Number Sense in Third Grade
Becca Mesecher
University of Missouri
Review of Literature and Theory
- Griffin (2004)-Number sense is difficult to define but easy to recognize
- Simply put, students should have flexibility in their use of numbers and number relationships when computing operations
- Vygotsky's Social-Constructivist theory
- Sherry Parrish's book- "Number Talks: Helping Children Build Mental Math and Computation Strategies" (2014)
- Number talks have profound impact on student growth
Research Background
About Me
Pleasant Lea Elementary
Ms. Mesecher's Class
- 25 third graders; 13 boys and 12 girls
- Student population: 21 White, 2 Black, 1 Asian, and 1 Hispanic
- 1 student on an IEP for math and reading; 2 students in AIM
- 2 students who received ELL services
- Blue Springs, MO
- Always been a Tiger--Fellowship Program and Mizzou
- Bachelor of Science in Elementary Education with a Minor in History
- Always wanted to be a teacher
- Back home in KC to complete Fellows
- 574 Students- Kindergarten through 6th grade
- 30.2% Free and Reduced Lunch
- 4.9% Asian, 8% Black, 6.8% Hispanic, 74.4% White/Non-Hispanic
- 10.1% English Language Learners (ELL)
- High district expectations, little resources
- Early frustrations with simple concepts
- sticking with one method, "stacking" and making errors with procedures
- Fixed mindset with little critical thinking
- Common Core State Standards focus on reasoning and understanding, not the tricks
Data Collection
Lee's Summit R-7
- Suburb of Kansas City
- 17, 600 Students
- 18 Elementary Schools, 3 Middle, 3 High Schools
- Teacher reflection journal
- Anecdotal notes
- Observations (photos and videos)
- Student interest inventories
- Student work samples
- Focus student interviews
"What happens when I focus on number sense with my third grade students?"
Data Analysis
Research Reflection
Changes in Ability
Ability Shifts
The Journey Begins:
Pre-Number Sense
- Noticed changes and growth in 2 areas: attitude and ability
- Attitude = effort to use strategies, engagement in lessons, risk taking
- Ability = computation accuracy and transfer to new operations or further than discussed
- Organized sequentially: Pre-Number Sense, Getting Started, and Making Progress
Getting Started:
Beginning Number Sense
- I could tell early that math was a struggle.
- Gave math interest inventory and analyzed the results
- I began to see improvements in observations I made of my students
- Unexpected surprises
- Came up with a test of their abilities, became aware of learning from one another
- Difficulty gauging impact on students' ability because it was a mental math exercise. I wasn't hitting the students I wanted to because they weren't willing to share as often.
- I decided to give a few different tasks to monitor the impact on all students.
- Vygotsky (1978): meet them where they are!
- Sherry Parrish's book and number talks were born
- Began with addition strategies: (1) making tens, (2) making landmark or friendly numbers, (3) doubles/near doubles, (4) break into place value, and (5) adding in chunks
Future Plans
- Never too late to take it back and build it up
- Just like Boonen et al. (2011) said, be aware of what strategies students are or are not ready for.
- Begin early and stay on it. Use the thinking in everything you do.
- Unfortunately, at the end of the year, I felt as though I didn't fully reach those students I was the most concerned about.
- "When we began to share out ideas, we were stuck at explaining as 'I added them'. By the time we finished, seven different strategies were on the board and had been fully explained."
--Teacher notebook reflection on November 18, 2014
- I also gave the same strategy development questions from the beginning of the year to the same focus students on March 26, 2015. This was my favorite response:
- On October 14, 2014, I reflected in my teacher journal-- "They don't enjoy talking about how they solved their problems. I need to encourage them more and show them it is okay to make mistakes and struggle."
- Number talks typically lasted 10-15 minutes in addition to our normal math instruction
- One problem written horizontally on the board, wait for signal that most students have solved mentally, then discuss
- ALL solutions accepted and discussed by students willing to share
"I cannot wait to start this with my students! It is going to be difficult starting these thoughts and ways of thinking when students are in the third grade but it's a place to start."
Important findings from Math Interest Inventory on October 14, 2014
Alex's Choice of Strategies to Solve.
March 13, 2015
"Sorry it took me so long! I was explaining and showing EVERYTHING that happened in my head to solve the problem!" --Sabrina
Sources
- Though, by the end of first semester I was still finding myself frustrated.
-Reflection in teacher notebook November 4, 2014
Image from the board during an early number sense lesson on November 30, 2014.
- I will be teaching fourth grade at Elm Grove Elementary in the Fort Osage School district with my best friend.
- I want to continue implementing number sense lessons and a critical thinking focus.
- I will use active research to improve instruction in my classroom.
- I get to utilize my history/social studies background as the content specialist for 4th grade.
- About to explore Costa Rica with my dad!
- Boonen, A., Kolkman, M., & Kroesbergen, E. (2011). The relation between teachers' math talk and the acquisition of number sense within kindergarten classrooms. Journal of School Psychology, 49, 281-299.
- Griffin, S. (2004). Building number sense with number worlds: A mathematics program for young children. Early Childhood Research Quarterly, 19, 173-180.
- Parrish, S. (2011). Number talks build numerical reasoning. Teaching Children Mathematics, 18(3), 198-206.
- Parrish, S. (2014). Number talks: Helping children build mental math and computation strategies. Sausalito, CA: Math Solutions.
- Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, Mass.: Harvard University Press.
Changes in Attitude
Making Progress
Wrap Up
My Fellowship Experience
- Saw a need for change so we sped up the pace of the strategy lessons
- Expand the "tool belt"
- As a third grade teacher, I was excited to jump in to the curriculum that was going to be all new to my students.
- We began hitting walls in the first unit--all of which was a review of skills.
- Students weren't sure how to react to them at first--some felt the problems were too easy.
- We practiced everywhere we could.
- I was impressed with first reactions, though not always using the strategy taught, they challenged themselves and others often.
- It takes a TEAM. Teaching is not about the individual, you need support.
- Relationships are the foundation of teaching
- Impact of coursework and professors
- West is best!
Attitude Shifts
I would like to thank...
- I felt good about where most of my students were with their addition abilities as we made our way into subtraction.
- Deficits in subtraction understanding made even more aware by new skills in addition.
- I could use what I had learned from my research to tackle a whole new
operation with my kiddos!
- Students much more excited to share and participate
- Their favorite strategy was right in their comfort zone.
- Willingness to take risks outside of what had been taught
Jeanie Cook- Fellows Mentor
Lindsey Donelson- Partner Fellow
- "While working with Jeanie today, Britney looked at 10-8 and stacked it, then wasn't sure how to solve because regrouping gave her the exact same problem." (November 11, 2014)
Britney's Strategy Development Answer (Sept. 12, 2014)
Student interviews of the focus group conducted on January 22, 2015 taught me 2 things:
Expanding Beyond
Interest Inventory Responses from October 14, 2014
On March 23, 2015, Alex described his process to solve the problem 70 x 3:
(Never discussed multiplication!)
- Looked for simple fact (7x3)
- Hadn't memorized his 3's or 7's yet
- Used the doubles fact 7+7, then friendly numbers
1) All 10 focus students interviewed responded that they liked explaining how they solved problems.
(up from only 6 in the entire class!)
Alex's Strategy Development Answer (Sept. 12, 2014)
Focus Student Interview Responses from March 13, 2015
2) We needed to move faster with more challenging problems to keep students engaged and motivated.
Interest Inventory Responses from April 9, 2015
Kelly Weimer, Angie Pinnell, and Trish Williams
(My third grade team/ "School Moms")
Pleasant Lea Elementary Staff and Students
My parents and family
My Fellows professors and
West cohort group