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The Six Secrets of Highly Effective Lesson Design!

For every student to succeed, mathematics teachers must work together by grade or course level to build a foundation of challenging mathematics that present students with rich, engaging mathematical tasks and require higher-order thinking. Mathematical experiences must be meaningful and relevant and connect to student knowledge and personal experiences. PRIME, p.11 @ 2008

October 7th, 2010

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OUT OF THE MOUTHSOF BABES

A 10-year old asked herfour-year old sister what

she wanted to be forHalloween, adding that it

should be “somethingreally scary.”

The little girl replied,“How about a math teacher?”

-Dorothea Kent

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The Six Secrets of Highly Effective Lesson Design!

…mathematics teachers must work together by grade or course level…

challenging mathematics that present students with rich, engaging mathematical tasks and require higher-order thinking.

Mathematical experiences must be meaningful and relevant...

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Every teacher implements research-informed best practices and uses effective instructional

planning and teaching strategies.

Develop and model knowledge of research-informed instructional strategies and best practices for effective student learning of mathematics.

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Examples of Well-Established Research Results

On-going cumulative distributed practice improves learning and retention. (Daily student active reviews)

Connection to an individual’s prior knowledge significantly influences what is learned in a particular situation. (Content Progression and Development)

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Examples of Well-Established Research Results

In class formative assessment increases students’ learning. (Students Demonstrate Understanding)

Accurate, fair specific, timely feedback improves learning. (Guided Practice/Formative Assessment)

.63 Vs. .57

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Loose Tight - Do we have to do this?

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The Teacher as a Reflective Practitioner

Professional development and learning is an ongoing, continuous, sustainable activity inside and outside of the school walls. Professional development lasting 14 or fewer hours showed no effect on [teacher] learning.

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The Teacher as a Reflective Practitioner

The largest effects were for programs offering 30 – 100 hours spread out over 6 – 12 months…

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Mathematics Curriculum Leadership

With a shoulder partner…– Share your understanding of the

difference between relevant mathematics and meaningful mathematics

– In your lesson design…

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Relevance Vs. Meaning

Relevant mathematics: References the context for the lesson as part of essential mathematics and mathematical tasks the student need to know. Does the lesson present important and essential mathematics? 

The CCSS will help us with this….

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Relevance Vs. Meaning

Meaningful mathematics: References the context for the lesson as containing elements that create meaning, reasoning and sense making for the student - while also connecting to the students’ prior knowledge and understanding…

Lesson Planning from the Students’ Point of View

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During a lesson Learners should...

Engage with challenging tasks that involve active meaning-making.

Acquire conceptual knowledge as well as procedural skills to enable them to organize their knowledge, transfer knowledge to new situations, and acquire new knowledge.

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The Six Secrets of lesson Design

Think back and reflect on the implementation of your 2-3 most recent lessons – specifically its successes…

1. What went well?

2. What could have been better?

3. What would you have done differently?

Discuss with a shoulder partner…

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The Six Secrets of lesson Design

Secret #1:   How was students’ prior knowledge addressed

in creating the lesson?

Secret # 2: How much of the lesson / material was covered

through student exploration or student questioning (instead of didactic lecture)?

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The CCSS Standards for Mathematical Practice

The 8 Standards for Mathematical Practice – place an emphasis on student

demonstrations of learning…

Daily… how do students experience the learning of mathematics?

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The CCSS Standards for Mathematical Practice

MP # 3 Construct viable arguments and critique the reasoning of others1) Students make conjectures2) Students justify their conclusions and

communicate them to others3) Students compare the effectiveness of

two plausible arguments 4) Students listen and respond to the

arguments of others for sense making and clarity

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The Six Secrets of lesson Design

Secret # 3: What kinds of varied activities were used to

engage students and stimulate intellectual rigor?

Secret #4: What kinds of in class formative assessments

were used to form the lesson as well as evaluate the effectiveness of the lesson?

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The Six Secrets of lesson Design

Secret # 5: Reflect on the depth of conceptual understanding of the content demonstrated by the students.

How did the lesson provide for high cognitive demand task opportunities?

How did the students demonstrate their understanding of the most essential concepts of the lesson through the tasks presented?

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The importance of Mathematical Task Selection by the Teacher

Tasks form the basis for students’ opportunities to learn what mathematics is and how one does mathematics

Differences in the level and kind of thinking of tasks used by different teachers, schools, and districts, is a major source of inequity in students’ opportunities to learn mathematics.

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The Six Secrets of lesson Design

Secret # 6: Reflect on the processes that students were asked to use to manipulate information, arrive at conclusions, and evaluate knowledge claims.

What kinds of questions and conjectures were proposed (by students) in the early stages of the lesson?

What kinds of student led summative exercises were used to measure student understanding and learning?

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The Secrets to Effective Classroom Communication

Lessons where teachers characteristically speak and students listen are not “reformed”.

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The Secrets to Effective Classroom Communication

It is important that students be heard, and often, and that they communicate with one another, as well as with the teacher. The nature of the communication captures the dynamics of knowledge construction in that community.

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The Secret to Effective Classroom communication

How did students express their ideas, questions, insights and difficulties?

Where are the most significant conversations taking place (student to teacher, student to student, teacher to student)?

How approachable and encouraging are you - as students explore? Do students see each other as reliable and valuable resources?

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The CCSS M.P.’s and Equity…

Equity begins with an understanding of how the

selection of tasks, the assessment of those tasks,

the technology used & the quality of feedback

Is so widely variant from teacher to teacher 25

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Teaching for Effective Lesson Design…

Traffic Signal 

o Red light - 1 thing you will stop doing that limits effective lesson design…

o Yellow light - 1 thing you will continue to do . . .

o Green light - 1 thing you will begin to do . . .

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Support for implementation of the CCSS

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I hope 2011-2102 Will be a Great Year for You!

Your greatest achievements are the triumphs of your students

“The level and kind of thinking in which students engage determines what they will learn.” Hiebert et al., 1997

PDF of this presentation will be posted on Monday at tkanold.blogspot.com