Reflections from a Kindergarten Lesson (Part 2)

After a lunch break and change of teachers, we experienced our afternoon model lesson. Here we continued to look at kindergarteners and how to all students to own their learning through Math Workshop. There were many similar thoughts and reflections from the morning groups of teachers.

Model Lesson: Afternoon Session

In this unit, students will be exploring measurement by developing strategies for measuring the length of an object. Students will practice recording their measurements. 

Model Lesson: Kinder Unit 4 Session 1.3
Date: November 17th, 2016
Presenter: Dr. Sandy Fluck

Math Workshop (Investigations Style)

Math Workshop is designed to:

• Provide students with repeated experience with the concepts being learned and time to practice important skills and refine strategies. 
• Provide time for the teacher to work with individual students and small groups and to assess students' learning and understanding. 
• Help students develop independence and learn to take responsibility for their own learning as they choose activities, keep track of their work, use and take care of classroom materials, and work with others.

Setting up the Lesson & Math Workshop

The opening and closing discussions are a critical part to the day's lesson. In this conversation, Dr. Fluck was asking students to consider how to measure the strip of paper. Students shared a few different ways:

Should they be lined up (up and down) and lined up across the strip (picture on the left)? or 

Should they be lined up around the edges of the paper strip (picture on the right)? 

Asking questions that guide students to think about which method might be better here is a challenging task, yet critical in allowing students problem solve.

In Kindergarten, teachers may feel the need to provide structures and support for students to engage in independent learning through Math Workshop. While grade level, class size, physical space, students population and management styles are all factors in designing a Math Workshop for your classroom, do not be afraid to give students full access to choice.


The video above demonstrates a lesson where students engaged in Math Workshop with complete control over the activities they chose for themselves. The introduction to the lesson provides the structure and expectations for Math Workshop. The picture to the right shows the students the 4 options for activities during workshop time:

1. Counting Jar
2. Measure paperstrips A, B, & C (with craft sticks)
3. Measure footprints (with snapcubes)

One the concepts the students will explore through the Unit is measuring various things using different units of measure - some big some small. Students will be ask to think about how many small units it takes compared to how many big units it takes. Which will take more units and why?
Asking students the question early in the unit allows students to begin to think about it and consider it as they gain more and more experiences measuring different items.

Classroom Layout & Manipulatives Management

Every classroom is different in regards to layout and space. However, consider how you can place manipulatives so that students can gather and cleanup manipulatives themselves. For the model classroom, the materials were either on a table or at the front of the classroom. Students selected their materials and were able to work either on the carpet (Counting Jar and measuring footprints ) or at the table (measuring paper strips). In addition, you may consider using various tubs, cups, plastic bags or bins to store manipulatives and materials that allows students self-manage their materials.

Measuring Footprints

Students used snap cubes to measure pre-drawn footprints. Snapcubes were located in one large bin in the middle of the carpet area for everyone to use. Students collected a footprint paper from the table and sat on the carpet to measure and record.

Monitoring Students

The teacher's role during math workshop is to walk around and monitor student progress. Many Investigation sessions provide Assessment Checklists or questions to guide teachers in what to look for.
There is a careful balance between guided students and allowing students to make discoveries on their own.

The picture to the right shows students measuring their own feet (which they did earlier in the week). However, today students needed to measure pre-drawn footprints that students had brought in from home.
While you may check for understanding before releasing students to Math Workshop time, there may be a need to check-in with each group or "station". Guiding students to stay on track to the goal of the activity may involve careful questioning so that students problem-solve themselves, or you may need to correct off-task activities.

The Counting Jar

The Counting Jar is a very important classroom routine that support students' Number Sense. While Number Sense is a cognitive skill that is related to brain development, young students need plenty of experiences and a variety throughout the year to target where they are at developmentally.
Students are working on a variety of skills that impact Number Sense:

• one-to-one correspondence
• number conservation
• number sequence
• cardinality
• subitizing

When students are counting objects from the counting jar, can they:

• count in number sequence
• count each object once (1:1 correspondence)
• know how many (total) 
• represent the quantity with a numeral
• represent the quantity with the same number of a different object

Measuring and Recording

Keeping track of student sheets can be a lot of work. There may be piles of papers everywhere is your classroom. What might be some solutions to managing all the student papers? Here are a few suggestions. Consider what might work in your classroom and tweak it to fit you and your students.
Possible ideas:

• using a student folder
• "station" bins for done work
• math notebook

Lesson Closure: The Discussion

Probably the most important part of the lesson is the closure discussion. Here students share what they noticed. As mathematicians, we are always looking for patterns. What did you notice about today's math investigations?
It may also  be a time to just listen. Listen to what your students notice about the activities. Used this information to inform how to move forward with tomorrow's math time. It may guide you in what the emphasis might be in your work.
In the discussion, you can also gather students insights and expand on them to provide students the formal understanding for the lesson.
There are a variety of purposes to the discussion time. Use the "Ongoing Assessment Questions" and the "Discussion Check-in" to guide your conversations. Each session included these two components.

Now What? Next Steps for Implementing Number Talks

So, you’ve heard about Number Talks or maybe your math coach has modeled a Number Talk in your classroom. Now what?

Establish the Routine:                  

• Use hand signals. 
  
•  Record all student solutions without teacher comment.
• Ask students to justify or defend an answer.
•  Provide students with sentence frames to support communication.
• Establish a classroom community that is supportive and helping everyone learn. There is not one best solution or strategy. We all can learn math.

How do I prepare for my next Number Talk?

• Consider the skills within your unit or skills that your students need more support.
•  Create or select one problem or a series of 3-4 problems. Refer to the Number Talks book by Sherry Perrish for a selection of problems. Or refer to the handout “Grades 3 through 5” by Boston Public Schools.
• Prior to the classroom Number Talks, solve each problem using strategies that students will possibly come up with. This prep work is worth the time. Consider using the Planning Guide (from Number Talks Quick Start Guide pages 15-25, Oakland by Unified School District)

Maximizing your Number Talk Experience

• Prior to the Number Talk, make sure you worked out all possible strategies. This will help you decipher students thinking and record the problem using good syntax.
• Start with easier problems. As you introduce the routine or want students to focus on a new strategy, start with problems that have smaller numbers. This will help students focus on the strategy and not get overwhelmed with the higher numbers.
• Connect the Number Talk to the math lesson for that day. This may not always be possible, but can really lead to good conversations and preloading students with strategies for that day’s lessons. 
• After the Number Talk, have students solve a problem, on paper, that is similar to the problem(s) from that day’s Number Talk. This could be an “Exit Ticket” for your Number Talk. 
• After the Number Talks have students use their math journals to answer an extension question.
• Which strategy was most efficient for “the problem”?
•  Pose a potential mistake or misconception and have students write how to fix it.
• Have students write to a friend explaining how to solve a similar problem.
• Scaffold Number Talks during the week to create problem sets that have the same strategy focus, but the numbers get increasingly bigger.

Number Talks & Talk Moves

Number Talks are powerful routines that can be used at any grade level.

What is the purpose of  number talks?

The purpose of  number talks at the beginning of kindergarten is to help students develop number sense. Later in the year, number talks should help students transition from the pictorial representation to a number sentence. (CCGPS Ongoing Standards for Mathematical Practice 1, 2, 3, 6, 7, 8).

What are Number Talks?

• Classroom conversations around purposely crafted computation problems that are solved mentally.
• The problems are designed to elicit specific strategies that focus on number relationships and number theory.
• They provide structured practice for mental math as well as promote the value in using mental math to compute.
• Number talks about the importance of being flexible with numbers and using a variety of strategies for computation.
• Students are given problems in either whole class or small-group settings and are expected to solve them accurately, efficiently, and flexibly.

Key components Number Talks

• Classroom Environment And Community
• Classroom discussion
• Teacher's role
• The Role of mental math 
• Purposeful computation problem

Number Talk Format

• Teacher presents the problem.
• Students figure out the answer on their own (use hand signals).
• Students share answers (all answers are accepted).
• Students defend their answer.
• Class Agrees on the "real" answer for the problem.
• Steps are repeated for more problems in the number string.

Note: During a number talk, the teacher only serves as a recorder and facilitator, not as a teacher


Teacher's role

• Provides a safe environment where each child's thinking is valued.
• Selects groups or strings of problems that allow access all children.
• Select problems intentionally highlight mathematical concepts.
• Focuses on how children got answer.
• Provides wait time.
• Shifts focus from "see what I see" to "what do you do see?"
• Records, clarifies, restates.
• Realizes that if the children do't "get it" then it is the teacher's responsibility to figure out the misconception  or lack of proficiency and to begin instruction at that point.

Questions for the teacher to ask

• Who would like to share their thinking?
• Who would like to defend their answer?
• What strategy did you use?
• How many people solved it the same way as (student)?
• Does anyone have any questions for (student)?
• (student), Can you tell us where you got that five from?
• How did you figure that out?
• What was the first thing your eyes saw, or your brain did?

Focus on the mathematical process process- not answer getting

• Students are asked to defend or justify their answers to prove their thinking.
• Students have a sense of shared authority In determining in determining whether the answer is accurate.
• Teacher is not the ultimate authority.
• Wrong answers are used as opportunities to unearth misconceptions.
• Students investigate their thinking and learn from their mistakes.
• Mistakes play an important role in their learningI and provide opportunities to question and analyze thinking, bring misconceptions to the forefront and solidify understanding.

Resources for Number Talks:

Elementary Math Level

• Number Talks: Helping Children Build Mental Math and Computation Strategies Grades K-5, update Common Core Connections by Sherry Parrish (Math Solutions Store) *There are resources at the bottom of the page on the Math Solutions Store for the book.
• Number Talks: Building Numerical Reasoning Article by Sherry Perrish, Math Solutions published in NCTM”s Teaching Childrens Mathematics October 2011 (click here for the article)
• Sherry Perrish: Number TalksYouTube Video “Number Talks: Building Numerical Reasoning” by Sherry Parrish, Scholastic (click here)

“Until I began to make some shifts in thinking about how students learn and maybe best practices.  That I avoided writing problems horizontally. Because for the very things you're describing. I justified that if I already had it recorded vertically that they could go into that procedure and get a correct answer. Why put the confusing out there.

Now, I’m going to write just about all of my problems horizontally. I want to push on that place value piece. I want the mis conceptions to come to the forefront so that we can deal with them and have conversations around it.”  

Sherry Parrish, Number Talks: Building Numerical Reasoning on YouTube (Time 11:32 - 12:13)

Other Resources:

1. Locust Grove Elementary School: The Math Coach Locus Grove has resources by grade level - Kindergarten through Grade 5. 
2. Math Perspectives: Math Perspectives has resources, including videos and articles, for Number Talks.                             
3. Pleasanton USD - Math Moodle: The Math Coach has  resources for Number Talks oragnized by grade level. These resources follow Sherry Parrish's structure and format in her book Number Talks.   
4. Billings Public Schools: Resources from Sherry Parrish's book, broken out by grade K-5.
5. Number Strings: The blog Number Strings poses series of 4-5 math problems student do mentally. The basic structure for the classroom discussion is the same as a Number Talk. The string of problems are strategically chosen to support students thinking and possibly highlight a specific strategy students should focus on.
• Personally, I read this one and was impressed with the amount of reflection included in the Number String analysis. The teacher does a great job explaining why the number string was chosen, purpose, skills working, and analyzing the student conversation after completing in class. The teacher even includes how they would change the Number String for next time.
6. Math Talks: A variety of Number Talks can be found here and span several grade levels. Even include Pattern Talks.

Secondary Math Level

1. Number Talk Blog: A High School Math Teacher blogging about her experience using Number Talks
2. Article from Math Perspectives: Number Talks
3. Article from MathWire.com: How can Talk Moves and Mathematical Discussions support Writing?