Teaching for Learning

Christa Lemily8th Grade Math

South Warren Middle School

Challenge Problem

• You have 2 minutes to work alone on the challenge problem before you.

• If you were one of your students, how would this have gone?

The Purpose of Today

• Teaching and assessing for learning – –What the research says

• Teaching for Learning – Modified quote “If the teacher is talking but students are not learning, it is not teaching. It is called lecturing.”

• This is a mind change for teachers to gain a mind change from students.

Warren County

• Began this Journey– January 2010– Ann Shannon as our guide

• Who Participated– Algebra I, Geometry, and Algebra II teachers–Warren Central and Warren East High School

Warren County

• Last school year• All middle schools, South Warren Highs,

Central High School, and Warren East High School participated in teaching strategies

• Next year • All middle and high schools in warren county will

participate

Teaching for Learning • 5 Strategies for Effective Daily Teaching for Learning– Strategies that should become just the way we

teach everyday (in all subject areas)

• Challenge Problems (medium cycle formative assessment lessons)• Challenging tasks that are out of the ordinary and

involve problem solving

• Day to Day Lessons – teaching by problem solving (short cycle formative assessment lesson)

Five Teaching Strategies of Assessment for Learning

1. Clarifying and sharing learning intentions and criteria for success

Clearly defined learning targets

Students should know what skills they are about to learn – give them the destination and the map to get there – just don’t chauffer them

Five Teaching Strategies of Assessment for Learning

2. Engineering effective discussions, questions, and learning tasks that elicit evidence of learning.– Classroom tasks should engineer discussion

about math– Problem solving bases – productive struggle with

meaningful math

Five Teaching Strategies of Assessment for Learning

3. Providing feedback that moves learners forward– Immediate feedback as you circulate about the

room– Feedback from fellow students– Feedback through groups discussions and

presentations

Five Teaching Strategies of Assessment for Learning

4. Activating students as the owners of their own learning– Students take responsibility for their own learning– As teachers, we are not the GPS system, our

activities are the map that lead them through their own learning journey

– Encourage students to find different routes to an end solution

Five Teaching Strategies of Assessment for Learning

5. Activating students as instructional resources for one another– Want students discussing math– Find the weak students and make them experts

to share with the class

The Big Idea

• Can students recreate the math several years later?– Do they have the math tools in their mental

toolbox to problem solve – Do they simply memorize steps and processes for

a short time in order to jump through hoops and make us happy.

–Most students have number sense and they want the chance to think for themselves

Math Practices – from Common Core

1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning

others4. Model with Mathematics5. Use appropriate tools strategically6. Attend to Precision7. Look for and make use of structure

Medium Cycle Formative Assessment Lesson

• Use one every unit about 2/3 to ½ of the way through the unit.

• These are assessment lessons that measure student understanding, student growth during the lesson, and are unique, difficult, collaborative, and problem solving based lessons.

• Middle/High have sets of these written by a research group (elementary – only versions created by content network teacher leaders available in CITIS)

Medium Cycle Formative Assessment Lesson Layout

• Step 1 – Pre-assessment, completed on their own with no assistance.

• Step 2 – Look at Pre-assessments and develop guiding questions to address misconceptions (move learning forward)

• Step 3 – Complete collaborative activity• Step 4 – Give Pre-assessment again as post

assessment (clean copy on the back of first attempt)

Pre-assessment Piece

Take about 10 minutes to work on this assessment completely on your own. It is ok if you struggle with answering some of these questions because we are about to work through a lesson on this material. Just do your best and put your name on the paper.

Collaborative Activity

I will put you into groups and bring you a set of cards. Work together to place the cards in order from least value to greatest value vertically in a column down a desk. Be sure to take turns placing cards in the column and explain to your partner why you are moving the card.

Collaborative Activity (Cont.)

The next stepI will now be bringing you another set of cards that represent the same values but in a different way. Match the new model of each value to its numeric value and check to make sure you still agree the values are in the correct order for least to greatest.

Time to Spy

As the theme song to Mission Impossible plays in the background turn to a group near you and compare cards. Discuss any differences in the way you have placed your cards on the desks.

Let’s Stop and Discuss

I need someone to present your choice for the smallest value and someone else to present your choice for the largest value

Collaborative Activity

I will be bringing your last set of cards that again represent the same values you already have but in a different way. Match your new cards to the existing sets and again check your order for least to greatest.

Let’s Discuss

I need two more groups to present to the class how you choose any two of your values (not the least or the greatest)

1. Tell how you knew the three cards matched to represent the same value

2.Tell which value it is in the line, 1st (smallest), 2nd (next to smallest), and so on.

Post Assessment

1. Copy a new version of the pre-assessment onto the back of the original

2. allow students to work through it a second time

3. demonstrate growth during the lesson 4. Discover what misconceptions still exist,

Group Discussion

Where did the five strategies of teaching a formative assessment lesson occur during the medium cycle Lesson?1. In Groups of 4 discuss this question2. Write your answers on chart paper for a gallery walk (8 minutes to complete)

1. Clarifying and sharing learning intentions and criteria for success

2. Engineering effective discussions, questions, and learning tasks that elicit evidence of

3. Providing feedback that moves learners forward

4. Activating students as the owners of their own learning

5. Activating students as instructional resources for one another

• Step 1 – Pre-assessment, completed on their own with no assistance.

• Step 2 – Look at Pre-assessments and develop guiding questions to address misconceptions (move learning forward)

• Step 3 – Complete collaborative activity

• Step 4 – Give Pre-assessment again as post assessment (clean copy on the back of first attempt)

Short Cycle Formative Assessment Lessons

So how do we prepare our students day by day for these formative assessment lessons

1.Problem solving lessons (unique tasks)2.Less memorization (which means only a few can

learn)3.Fewer shortcuts that have no make basis (again

making math more complicated)4.More explaining, collaboration, and thinking for

themselves

Modeling a Lesson• Fractions: 3rd Grade Standards3.NF.1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned

into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

3.NF.2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.

3.NF.2a . Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

3.NF.2b . Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

3.NF.3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

3.NF.3a . Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

3.NF.3b . Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

Short Cycle Formative Assessment Lesson

Focus: take what you already know about fractions and apply it to graphing fraction values on a number line graph.

Let’s talk about pizza and leftovers. What do you do at home when you have leftover slices of pizza in several different boxes?

Working With Your Partner

You will be arranging slices of pie with your partner to answer only questions 1 – 3 (5 minutes to complete)

Group discussion about questions 1 – 3, any volunteers?

Working with Your Partner

Complete the number line questions 4 – 5 (5 minutes to finish)

Let’s Share out our results using cards and a number line

How else can we use this type of number line during classroom instruction?

Continued Work

Wrap up day one with group discussion of question 6

Begin day 2 with review of question 6 then move on – Work with your partner to complete questions 7 – 9 only (5 minutes)

Fractions Continued

More Leftovers Section – New pieces, in a different color, complete this section in the next 10 minutes.

Challenge Problems: work together to complete questions 1 – 5 (10 minutes)

Let’s discuss how to support our students through this section

Math Practices – from Common Core

1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning

others4. Model with Mathematics5. Use appropriate tools strategically6. Attend to Precision7. Look for and make use of structure

Formative Assessment LessonsShort cycle formative assessment lessons and

medium cycle formative assessment lessons1.Five strategies are part of just good teaching2.Formative assessment does not just apply to

math3.Students need to make sense of math – not just

memorize it4.There is always more than one way to answer a

math problem – let them struggle productively