THE INSTRUCTIONHighly Eff ective Services, Inc. 2012

PRIME K-8 Mathematics Leadership: Fining Tuning

and Assessing

Problem Solving

Communication

Reasoning

Connections

Representations

Process Standards [NCTM and VA SOLs]

Apply proportional and spatial reasoning

Planning and understanding the RIGOR

CommunicatingUse mathematical language while solving and arguing for the correct solutionMake conjectures to build logical progression and explore ideasDefend reasoning using representationsListen and make sense to other arguments or explanations and ask probing questions

A Structure to Decode A Problem

CommunicationUse the language of the learning by decoding the mathematics vocabulary to unleash the “big Ideas.” [Frayer Model, Frames, etc.]

ConnectionsPrior Knowledge Select one of the (8) Eight Problem Solving Strategies

Indicator 4:Connecting Apply prior knowledge to solve real

world problems Make connections with science and

other disciplines Look for patterns and recognize

that quantities can be represented in different ways

Recognize the concepts and model by using a structure for a similar problem

Eight Problem Solving Strategies Draw a pictures or a modelMake an organized listLook for a patternGuess and checkWork a simpler problemMake a tableGuess and checkWork BackwardAct it out

Structures are made up of parts that go together and help one another.

A structure is only as strong as its parts.Structures can be both natural and man-

made.Structures can combine to form other

structures.Structures can facilitate or hinder change.

Building Structures

Communication - Discourse

Having a conversation about the framework

We cannot “see” a student’s understanding, we make inference about what it may be.

The theory of constructivism suggests that telling does not help us understand the ideas, the ideas must be constructed to make meaning.

Classroom Influence onLearning

Ball et al. (2009) suggest a set of criteria for high leveraging practices:

1. Supports work that is central to mathematics.

2. Helps to improve the learning and achievement of all students.

3. Is done frequently when teaching mathematics.

4. Applies across different approaches to teaching mathematics.

Responding to the framework

5. Can be articulated and taught.6. Is accessible to learners of teaching.7. Can be revisited in increasingly

sophisticated and integrated acts of teaching.

8. Is able to be practiced by beginners in the field-based settings. (p.461)

Responding to the framework

Actively engaged minds in thoughts equal effective learning.

No ideas exist in isolation.Existing ideas give meaning to the new idea,

new connections are formed between the new idea and the existing ones.

Ideas…Understanding…Learning

Constructing Ideas

Three Factors that Influence Learning

Student Reflective Thinking

Social Interaction

Use of models or tools

Models are not the same as conceptsModels are objects, pictures, drawings or

manipulatives that represent the concept and its relationship

Models and other Tools for LearningTools to help learn concepts

Procedure Knowledge as a ToolLearn hand and hand with concepts

Tools for Learning

Involve s directing student attention toward specific learning

Highly structured environmentContent/concepts broken down into partsInvolves modeking skills , behaviors and

thinking

Engage and HookExplain and modelExplore and applyEvaluate and close

Explicit Thinking

… it is the teachers using particular teaching methods, teachers with high expectations for all students, and teachers who have created positive student-teacher relationships that are more likely to have above average effects on student achievement.

The Framework is Explicit Teaching

High cognitive demand(Stein et. Al. 1996: Boaler & Staples, 2008

Significant content(Hiebert et. al, 1997)Require justification or explanation (Bolaer &

Staples, in press)Make connections between two or more

representations (Lesh, Post, & Behr, 1988)Open-ended (Lotan, 2003; Borasi & Fonzi, 2002)Allow entry to students with a range of skills and

abilitiesMultiple ways to show competence (Lotan, 2003)

Have Rich Mathematical Tasks with RIGOR

Follow the blueprint and build a solid frame.

This Math House is on FIRE with Effective Teachers holding the keys. Students in their classes are not struggling