Each module begins with an introduction video, and then a 20-30 minute presentation. After those are the complimentary videos and materials you see below, such as Focus on the Child videos and ideas to help you Look for Math All Around You. So please review the introductory video and text and launch the Sets presentation when you are ready.
About this module
Sets are basic to children’s thinking and learning. They are also basic to our number system. One of the most important jobs of each number is to describe “how many” there are in a set of things. Before we can figure out how many apples there are, we have to decide which things are apples, and which are not. Once we’ve created the set of things that are apples, perhaps by separating them from the oranges, then we can count them. Counting requires a set, and as a result, the properties of sets have a large influence on mathematics.
Focus on the Child
Focusing on children’s mathematical thinking is big.
These videos are taken from our Focus on the Child video series. They are one-on-one interviews with individual children. The interviews are designed to elicit evidence of children’s mathematical thinking. They are not teaching episodes or formal assessments.
Overall guiding questions as you watch them include:
- Where is the math?
- Which big ideas does this child understand?
- What evidence do you see of the child’s thinking?
- Where is this child along the developmental trajectory?
- How would you assist the child to enhance understanding?
Focus on the Lesson
Focusing on the lesson is big.
These videos are taken from our Focus on the Lesson video series. They represent planned activities for children designed to teach specific mathematical ideas that can compliment (not replace) existing math curricula. Overall guiding questions as you
watch the video includes:
- What evidence do you see of the children’s thinking?
- What evidence do you see of the teacher’s thinking?
- How might this experience connect to other math?
People Sort: Details
Big Idea Focus
In this lesson, children:
Identify and describe observable attributes of children and clothing Physically form sets according to given attributes Use rules to sort and re-sort each other into sets using various attributes (KG goal)
- Five Creatures by Emily Jenkins
- Two large circles made with masking tape or yarn for children to stand in, or two hula-hoops
- Dress-up clothes (for children wearing school uniforms)
Read Five Creatures at least once prior to this lesson. It is best to introduce this activity with a group of about 10 children. Later, this is a good whole-group or transition activity. For example, call all children with tie shoes to line up, then children wearing shoes with straps.
People Sort: Video
Listen before viewing
Listen after viewing
Questions to Answer
- children label attributes
- children define attributes
- children make sets
- teacher does activity with small group of children
- teacher focuses children on observable attributes
- teacher labels the set created
- builds understanding of the concept of attribute, which is key to all areas of mathematics.
Look for Math All Around You
Helping children find math all around us…
Organized by different areas of the classroom, Math All Around You sections are meant to be idea generators. For each area, there are ideas of what children might be saying or doing mathematically and what teachers might say or do to build understanding. These are not intended to be checklists, but rather a jumping off point for discussion of how adults can “mathematize” the world around them.
Children's Literature: Data, Attribute & Pattern
Finding math in the books we read…
Good math can be found in good children’s books! Below is a list of books that are rich in opportunities for mathematical thinking and math talk. They serve as jumping-off points for engaging math activities and math discussions. They are not books that explain math to children, which are already found in the various curriculum but can often be lacking in chances to inspire children in a more fun, meaningful, and concrete way.
Aardema, V. & Vidal, B. Bringing the Rain to Kapiti Plain. (Puffin Books, 1992)
This classic cumulative rhyming tale shows one form of growing pattern.
Aston, D. & Long, S. An Egg is Quiet. (Chronicle Books, 2006)
Descriptions of many sorts of eggs could lead to discussion of attributes or questions to answer with data.
Carle, E. Today is Monday. (Philomel Books, 1997)
Another rollicking cumulative rhyme to show the idea of a growing pattern.
Geringer, L. and Lobel, A. A Three Hat Day. (HarperCollins, 1987)
Questions to answer with data: How many hats do you have? What different kinds of hats do you have?
Hoban, T. is it red? is it yellow? is it blue? (Greenwillow, 1978)
Beautiful photos inspire exploration of color and other attributes.
Komiya, T. Life-Size Zoo. (Seven Footer Kids, 2008) Komiya, T. More Life-Size Zoo. (Seven Footer Kids, 2010)
Lots of information about animals to stimulate discussion, analysis, and further data collection.
Martin Jr, B. & Carle, E. Baby Bear, Baby Bear, What Do You See? (Henry Holt, 2007)
Martin Jr, B. & Carle, E. Brown Bear, Brown Bear, What Do You See? (Henry Holt, 1967)
Martin Jr, B. & Carle, E. Panda Bear, Panda Bear, What Do You See? (Henry Holt, 2003)
Martin Jr, B. & Carle, E. Polar Bear, Polar Bear, What Do You Hear? (Henry Holt, 1991)
All four of these favorites follow a different, yet similar, repeating pattern.
Morris, A. & Heyman, K. Hats Hats Hats. (Lothrop, Lee and Shepard Books, 1993)
Morris, A. & Heyman, K. Houses and Homes. (HarperCollins, 1995)
Morris, A. & Heyman, K. On the Go. (HarperCollins, 1994)
Morris, A. &Heyman, K. Shoes Shoes Shoes. (HarperCollins, 1998)
Different examples of the same class of object from around the world to motivate data collection close to home.
Swinburne, S. Lots and Lots of Zebra Stripes. (Boyds Mills Press, 2002)
Photos of patterns in nature to encourage young pattern noticers and pattern describers.
Swinburne, S. Whose Shoes? (Boyds Mills Press, 2010)
Photos and simple text spur children to consider questions about shoes and jobs.
Williams, S. & Vivas, J. I Went Walking. (Harcourt, 2004)
This story shows the simple growing pattern of “one more.
Adult Learning Activities
Learning as an adult…
Adult Learning Activities get adults engaged in doing math as adults. While they involve basic math concepts, they are not children’s math that we are asking adults to do; nor are they activities to try with young children. They are designed so that they:
- are based on a central and coherent concept of the discipline being explored;
- pose a puzzle or problem;
- are interesting/non-routine enough to capture and retain adult attention;
- clearly focus thinking on the relevant content/ideas;
- are easy to implement in an adult PD setting;
- may have more than one solution or route to solution;
- set the stage for understanding foundational Big Ideas.
Focus on the Child with Viewing Notes
This child successfully attempts to match geo-solids using triangular prism-shaped blocks. Focus on the Child videos are taken from one-on-one interviews with individual children. The interviews are designed to elicit evidence of children’s mathematical thinking. They are not teaching episodes or formal assessments.
A second grader has a partial understanding of counting in equal groups. Focus on the Child videos are taken from one-on-one interviews with individual children. The interviews are designed to elicit evidence of children’s mathematical thinking. They are not teaching episodes or formal assessments.
This second grader uses a known number combination (3 + 9) to solve a subtraction problem, showing an understanding of how addition and subtraction are related as inverse operations. Focus on the Child videos are taken from one-on-one interviews with individual children. The interviews are designed to elicit evidence of children’s mathematical thinking.
Traditions around food and feasts provide rich opportunities to connect math at school with children’s experiences at home. From Diwali to Thanksgiving, fall is a season of special meals with loved ones.
A panel of early math experts engage with the audience at Promising Math 2017 to consider the challenges of getting a true picture of what young children understand about numbers.
The role of play and importance of shared experiences in early math is discussed with Rodrigo Gutiérrez, Co-Director of the Center for Retention-Recruitment for Math Teachers at University of Arizona.
How is it possible to have too many tamales? Well, Maria finds out in the holiday storybook Too Many Tamales by author Gary Soto.
Halla Jmourko discusses two innovative instructional tools for integrating language and math concepts in the classroom, The Cubing Game and Three Way Tie.