesFlip

• Differentiated Math Practices

Formative Assessmen

t

Formative Assessment

Supportive Classroom Climate Conveyed Unit Targets Continuous Assessment Student Self-Direction Flexible Student Groups Data-Informed Instruction Differentiation of Student Work

Key Strategies for Differentiated Classroom

What technological tools are at your disposal to implement formative assessment?

What types of formative assessments have you used?

Let’s share!

Technology and Formative Assessment

You have identified the following:1. Transfer of knowledge2. Decoding Application Questions and

Situational Problems3. Student Engagement and Motivation

Student Learning Problems

Choose one of the identified student learning problems to focus on this afternoon in small groups.

1. Transfer of knowledge2. Decoding Application Questions and

Situational Problems3. Student Engagement and Motivation

Focus Groups

What can we do?

Reflect and record current practices Develop further questions to explore Online exploration Google Scholar Identify key strategies identified in research

to address issue Plan for further meetings

Group Exploration

Change of Date- May 7th

Final Meeting This Year