## TEST CORRECTIONS: A NEW APPROACH TO AN OLD IDEA by Patty Rhoney

“We were cruising through the school year, and I felt proud of my students’ performance.” . . .”Then I graded my first batch of written response tests which fell far short of my expectations.” [Sound familiar??] “Knowing that I couldn’t go back and re-teach the whole chapter and afraid to admit my students had not, in fact, mastered the concepts that I had so confidently taught them, I felt panicked. If I moved on to the next chapter and never addressed the glaring gaps in my students’ understanding, when would my students get the chance to improve? Next year? Never? When?” And were the errors due to a “misunderstanding of math concepts or because they had trouble responding in a short answer/extended response format?” [Can anyone relate??]

The paragraph above is a quote from an article in the Ohio Journal of School Mathemetics (Fall, 2012), Always Improving: Turning Test Responses into Learning Opportunities, by John S. Parke (Twinsburg, OH). His article offers a possible approach to attacking this problem.

Before returning the graded tests to his students, Mr. Parke “played a game” with the class – “What Went Wrong?” After identifying the five most commonly missed problems, he selected the best student response, and one or two poorly constructed responses. He showed the incorrect responses (re-written in his handwriting, so as not to embarrass the incorrect student) and asked the class to read the problem and the incorrect solution. They were to try (on their own) to determine why the response was not correct. Then, they were to discuss those thoughts with their neighbor, and finally share them with the class. After deciding “what went wrong”, he showed the “perfect response” (in the original handwriting). That process was repeated for each of the 5 selected questions, allowing students to see how they could correct their responses, even before the tests were returned. He then returned the graded tests, and their assignment was to correct the errors they made on just those 5 questions. If a student answered the question(s) correctly, they were encouraged to help their classmates with the corrections. (He used the “three before me” rule – students had to ask for assistance from 3 of their peers before asking for his help.) The test corrections were done on a specific form (see below), attached to their test when complete, and a parent signature was required.

While the process of “test corrections” is certainly not anything new, I really liked his idea of showing incorrect and “perfect” responses before returning the tests. It seemed to encourage “math talk” and allowed students to “teach” their peers. I have used this with my students several times this year, and it seems to make a difference in their approach to making the corrections – they are more focused on actually understanding their errors, rather than just “getting the answer right.” They have also enjoyed the “game” of figuring out “what went wrong”, along with trying to guess whose answer was the “perfect response”.

This is the top of the form used by Mr. Parke. (He makes the table with 5 rows: 1 for each commonly missed response.) It is very similar to a form shared with me by Val Muller quite a while ago. As you can see, the basics of this idea are really not new – but I do like the “new” approach of getting the students to “talk math” to each other!

## Common Core Mathematics and the Power of Mindset by Rita Bixler

Mindset is a simple idea discovered by world-renowned Stanford University psychologist Carol Dweck in decades of research on achievement and success—a simple idea that makes all the difference. The research shows that intelligence is malleable. The brain is like a muscle. It gets stronger when exercised. We now have the technology to see the positive changes that occur in the brain when it encounters challenging tasks.

Mindsets are the assumptions, expectations and beliefs that guide our behavior and our interactions with others.

Individuals with a fixed mindset believe that their intelligence is simply an inborn trait—they have a certain amount, and that's that. The fixed mindset contributes to one of the biggest myths in mathematics: being good at math is a gift or an inherited gene.

Individuals with a growth mindset believe that they can develop their intelligence over time. Growth mindsets lead to the love of challenge, belief in effort, resilience in the face of setbacks, and greater (more creative) success.

Understanding and applying this research will enable teachers to help their students be more successful in meeting the challenges of the Common Core Mathematics Standards. The rich mathematical tasks called for by Common Core support and promote a culture for growth mindsets. Engaging students in the Standards of Mathematical Practice also promotes growth mindsets. Consider the growth mindset connection to the Standard of Mathematical Practice 1: Make sense of problems and persevere in solving them. Students with growth mindsets will eagerly engage in “productive struggle” when confronted with challenging problems.

Dweck suggests that teachers actually teach students to recognize the different mindsets. Students should know that effort can actually change the brain and improve their abilities and achievements. In addition students should understand that fast learning is not always the deepest or best learning. Teachers should provide the right kind of praise and encouragement. Praise students for the processes in which they have engaged:

l The effort they applied

l The strategies they used

l The persistence they displayed.

Language of Growth Mindset

l ‘Well done. You are learning to…..’

l ‘I’m really pleased you tried at that.’

l ‘That’s fantastic. I liked the way you…..’

l ‘That’s skillful.’

l ‘What are you most proud of?’

l ‘What is a good learner?’

l ‘How are you more successful with this skill than before?’

l ‘This is what we did before. What more can you do now?’

Mindset change is not as simple as tweaking a few things here and there. It is about seeing things in a new way so that our students will come to believe “My ability and competence grow with my effort”.

## Elementary News

Math Olympiad is a problem solving contest for students in grades 4 through 8. Students participate in five monthly contests with every problem requiring careful mathematical thinking. This year, GCCTM sponsored two schools – Brook Glenn and Sara Collins. Brook Glenn had a single team of 32 students while Sara Collins had five teams with over 150 students participating. Instructional coaches and teachers led the teams either before or after school. Hats off to the leaders and students for making math meaningful!

## STEM Saturday (Elementary)

Do you know how to…Store six in the memory of the calculator? Count back from 100 by 2s to 50? Solve 6 x (7 + 4)? Teachers spent a rainy Saturday morning answering these questions and many more using the TI-15. Engaging calculator lessons and activities correlated to the Common Core State Standards for Mathematics were shared. Calculators help children develop number sense and mathematical ideas and understand connections, relationships, and patterns. Teachers using calculators have the opportunity to expand the teaching possibilities in their classroom, greatly assisting students’ learning. Thanks to Linda Manley from Bethel Elementary for facilitating the session!

Textbook Therapy 101– an orientation to the new Houghton Mifflin Harcourt Go Math! textbooks

· July 17 (K-2) am and pm session

· July 22 (K-2) am and pm session – a repeat of July 17th!

· July 18 (Grades 3-5) am and pm session

· July 23 (Grades 3-5 am and pm session – a repeat of July 18th!

Calendar Math sessions for new teachers in grades K-5 – July 24

Connecting Calculators to Common Core – July 25

Math Games – July 18

Math tips and Tricks for 5th grade – July 23

Thinking on Paper: Writing in Math Class – July 24

## Summer Textbook in-services for Middle Schools -tentative

will be cancelled if not funded- Teachers only need to sign up for one session- morning or afternoon.

o July 23 8:30-11:30 and 12:30-3:30 MT Anderson Training Room 103

o July 25 8:30-11:30 and 12:30-3:30 MT Anderson Training Room 103

o August 5 8:30-11:30 and 12:30-3:30 LOCATION TBD

## Super STEM Saturday Session (High School)

The high school workshop attracted teachers interested in beginning to use TI-Nspiretechnology. We covered the basics of getting started with the new technology and examined ways to teach with it in lieu of a classroom set of calculators. It turns out that TI-NspireTeacher Software is a flexible presentation tool, too. The five-hour session provided an opportunity for participants to re-connect with colleagues across the district and to meet new folks from middle school and high school. Folks valued the time to explore ideas and applications in greater depth. TI continues to grow the teacher resources to support this technology.

GCCTM truly appreciates the time and expertise of both Sherri Abel (Legacy Charter School) and Jamila Gadsen (Texas Instruments). We also give an appreciative nod to EHS curriculum resource specialist Kathryn Brooks – her behind the scenes support enabled many of us to wear a learner hat. And last but not least, thank you Daniel Wilkie (Woodmont High School) – you are the Greenville County Schools Nspire fix-it guy!

Valerie Muller, GCCTM Past President

## Thank you to all that made the 2013 GCCTM Spring Banquet a success!

Honorees
Berea High School
Alex Giron
Neris Soto

Blue Ridge High School

Aaron Anderson

Carolina High School
Cameron Ross Fritz Farr

Eastside High School
Gareth Tate

Greenville High School
Michael Dantzler Spiers Jr

Greenville Technical Charter High School

Alen Simmons

Greer High School
Mary Kate Nicholson

Hillcrest High School
Kimberly Rowland

JL Mann High School

Robert Borowicz
Thomas Coe
Zachary Hargett
Jacob Jones

Mauldin High School
Robert Isaac McGill

Riverside High School
Nathan Harrison Cotterman
Joshua Tran
Jiawei Zhang

Southside High School
Pooja Jayaraman
Aahil Merchant
Ann-Elise Caroline Siden

Travelers Rest High School
James Albert

Weston Catron

Woodmont High School
Cody Michael Davidson

★★ MathCounts™ Honorees★★
Sterling School/Charles Townes Center placed first at the Chapter
Competition and second at State Competition
Team Members:
Kevin Tian
Guanpeng "Andy" Xu
Chris Gantt
Griffin Gatchell
Constans Gordon - coach

## Looking for a great hands-on activity to use with volume?

Tired of the same build a cube with blocks activity? This lesson incorporates measuring to the inch, area, nets, and estimating.

By Barbara Key and Linda Manley

Prior to the lesson choose a rectangular prism that can hold the paper cubes. This needs to be a container that is to the whole inch in dimensions (see example figure). Have one paper cube already created and show the class.

1. As a class, estimate how many of the cubes will fit inside the container.

2. Each student draws a net of a cube with each square being one square inch.

3. Fold the net into a cube, and secure with one piece of tape.

4. Place the cubes in the container and count how cubes it takes to fill the container. Students draw, fold, and tape cubes as needed until the container is filled.

5. The number of cubes is your volume.

Closure- Discuss how the cubes were placed in the container. How many cubes in each row? How many rows? Why do we use cubic units when discussing volume?

Technology extension http://illuminations.nctm.org/ActivityDetail.aspx?ID=6

## TI Summer Institutes in Greenville 6/17/2013 - 6/19/2013

o Getting Started with TI-Nspire Technology in Connecting Science and Mathematics

o Getting Started with TI-Nspire Navigator(tm) System in High School Mathematics

o Getting Started with TI-Nspire Technology and the Common Core in Middle Grades Mathematics

o Register at: http://education.ti.com/go/t3summer

## State Dept of Education PD

Office of Instructional Practices and Evaluations Mathematics PD Plan Registration Begins at 8:30 and Sessions Run 9:00 – 3:30

## Visual Models for Division of Fractions with Mary Ruzga

https://ed.sc.gov/Survey/index.php?sid=21563&lang=en

The registration deadline is May 27, 2013. Each session is limited to 50 people.

June 18 - Anderson 1&2 Adult Ed Center, 214 Lebby Street, Pelzer, SC 29669

June 19 Session Repeated - Lyon Street Teleconference Center, 1310 Lyon Street, Columbia, SC 29204

While this session addresses visual models for division of fractions as required by the 5th and 6th grade CCSSM, 3rd and 4th grade teachers are also encouraged to participate. Teachers will examine problems in context related to the CCSSM Common Structures for Division and engage in experiences related to division of fractions as set forth in CCSSM. All participants will learn how to draw visual models for division of fractions as required by 5th and 6th grade CCSSM and gain an understanding of the relationship between fractional and ratio reasoning required in 6th grade. 3rd and 4th grade teachers will gain a better understanding of fraction-related expectations for their grades and how those expectations lay important foundations for 5th and 6th student work with fractions.

## Using the TI-84 Plus to Improve Teaching Efficiency and Student Understanding with Sherri Abel

https://ed.sc.gov/Survey/index.php?sid=47934&lang=en

The registration deadline is June 3, 2013. Each session is limited to 50 people.

June 25 Beginner Session - Lyon Street Teleconference Center, 1310 Lyon Street, Columbia, SC 29204

This session is designed for middle school teachers who have little to no knowledge of how to use a graphing calculator. It will answer questions as basic as “How do I turn on the calculator?” The participants will then use basic understanding of the tool to engage in lessons designed to demonstrate ways in which it can be used to maximize teaching time and promote student understanding of certain math topics as set forth in CCSSM.

June 26 Advanced Session - Lyon Street Teleconference Center, 1310 Lyon Street, Columbia, SC 29204

This session is designed for secondary teachers who have some comfort level with a graphing calculator. Participants will engage in lessons designed to demonstrate ways in which graphing calculators can be used to maximize teaching time and promote student understanding of certain math topics as set forth in CCSSM.

## High School Geometry as Set Forth in CCSSM – A Learning and Sharing Session with Lisa Donnahoo

https://ed.sc.gov/Survey/index.php?sid=47897&lang=en

The registration deadline is June 17, 2013. Each session is limited to 50 people.

July 9 - Anderson 1&2 Adult Ed Center, 214 Lebby Street, Pelzer, SC 29669

July 10 Session Repeated - Lyon Street Teleconference Center, 1310 Lyon Street, Columbia, SC 29204

Participants in this session will examine different types of proofs (two column, paragraph and coordinate), work problems using coordinates, discuss dilations, and examine the statistics now in Geometry. In order to learn from each other and to guide future professional learning opportunities, participants will be asked to share geometry related concepts about which students experienced understanding difficulty. Likewise, participants are asked to bring, on a flash drive, electronic copies of CCSSM based geometry activities or lessons that worked well this school year. Participants will be given an opportunity to share those activities/lessons and electronic copies will be emailed to all registered participants after the session.

## K-5th Grade Geometry Through the Lens of the Mathematical Practices with Morgan Nolte and Mary Ruzga

https://ed.sc.gov/Survey/index.php?sid=78624&lang=en

The registration deadline is June 24, 2013. Each session is limited to 50 people.

July 16 - Anderson 1&2 Adult Ed Center, 214 Lebby Street, Pelzer, SC 29669

July 17 Session Repeated - Lyon Street Teleconference Center, 1310 Lyon Street, Columbia, SC 29204

In this session participants will be provided with a newly developed document that gives specificity to the geometric attribute/property knowledge expected at each grade K-5. Participants will engage in sample lessons/activities that begin with K and build through 5th grade, each linked to the mathematical practices. The focus will be on improved teacher pedagogical content knowledge and the lessons/activities will be the vehicle to achieve that goal.

## Unique Strategies for Teaching Multiplication and Division of Whole Numbers with Cindy Doolittle

This is a video made in collaboration with ETV and describes unique, hands-on strategies for teaching multiplication and division using a constructivist approach. The video will introduce a variety of techniques that can be used to meet multiple learning styles. The video will be available through Streamline SC after June, 2013.

## Engaging Students in Learning: Math Practices and NCTM Process Standards for grades 9-12

Aug 1-3 2013, Washington DC

Program & Presentations

You’ll dedicate 2½ days of professional development to the Common Core mathematical practices and NCTM Process Standards, and walk away with practical strategies to prepare your students for success.

The experience will be suited to your interests—you’ll take part in sessions and be grouped with educators according to the grade level you select for your strand of focus. Each strand will experience a progression of activities to address mathematics content related to the Common Core mathematical practices and NCTM Process Standards.

Strands

• Algebra 1/Integrated Year 1
• Algebra 2/Integrated Year 3
• Geometry/Integrated Year 2
• Probability and Statistics

http://www.nctm.org/profdev/content.aspx?id=35182

### 2100 College St

#### Newberry, SC

Wednesday, June 12 - Thursday, June 13, 2013

8:00am - 5:00pm (Eastern Standard Time)

T³ Regional Conferences are open to all middle grades to University educators interested in using educational technology to enhance the teaching and learning in Mathematics and Science. Attendees can count on networking with teachers from across the region; learning from experienced educators; and participating in hands-on and demonstration sessions for new and experienced educators. You will receive lots of great classroom activities and ideas, along with the latest news on TI technology.

Cost: Wednesday only - \$75
Thursday only - \$75
Wednesday & Thursday - \$100
Newberry Information

## GCCTM Officers

President, Patty Rhoney
Past President, Valerie Muller
President-Elect, Linda Manley
Vice-President Primary, Faith Deaver
Vice-President 3-5, Sara Awtrey