1 Overview of Class#8 Continue work with base ten blocks –Modeling addition and subtraction with whole numbers –Ordering decimals –Modeling addition and subtraction with decimals Overview of Part 3 of our course –Learning to remediate student difficulties with computational algorithms –Attend actively to equity Assignment and wrap up

2 Modeling with Base Ten Blocks Work with a partner Use language of base ten blocks Remember to model the steps of the conventional algorithm and make the meaning clear Attend to the way you are representing addition and subtraction

3 Ordering Decimals Put the following strings of decimals in order however you usually do it: a) b) What do you think makes ordering decimals difficult for kids?

4 What Makes Ordering Decimals Difficult The length of a number no longer a clue Multiple representations for same number:.4,.40, and 0.4 Lack of understanding of what the numbers mean (how we read decimals) Money overly supports “correct” answers with tenths and hundredths

5 Modeling Computation of Decimals with Base Ten Blocks: Issues to Attend to Choice of unit with base ten blocks Language of decimals, materials, and operations Correspondence between model and written algorithm

6 Modeling Computation of Decimals with Base Ten Blocks

7 Question Why is it important to line up the decimal places when adding or subtracting decimal numbers?

8 Part 3 of Our Course Learning to design, teach, and improve lessons –Designing lessons (structure of lessons) –“Types” of lessons –Assessing students’ learning –Remediating –Extending –Out-of-class assignments Attending actively to equity

9 Four Common Student Errors

10 Remediating What does NOT work? Repeating the same things over again, slower, more loudly Re-teaching everything Teaching that forces students to get the “right answer” Teacher does the problem for the student Teacher refers the student to easier problems that they could handle and cuts off work returning student to work on building block concepts Teacher gives students more problems since practice is the issue What DOES work? Identifying carefully where the problem(s) lie(s) Helping student to initially “see” the problem Drawing upon/helping to develop student’s estimation skill Using manipulatives or other representations to focus on the meaning and the procedure Sharing the talk with the student, scaffolding Offering a similar example to try Reducing complexity in some way and then encouraging connection of that work with previous problem

11 Discuss and Practice Remediating Common Student Errors 1.For each student error, what might the conceptual difficulty be? 2.Focus on one student error and work individually to design a scaffolded approach to remediating the procedure and its meaning (5 minutes) 3.Present your approach to remediating to your group and receive their feedback.

12 Part 3 of Our Course Learning to design, teach, and improve lessons –Designing lessons (structure of lessons) –“Types” of lessons –Assessing students’ learning –Remediating –Extending –Out-of-class assignments Attending actively to equity

13 What Do We Mean by “Equity”?  Differences among students are a given  These differences shape teaching and learning  Some differences in student outcomes are associated with demographic groups -- patterns of inequitable access to instruction  Equity means that school outcomes are not associated predictably by race, class, gender (RAND, 2003)  Changing these patterns  achieving “equity” in teaching practice

14 The Endemic Problem of Inequity in School Mathematics Persistent achievement gaps: race, social class Gatekeeping role of mathematics Unequal access to opportunity Unequal participation in mathematical fields

15 Working to Create Equitable Practice  Inequity is partly reproduced inside of instructional practice.  Breaking this cycle depends on joining concerns for equity with the daily and minute-to-minute work of teaching.  Teachers can have leverage at strategic points that can help them make an equitable practice part of the work of teaching

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17 Where Teachers Can Try to Gain Some Leverage ( in the face of “defaults” that tend to create inequities in opportunity and achievement ) 1. Selection of mathematical tasks: consider assumptions, contexts, scaffolding 2. Work on becoming more self-aware of how our identities and experiences as teachers shape our interactions with students 3. Unpacking and scaffolding important mathematical practices 4. Knowing and using more about students’ out-of- school experiences

18 Wrap Up Assignments –Reading –Design a decimal task –Teaching Segment #3