Number Sense and Computation Professional Development Plan

Alaine Fowler Langford Elementary School, Austin ISD

Overview: The purpose of this professional development series is to aid in the instruction of teachers and the student mindset associated with mathematics. Having number sense and computation skills is an important concept to develop at the elementary level. These mathematical elements are the building blocks for the learning to come throughout the school year as well as the learning they will do throughout their life. It is important to focus efforts on students being successful in these areas in order to prepare for the future. As a teacher of an upper elementary school grade, I have seen first hand the effects of years of falling behind in school. Children cannot move forward with learning until they have something to build off of. This professional development series will help close learning gaps by helping students develop number sense and computation skills at all elementary grade levels. Objective/Big Idea: The students will be able to master number sense and computation objectives with scores of 75% or higher on formative, summative, or benchmark assessments. TEKS Addressed: K.2A-I, K.3A-C, K.5 1.3A-F, 1.5A-G 2.4A-D, 2.6A-B, 2.7A-C 3.4A-J, 3.5A-D 4.4A-H, 4.5A 5.3A-L, 5.4A-H Needs Analysis: Langford Elementary School has a need for a professional development session focusing on math. Langford is a Title I school with 91% of the students being Hispanic. Across grade levels, the majority of students perform at grade level, most barely making the mark, and 25% of the students are performing below grade level. These students are continuing to get more behind each year as the concepts get more difficult and their number sense does not get better. Despite having 3 math specialists on campus, teachers are still doing interventions in class for many. The staff learning how to teach number sense and computation in a way that best suits the students would greatly increase achievement, as well as decrease learning gaps and retention rates. Students need the building blocks of mathematics first in order to continue learning. Growth mindset will also be incorporated into this professional development series. Increasing self-esteem pertaining to school subjects will help students stop thinking “I can’t” and start thinking “I’ll try, even if I fail”. Many students at Langford let their mindset get in the way of the reality that they could do something but they have to fail a few times first. Some students do not have parents around to tell them to keep trying or that they are good enough. It is vital that teachers take the time to build these children up and ensure they have the confidence in themselves to be successful.

SMART Goals (specific, measureable, attainable, results-oriented, timely): By the end of the 5 month professional development series, 70% of educators that have attended all in-service meetings will be able to implement new number sense and computation strategies, knowledge and activities into the classroom with students mastering the objective at 80% accuracy. By the end of the first semester, the students will be able to master number sense and computation objectives with a scores of 75% or higher on formative, summative, or benchmark assessments. Application Professional Development Activities/Sessions: August (before school starts): Growth Mindset (25 minutes): Each teacher receives a copy of Mathematical Mindsets by Jo Boaler. This will be the book used throughout the semester in-services. Before the first in-service, teachers must read Chapters 1 and 2 and be ready for discussion. Teachers sit with respecting grade levels and sit near the grade level above/below. Ask groups to come up with a list of 5 things they have learned out to do in their lifetime (ex: walk, ride bike, do algebra, etc.). Each grade level shares out. Show teachers the video “You Can Learn Anything” from Mindset Kit.(https://www.khanacademy.org/youcanlearnanything) Each grade level will have chart paper to document answers to questions on. Display the following questions on the projector so that grade levels can discuss and write down answers Discussion Questions:

• What is growth mindset? • What does growth mindset mean? • How can we help students get growth mindset?

After 10 minutes, have grade levels stand up and share out. Share with teachers that we will be doing weekly growth mindset lessons with our classes. Explain what is expected from a lesson. Book Study Chapters 1 and 2(30 minutes): Teachers sit with PLC groups so that they are mixed among grade levels. Ask for share-outs about anything from the book that particularly stood out. Have a campus discussion. With PLC groups, teachers discuss the following discussion questions:

• How can we as teachers be more accepting to mistakes in our classroom? • How does learning to embrace mistakes help with growth mindset? • In having students with a growth mindset, how do you predict this will affect the progress

students will make throughout the year? Teachers write their answers on chart paper. Give teachers 20 minutes to discuss and then share out to the campus. Number Sense and Computation- Beginning with the End in Mind (1 hour): Teachers sit with grade level and sit near grade levels above/below. Teachers read article “Number Sense-Right Now” http://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Skip-Fennell/Number-Sense—Right-Now!/ Display the following questions for discussion among grade levels:

• Why is it important for number sense to be developed (and continued to be practiced) at a young age?

• What do you notice about the mathematical performance of students who have a strong

sense of number sense? What about those who have a weak sense of number sense? Each grade level will then brainstorm the most important mathematical foundations they feel necessary for a student that is coming into that particular grade level (example: 5th grade teachers will list necessary foundations that a fourth grade student should be able to do at the end of the year to be mathematically successful in fifth grade). Grade levels share out and have discussions about how they can ensure students have mastered the content before moving on. Action Steps:

• Design an activity that will change opinions on mistakes and use it in your classroom at least 1 time during the first week of school.

• Next time: bring an artifact that shows how you have been building mathematical growth mindsets in your classroom.

• Next time: have chapters 3 and 4 of Mathematical Mindsets read and ready for discussion • Growth mindset class lesson/activity/game at least once a week.

September: Growth Mindset (25 minutes): Teachers sit with respecting grade levels and sit near the grade level above/below. Show teachers the video A Pep Talk from Kid President to You https://www.youtube.com/results?search_query=kid+president&spfreload=10 Quickly review the importance of growth mindset. Give teachers 10 minutes to share out about their growth mindset artifact at their tables. Have whole group share-outs, at least one per grade level. Ask for share-outs about mindset activities from the first week of school (what were the activities, how did they go with the students, did students have a change of attitude?) Book Study Chapters 3 and 4 (30 minutes): Teachers should have read chapters 3 and 4 of Mathematical Mindsets to prepare for in-service. Teachers sit with PLC groups so that they are mixed among grade levels. Ask for share-outs about anything from the book that particularly stood out. Show on projector Table 3.2: Fortune 500 “Most Valued” Skills in (1999) Page 29 of Mathematical Mindsets). Ask teachers “If these are some of the most valued traits in order to be successful, how does that effect the way that we teach?”, “How does knowing this effect the way we might present material in the classroom?” Teachers discuss with PLC groups for 10 minutes. Each PLC group shares out. Display Figure 4.1: Mathematics Methods and Concepts (page 36) as well as discussion questions:

• How can we help students approach math conceptually in order to grow the brain, as opposed to students viewing math as rules to remember?

• What are some alternatives to math drills? What are some ways to deemphasize memorization and instead emphasize rehearsing?

Number Sense and Computation- Using Visual Representations (1 hour): Teachers sit with grade level and sit near grade levels above/below. Go over a PowerPoint about number sense that reviews:

• What is number sense (components of number sense) • Why is it important • What can we do to help build it (leads into next activity)

Each teacher gets a copy of chapter 6 titled “Habit 4: Representing Mathematics Nonlinguistically” from the book Teaching Numeracy by Marie Pearse.

The chapter details how to create and use visual representations in the classroom to promote understanding of mathematics. Go over each of the key ideas for visual representations:

• Make physical models using manipulatives or physical representations • Construct meaning by generating mental images/visualizing • Draw pictures or diagrams • Create graphic representations make a list, table, or pictograph • Engage in kinesthetic representations of the content

Have examples of each of the above 5 key ideas to share with teachers. Ask for teacher share-outs of how they already incorporate/could start incorporating these into their classrooms. Stress to teachers that nonlinguistic representations are necessary to children’s understanding of mathematical relationships and concepts. Give teachers 20 minutes to read the remainder of chapter 6, which gives many activity/game/lesson examples of how to incorporate these ideas across multiple grade levels. Teachers discuss with their grade level teams:

• How do you already/can you start using manipulatives and other visual representations in the classroom to aid in your students’ development of number sense?

• Which activity or activities could you see yourself using in your classroom? Grade level share-outs. Action Steps:

• Continue once a week growth mindset lessons in the classroom. • Incorporate visual representations into math lessons to express mathematics in a

nonlinguistic way. • Next time: bring an activity or artifact that shows teacher use of visual representations

during math. • Next time: have chapters 5 and 6 of Mathematical Mindsets read and ready to discuss

October: Growth Mindset: Teachers sit with grade level and sit near grade levels above/below. Teacher share-outs of any positive or negative experiences they have had in implementing their growth mindset lessons. Share artifacts with table groups. Whole group share-outs. Pass out a worksheet that goes with the video. Have teachers fill out side 1, answering the questions “List things that you find difficult” and “Things I say to myself about doing these things” Show the video “The Force: A Growth Mindset” https://www.youtube.com/watch?v=HYUJxzh8Raw Ask the following questions:

• What was Yoda asking Luke to do? • What words did Luke say to Yoda? What words did Yoda say to Luke? • In the video, who had a growth mindset and who had a fixed mindset and how do you

know? Which Jedi was successful? Teachers work with their grade level teams to answer the last question on the worksheet “When you are doing something difficult, what are some things you could say to yourself to be more like Yoda? Share-out phrases. Star Wars Growth Mindset lesson from: Mrs. Crabtree’s Counseling Corner http://crabtreecounseling.blogspot.com/?m=1

Book Study Chapters 5 and 6 (45 minutes) Teachers sit with grade level and sit near grade levels above/below. Display the 5 suggestions for opening mathematics tasks and increasing learning potential:

• Open the task so there are multiple methods, pathways, and representations • Include inquiry opportunities • Ask the problem before teaching the method • Extend the task to make it lower floor and higher ceiling • Ask students to convince and reason; be skeptical

Teachers work with their grade level: “After reading this chapter and looking back on any past math lessons (from earlier this year, previous years), think of one specific activity or lesson. Use at least 1 of Boaler’s suggestions to recreate the activity so that you are offering more and deeper learning opportunities to students.” Grade levels work on chart paper to recreate the activity decided on as a team. Give teachers 25 minutes to finish. Grade level share-outs. Number Sense and Numeration (30 minutes) At this point in the school year, all of the grade levels have started teaching number sense. In the lower grade levels students are learning subitizing and place value. In grades 1 and above students are learning place value as well as computation. Teachers will be introduced to activities that will be used to review number sense and computation during intervention (Guided Math). Before teachers get there, set up the room with a table labeled for each grade level. Set up examples of the activities on the respecting grade levels tables. Have all materials ready on the tables so that teachers can test out the games and activities. Teachers will come in, sit at their assigned grade level table and explore the activities. Once they have explored all the activities at their table, they may explore the activities on the grade level above/below or any grade level they wish. Math Specialists will make their way around all the grade level tables. Kindergarten: “Ten Frame Puzzle” activity http://missgiraffesclass.blogspot.com/2015/07/building-number-sense-in-first-grade.html Recycled Egg Carton Ten Frameshttp://missgiraffesclass.blogspot.com/2015/07/building-number-sense-in-first-grade.html “Roll On” (dice version) activity http://missgiraffesclass.blogspot.com/2015/07/building-number-sense-in-first-grade.html “M and M Addition” activity http://whoosinfirst.blogspot.com/2012/09/m-addition.html “The Pocket Game” https://www.youcubed.org/task/the-pocket-game/ Recycled Egg Carton Ten Frames: Roll a ten-sided dice, create the ten frame out of the egg carton and fuzz balls for the number rolled, explain thinking to partner, partner checks answer (is a skeptic), switch roles.

Photo from Miss Girrafe’s Class Blog http://missgiraffesclass.blogspot.com/2015/07/building-number-sense-in-first-grade.html First Grade: “Popcorn Math” activity: http://reliefteachingideas.com/popcorn-maths/ “Snap It” game https://www.youcubed.org/fluency-without-fear/ “Lego Math Challenge Cards” activity http://littlebinsforlittlehands.com/lego-math-challenge-cards/ “Subtraction Smash” activity http://www.recipeforteaching.com/2016/04/subtraction-smash.html Popcorn Math: Student pulls 2 white pieces of paper and one yellow piece of paper from the popcorn bin. Student creates a true number sentence using the three sheets of paper. Student writes the true statement in their math journal.

Photo from Relief Teaching Ideas http://reliefteachingideas.com/popcorn-maths/ Second Grade: “Place Value Picture” http://www.tunstallsteachingtidbits.com/wp-content/uploads/2015/04/pv8-1200x1270.jpg “How Can You Win Every Prize at Chuck E. Cheese’s?” http://robertkaplinsky.com/work/skeeball/ “Base 10 Game” http://www.cassiedahl.com/2015/10/teaching-place-value-with-game.html “Popsicle stick subtraction with regrouping” activity http://www.lessonthis.com/math/popsicle-stick-regrouping-fun/ Subtraction with Regrouping: Use bundles of 10 popsicle sticks to help students understand regrouping. If they have to borrow from the tens place, they take off the rubber band of one cluster and add those sticks to the ones place.

Photo from Lesson This: Popsicle Stick Regrouping Fun http://www.lessonthis.com/math/popsicle-stick-regrouping-fun/ Third Grade: “How Close to 100?” game https://www.youcubed.org/task/how-to-close-100/ “Place Value Beanbag Toss” game http://lightafire3.blogspot.com/2012/01/math-games.html Multiplication with Legos activity http://frugalfun4boys.com/2014/01/09/multiplication-legos-candy-store-math-problem/ Interactive Number Lines http://mrelementarymath.blogspot.com/2015/09/using-interactive-number-lines-to.html “Circles and Stars” https://www.youcubed.org/task/circles-stars/ Interactive Number Lines: Tape a line on the wall and have benchmark numbers to aid students. Can be used for whole numbers, fractions, decimals, etc.

Photos from Mr. Elementary Math: Using Interactive Number Lines http://mrelementarymath.blogspot.com/2015/09/using-interactive-number-lines-to.html Fourth Grade: “Multiplication Squares” game http://games4gains.com/blogs/teaching-ideas/41372740-weve-mathified-the-squares-game “Glow in the Dark Geometry” activity https://www.youcubed.org/task/glow-in-the-dark-geometry-2/ Cupcake trays and unifix math cubes http://teachbesideme.com/fun-ways-to-teach-division-to-kids/?showComment=1378587984169 “Ice Cream Scoop” activity https://www.youcubed.org/task/ice-cream-scoop/ Cupcake trays and unifix math cubes: Student selects a division number sentence. Student gathers the appropriate number of unifix cubes (dividend) and places them one by one into the cupcake tin using the appropriate number of groups (divisor). Student does this until he/she is out of unifix cubes. Student counts the number of cubes in each group to find the answer (product)

Photo from Teach Beside Me: Fun Ways to Teach Division http://teachbesideme.com/fun-ways-to-teach-division-to-kids/?showComment=1378587984169 Fifth Grade: Scholastic Math Maven’s Mysteries (need computer or iPad) http://teacher.scholastic.com/maven/ “Multiplication Battleship” game https://www.teacherspayteachers.com/Product/Multiplication-Battleship-1492384 KenKen Puzzles www.kenkenpuzzle.com “Cheeze-It Area and Perimeter” activity http://www.scholastic.com/teachers/top-teaching/2012/12/10-hands-strategies-teaching-area-and-perimeter Cheeze-It Area and Perimeter: Students explore using Cheeze-Its to see how to create larger or smaller areas and perimeters. Students explore the effects of putting the Cheeze-Its into various shapes and sizes. Can be used purely as exploration or teacher can say “make a shape with __ area/perimeter”

Photos from Scholastic Inc. http://www.scholastic.com/teachers/top-teaching/2012/12/10-hands-strategies-teaching-area-and-perimeter Action Steps:

• Implement 1 or more of the activities suggested for your grade level (or above/below your grade level- choose one that works for your students) during intervention time.

• Continue with once a week growth mindset lessons in the classroom. • Next time: have chapter 7 and 8 of Mathematical Mindsets read and ready to discuss. • Next time: bring an artifact to represent your students learning of number sense (can

support good number sense or poor number sense). November: Growth Mindset (25 minutes) Teachers sit with grade level and sit near grade levels above/below. Take a survey with the teachers at the in-service. On polleverywhere.com select the “live survey” option. Display the website with the survey question on the projector. The question is “Have growth mindset lessons impacted your classroom in a positive way?” Teachers text their answers anonymously to the survey poll number and immediate results are seen on the screen. Use the data gathered to answer questions collaboratively:

• Why do we feel it has had this impact on the campus? • If many people voted “yes”: How can we ensure that students continue to have a growth

mindset? • If many people voted “no”: What is making it a negative experience? What can we do to

change this? Display on the projector and give each teacher a copy of the Effective Effort Rubric http://www.mindsetworks.com/websitemedia/resources/effort-rubric-for-students.pdf As a grade level, teachers must make an Effective Effort Rubric that they could hand out to their students. It does not have to be in rubric form (a table), but using the expectations create a visual for your students to reference the expectations of effort. This can be something you hand out to the students or a visual for the bulletin board. Give the teachers 20 minutes. Grade level share-outs. Book Study Chapters 7 and 8 (30 minutes): Project the following task on the board: As a grade level team, create a self-assessment for students on the current unit of study to use in your classrooms. Make sure the assessment:

• Gives clear statements about the math they are learning • Statements communicate mathematical content • Helps students reflect on what they have learned and what they still need to work on • Has a minimum of 4 statements

Grade levels work together for 20 minutes to create the self-assessments. Grade level share-outs. Number Sense and Computation (50 minutes): Artifact share-out at tables. Whole group share-outs. Hand out the article “At last, A Comprehensive Guide to Help Your Students Develop Good Number Sense” http://topnotchteaching.com/experts/guide-to-develop-number-sense/ Go over the article with teachers, reviewing the skills needed for number sense. Then go over the sections about recognizing good number sense versus poor number sense. Give concrete examples of what to look for (specific actions of children, examples of work). Show “Developing Number Sense Using Tiles, 10-Frames, and The Number Chart” video https://www.youtube.com/watch?v=UYE876S_OzM Continue reading ways to help develop number sense. Remind teachers that intervention (Guided Math) is a way that we are helping develop number sense. Activities in the classroom should be working with children’s needs as well as following Boaler’s 5 components to increase learning potential. Action Steps:

• Carefully monitor students, try to determine who has good number sense and who has poor number sense. Be ready to answer: “How did you help the students with poor number sense? Challenge those with strong number sense?”

• Continue with once a week growth mindset lessons in the classroom. • Next time: have chapter 9 of Mathematical Mindsets read and ready to discuss (last

chapter). • Next time: bring an artifact to represent your students learning of number sense (can

support good number sense or poor number sense). December: Growth Mindset (30 minutes): Teachers sit with PLC groups. Place multiple magazines on each table. Each teacher receives a small rock. Teachers cut out words in the magazines that represent their class’ journey during the implementation of the growth mindset activities this semester. Teachers glue the words on to the rocks. Discuss with your PLC group why you are selecting the words/phrases that you are. How has your class grown over the past 4 months? Give teachers 15 minutes to create their rocks and discuss. Group share-outs.

Photo from Media Cache https://www.pinterest.com/pin/131519251593389284/ Campus wide discussion:

• How can we continue growth mindset activities in our classroom once the PD ends? • Would we do it again next year? Why or why not?

Book Study Chapter 9 (20 minutes): Teachers sit with grade level teams. Project the following questions on the board for group discussion:

• Boaler says that we should value struggle and failure. How can we do this without having the students feel like failure is good enough and there is no need to complete the task correctly?

• What are some of the ways you incorporate technology into your math lessons? • What strategies from the book have you already tried in your classroom? How did it go?

Grade levels discuss for 10 minutes. Grade level share-outs. Number Sense and Computation: Wrap up/ Conclusions. Reflection on previous PD. Teachers were supposed to monitor students (they choose how) to determine each student’s ability in terms of number sense. Table share-outs. Teachers answer the question “How did you help the students with poor number sense? Challenge those with strong number sense?” Whole group share-outs. Discuss the techniques and activities that have been used in the classroom this semester to help develop number sense and computation skills. Ask teachers:

• What specifically stuck out to you the most from this professional development? • Which aspects do you feel that you are going to continue to implement in your classroom

throughout this year or on to future years? • Which idea do you feel was most effective for your students?

Exit ticket: give each teacher an index card. Teacher writes 2 things they learned from the PD on it. Tell teachers that you hope they continue to have children making progress in their classrooms. After all, we don’t want to be the math teacher responsible for someone losing $1,000,000. Show “Lady CLEARLY Does Not Know Her Math on Millionaire” video

https://www.youtube.com/watch?v=hJY5Z13q2LY Thank teachers for taking the time to come to all of the in-services. Evaluation/Accountability Teachers are held accountable for in-service tasks by bringing artifacts to in-services as well as sharing-out with group members. Motivation Math workbooks as well as unit assessments will be used for formative assessments. Benchmark assessments given by Austin ISD will be used for summative assessments (MOY I and MOY II). Students must score a 75% or higher on assessments to at mastery.

Resources: August Mathematical Mindsets by Jo Boaler “You Can Learn Anything” video https://www.khanacademy.org/youcanlearnanything Mindset Kit lesson: https://www.mindsetkit.org/practices/ckjOuOKvRDdmsDTJ “Number Sense-Right Now” by Francis Fennell http://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Skip-Fennell/Number-Sense—Right-Now!/ September “A Pep Talk from Kid President to You” video https://www.youtube.com/results?search_query=kid+president&spfreload=10 Table 3.2 from pages 29 of Mathematical Mindsets by Jo Boaler Figure 3.4 from page 36 of Mathematical Mindsets by Jo Boaler Chapter 6 “Habit 4: Represent Mathematics Nonlinguistically” from Teaching Numeracy: 9 Critical Habits to Ignite Mathematical Thinking by Margie Pearse

October “The Force: Growth Mindset” video https://www.youtube.com/watch?v=HYUJxzh8Raw Star Wars Growth Mindset lesson https://www.youtube.com/watch?v=HYUJxzh8Raw November Mindset Works: Effective Effort Rubric http://www.mindsetworks.com/websitemedia/resources/effort-rubric-for-students.pdf “At last, A Comprehensive Guide to Help Your Students Develop Good Number Sense” article from Top Notch Teaching http://topnotchteaching.com/experts/guide-to-develop-number-sense/ “Developing Number Sense Using Tiles, 10-Frames, and The Number Chart” video https://www.youtube.com/watch?v=UYE876S_OzM December Rock activity https://www.pinterest.com/pin/131519251593389284/ “Lady CLEARLY Does Not Know Her Math on Millionaire” video https://www.youtube.com/watch?v=hJY5Z13q2LY Assessment Resources Mentoring Minds: Motivation Math workbook

The book Mathematical Mindsets brings together teaching mathematics with growth mindset. All of the mindset lessons and videos can be implemented in the classroom (tweak to grade level) to students as part of a mindset lesson. The articles give details about number sense, which is necessary for an elementary teacher to know the meaning, signs of success, and how to help struggling students. The assessment material Motivation Math is the math workbook Langford uses across grade levels. It will be used for formative assessments.