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# Incorporating the “8” to Develop K-2 Students’Understanding of Mathematics

How to infuse the "8" Standards for Mathematical Practice in mathematics content that we are teaching NOW.

by

Tweet## Graham Fletcher

on 2 November 2011#### Transcript of Incorporating the “8” to Develop K-2 Students’Understanding of Mathematics

Incorporating the "8" in the k-2 Classroom what are the "8"? The Teaching Principle The Learning

Principle Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well. 1.Students learn mathematics through the experiences that teachers provide

2. There is no one "right way" to teach…but there are actions good teachers take every day

3. The teacher is responsible for creating an intellectual environment in the classroom where serious engagement in mathematical thinking is the norm.

4. Effective teaching requires continuing efforts to learn and improve.

5. Teachers need ample opportunities to engage in this kind of continual learning.

Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.

4.Students of all ages bring to mathematics class a considerable knowledge base on which to build.

(cc) photo by theaucitron on Flickr & presented by Graham Fletcher We must understand 4 key componants.... 1.Research has solidly established the importance of conceptual understanding in becoming proficient in a subject. 2.Learning the "basics" is important; however, students who memorize

facts or procedures without understanding often are not sure when

or how to use what they know. 3.Learning with understanding also helps students become autonomous learners. Broken Squares Broken Squares

Broken Squares Broken Squares Broken Squares Broken Squares Broken Squares 1. Make sense of problems and persevere in solving them

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of others

4. Model with mathematics

5. Use approriate tools strategically

6. Attend to precision

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

In this workshop we'll focus on....

3. Construct viable arguments and critique the reasoning of others

5. Use approriate tools strategically

6. Attend to precision

8. Look for and express regularity in repeated reasoning what should these practices look like in our classroom? How do you embed the Standards for Mathematical Practice into a K-2 classroom?

ESSENTIAL QUESTION On Chart Paper

Summarize/Describe your SMP

What would it look like in the k-2 classroom We want to find all the nets that can be folded into a cube. For this investigation we will define two nets as being the same, if we can turn (rotate), move (translate) or flip (reflect) the net and the two nets cover each other exactly.

• How many unique nets fold into a cube? Draw all possible nets that can be folded into a cube.

The Handshake Problem If there were 10 people in this room right now, how many handshakes would need to take place for everyone to shake hands with each other one time? Explain your thinking. Draw the blocks in the diagram to make the fourth step.

How many blocks in all are needed to make a staircase with five steps?

How many blocks does it take to build just the twelfth step?

How many blocks in all are needed to make a staircase of ten steps?

A staircase has 105 blocks, how many stairs does it have?

Explain your answers.

Look at the stairs The Wheel Shop sells a variety of vehicles. There are bicycles and go-carts in a different room of the shop. Each bicycle has only one seat and each go-cart has only one seat. There are a total of 21 seats and 54 wheels in that room. How many are bicycles and how many are go-carts? Explain how you figured it out. ? Questions 8. Look for and express regularity in repeated reasoning 3. construct viable arguments and critique the reasoning of others

4. use appropriate tools strategically How can I connect games and the SMPs? • How did you go about determining the number of nets?

• How do you know that you have found all the unique nets that fold into a cube?

• Convince a skeptic that you have found all the possible nets of a cube. 6. Attend to precision

Full transcriptPrinciple Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well. 1.Students learn mathematics through the experiences that teachers provide

2. There is no one "right way" to teach…but there are actions good teachers take every day

3. The teacher is responsible for creating an intellectual environment in the classroom where serious engagement in mathematical thinking is the norm.

4. Effective teaching requires continuing efforts to learn and improve.

5. Teachers need ample opportunities to engage in this kind of continual learning.

Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.

4.Students of all ages bring to mathematics class a considerable knowledge base on which to build.

(cc) photo by theaucitron on Flickr & presented by Graham Fletcher We must understand 4 key componants.... 1.Research has solidly established the importance of conceptual understanding in becoming proficient in a subject. 2.Learning the "basics" is important; however, students who memorize

facts or procedures without understanding often are not sure when

or how to use what they know. 3.Learning with understanding also helps students become autonomous learners. Broken Squares Broken Squares

Broken Squares Broken Squares Broken Squares Broken Squares Broken Squares 1. Make sense of problems and persevere in solving them

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of others

4. Model with mathematics

5. Use approriate tools strategically

6. Attend to precision

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

In this workshop we'll focus on....

3. Construct viable arguments and critique the reasoning of others

5. Use approriate tools strategically

6. Attend to precision

8. Look for and express regularity in repeated reasoning what should these practices look like in our classroom? How do you embed the Standards for Mathematical Practice into a K-2 classroom?

ESSENTIAL QUESTION On Chart Paper

Summarize/Describe your SMP

What would it look like in the k-2 classroom We want to find all the nets that can be folded into a cube. For this investigation we will define two nets as being the same, if we can turn (rotate), move (translate) or flip (reflect) the net and the two nets cover each other exactly.

• How many unique nets fold into a cube? Draw all possible nets that can be folded into a cube.

The Handshake Problem If there were 10 people in this room right now, how many handshakes would need to take place for everyone to shake hands with each other one time? Explain your thinking. Draw the blocks in the diagram to make the fourth step.

How many blocks in all are needed to make a staircase with five steps?

How many blocks does it take to build just the twelfth step?

How many blocks in all are needed to make a staircase of ten steps?

A staircase has 105 blocks, how many stairs does it have?

Explain your answers.

Look at the stairs The Wheel Shop sells a variety of vehicles. There are bicycles and go-carts in a different room of the shop. Each bicycle has only one seat and each go-cart has only one seat. There are a total of 21 seats and 54 wheels in that room. How many are bicycles and how many are go-carts? Explain how you figured it out. ? Questions 8. Look for and express regularity in repeated reasoning 3. construct viable arguments and critique the reasoning of others

4. use appropriate tools strategically How can I connect games and the SMPs? • How did you go about determining the number of nets?

• How do you know that you have found all the unique nets that fold into a cube?

• Convince a skeptic that you have found all the possible nets of a cube. 6. Attend to precision