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## Contents

**Developing Preschool Number Sense: An Overview**

Children show their developing number sense in a multitude of ways. It is the role of the teacher to notice when students have mastered a certain concept so that they can assess and understand their students' progress effectively. With the insight gained from quality and developmentally-appropriate assessment, preschool teachers can plan their math curriculum in a way that best supports the learners they serve.

This course is intended for:

- Teachers who currently work with children in preschool settings

- Students in teacher-training programs who intend to teach preschool aged children

- Teachers of older children who wish to understand the framework of mathematical understanding

The topics covered will be:

- Numeral Recognition

- Rote Counting

- One-to-One Correspondence

- Connecting Numbers to Quantities

During this course, learners will be required to reflect on their teaching and knowledge through responding to prompts, media, and interacting with classmates. It is my hope that in completing this mini-course, students will learn not only from the presented text, but also from their interactions with peers in the discussion sections of each unit. The course begins with a discussion forum that is fairly open-ended. This aligns well with a big idea in project-based learning environments. Students learn well when they "relate ... to their prior knowledge and experiences, they can form connections between the new information and the prior knowledge to develop better, larger, and more linked conceptual understanding" (Kracjik & Blumenfeld, 2006, p. 319).

**Needs Assessment**

**Instructional Problem**
Early childhood educators should have a solid background in early mathematical development in order to best serve their students. Being aware of how preschoolers show their understanding of number concepts assists teachers in their assessments. When a teacher knows of the different capabilities to look for, in turn realizing their students' knowledge, they can plan developmentally-appropriate activities that best fit the curriculum's mathematics goals (Center for Innovation in Education, 2011).

**What Will be Learned?**
People who complete this course will learn about how children develop number sense in early childhood. Specifically, learners who complete this course will explore four different ways in which children show their counting abilities.

**Who are the Learners?**
The learners are primarily early childhood educators, specifically those who teach preschool. Other interested candidates might be Kindergarten teachers, day care providers who work with young children, or teacher candidates.

**What is the Instructional Context?**
The instruction occurs online, in the form of a wiki. Therefore, the learner must have access to a computer with internet service. There is no limit to the amount of people who can log onto the course at any time. The course is not timed, so can therefore be completed at the leisure of the learner. Some aspects of instruction might be enhanced by the use of pen and paper or a word-processing program.

**Exploring the Problem and a Proposed Solution**
Learners should understand, explain, reflect, and be able to create lessons pertaining to the four presented ways that children show that they can count.

Unit 1: Numeral Recognition

Unit 2: Rote Counting

Unit 3: One-to-One Correspondence

Unit 4: Connecting Numbers to Quantities

**Goals of the Mini-Course**

- Learners will reflect on their own mathematics instruction or philosophy of education.
- Learners will reflect on the mathematics instruction presented in the mini-course content and the postings of peers.
- Learners will be able to describe the four discussed ways in which children show their counting abilities.
- Learners will apply what they have learned in the course to early childhood instruction by creating activity ideas.

**Performance Objectives**

- Learners will reflect on their teaching or understanding of children's number sense by answering prerequisite questions in the form of writing or a self-designed diagram.

- Learners will suggest various ways to incorporate numeral recognition into their classroom and/or daily routine.

- Learners will explain the place of rote counting in the developmental understanding of number sense.

Unit Three: One-to-One Correspondence

- Learners will share at least one way to reinforce one-to-one correspondence in a preschool classroom.

- Learners will comment on and critique classmates' classroom integration ideas.

Unit Four: Connecting Numerals to Quantities

- Learners will state an example of an assessment to figure out if a child can connect numerals to quantities.

Review and Conclusion This is a self-reflective period of closure with no specific performance objectives.

**Task Analysis**

**Course Purpose:**
The purpose of this course is to present students with number sense lesson ideas, encourage critical examination of these lessons, and foster students' development of sample lessons that they create during the course.

**Learning Outcomes:**

Upon completing this mini-course, students will:

- Be more informed of their own teaching or teaching philosophy.

- Be able to give examples of the four presented ways that children show their sense of numbers.

- Critically reflect on the sample lessons presented in the mini-course and by peers.

- Create sample activity ideas relating to the main ideas.

*Essential Prerequisites*

- An understanding of early childhood development. A developmental psychology course and/or experience working with young children will greatly assist the student in creating developmentally appropriate lesson ideas.
- A positive attitude toward including mathematics instruction in early childhood education.
- A teaching philosophy that embraces interdisciplinary learning.

*Supporting Prerequisites*

- Experience planning lessons for young children.
- An intrinsic motivation to learn.

**Curriculum Map**

**References and Resources**

Alchin, L. K. (2009). One two three four five rhyme. Retrieved from http://www.rhymes.org.uk/one_two_three_four_five.htm

Canida. (2006, Dec 2). How to make playdough (play-doh). Retrieved from http://www.instructables.com/id/How-to-Make-Playdough-Play-doh/

Center for Innovation in Education. (2011). Chapter 5: Counting. Retrieved from http://www.center.edu/NewsletterText/documents/Chapter5.pdf

Essackducks. (Producer) (2011). By the numbers - one to one correspondence games [Web]. Retrieved from http://www.youtube.com/watch?v=1dlKXYv4x-A

Gayle. (n.d.). Preschool fingerplays, action poems, nursery rhymes, and songs. Retrieved from http://www.preschoolrainbow.org/preschool-rhymes.htm

Hubbard, M. (2012). Numeral writing. Retrieved from http://www.hubbardscupboard.org/numeral_writing.html

Krajcik, J., & Blumenfeld, P. (2006). Project-based learning. In K. Sawyer (Eds.), Cambridge handbook of the learning sciences (pp. 317 - 334). New York: Cambridge University Press.

Montessori preschool: Introduction to numeral recognition[Web]. (2010). Retrieved from http://www.youtube.com/watch?v=REfB7zkbIwo

Number and operations grade by grade. (n.d.). Retrieved from http://www.ride.ri.gov/instruction/curriculum/rhodeisland/expectations/numbers.pdf

Paperback sample of anno's counting book by mitsumasa anno. (n.d.). Retrieved from http://www.barnesandnoble.com/sample/read/9780064431231

Pica, R. (2012). Help your child understand one-to-one correspondence. Retrieved from http://www.education.com/magazine/column/entry/Help_Your_Child_Understand/

seelis99. (2009). Mouse count book [Web]. Retrieved from http://www.youtube.com/watch?v=7zVGy0AiyzI

Sesame Street: Feist sings 1,2,3,4. 2008. Film. 15 Nov 2012. <http://www.youtube.com/watch?v=fZ9WiuJPnNA>.