Hailey Sternberger ID Portfolio

About Me

Hi! My name is Hailey Sternberger, and I am a Childhood Education 1–6 teacher with a concentration in mathematics. I graduated from SUNY Old Westbury with my Bachelor’s degree in Childhood Education and am currently pursuing my master’s degree in Curriculum and Instruction. I currently work as a math support teacher in an elementary school, where I enjoy helping students build their confidence and understanding in mathematics.

I am especially interested in learning more about instructional strategies that make learning meaningful and accessible for all students. Through my teaching experience, I have become interested in how hands-on learning and math manipulatives can help students develop a deeper understanding of mathematical concepts.

Outside of teaching, I enjoy trying new coffee shops, reading, and being creative. I look forward to continuing to grow as an educator and sharing ideas with other teachers through KNILT!

My Topic and Purpose

My mini-course, Using Manipulatives to Build Mathematical Understanding, will focus on how elementary teachers can use hands-on math materials, such as linking cubes, counters, and base-ten blocks, to help students develop a deeper understanding of mathematical concepts. The course will explore how manipulatives can support students in connecting concrete materials to drawings, numbers, and mathematical symbols. I chose this topic because I currently work as a math support teacher in an elementary school and want to learn more about effective strategies for helping students understand math. In my role, I work with students who have different levels of mathematical understanding, and I am interested in learning how hands-on activities can help students make sense of challenging concepts. This topic also connects to our course readings, particularly Perkins and Blythe’s (1994) ideas about teaching for understanding and A Private Universe, which demonstrated how students can have misconceptions even when they believe they understand a concept. Through this mini-course, I hope to help teachers learn practical strategies for using manipulatives to make math more meaningful and support students in developing confidence and a deeper understanding of mathematics. As a newer educator, I want to continue developing my instructional strategies and learn how to better support students with different learning needs in mathematics.

Scope of Learning Outcomes and Content

This mini-course is designed to develop teachers’ knowledge, skills, and attitudes toward using hands-on learning in elementary mathematics. In terms of knowledge, teachers will develop a better understanding of how manipulatives can support conceptual understanding and help students connect concrete representations to abstract mathematical ideas. They will also learn about the importance of identifying student misconceptions and recognizing that students may be able to solve a problem without fully understanding the concept.

In terms of skills, teachers will develop the ability to select appropriate manipulatives for different math concepts, design hands-on learning activities, and use questioning and observation to support student thinking. They will also learn how to connect manipulatives to drawings, numbers, and mathematical symbols to help students develop a deeper understanding of mathematics. In terms of attitudes, I hope teachers will develop a greater appreciation for hands-on learning and become more confident in using manipulatives as part of their instruction. I also want teachers to recognize the importance of being patient with students’ learning processes and encouraging them to explain their thinking rather than focusing only on getting the correct answer. Overall, the mini-course aims to help teachers become more intentional in their use of manipulatives and develop a positive mindset toward using hands-on strategies to support all learners in mathematics.

Needs Assessment

The Educational Opportunity

My mini-course, Using Manipulatives to Build Mathematical Understanding, will focus on helping elementary teachers use hands-on math materials to support students’ conceptual understanding. The educational opportunity is to help teachers become more intentional in how they use manipulatives to support learning, rather than using them only as a way to make math activities more engaging. Students may be able to memorize math facts or follow a procedure without fully understanding the mathematical concepts behind it. This connects to Perkins and Blythe (1994), who emphasize the importance of teaching for understanding, as well as the video A Private Universe, which demonstrates how students can have misconceptions even when they believe they understand a concept.

Shambaugh and Magliaro (1997) explain that needs assessment helps designers understand what is already known about a problem, what has already been done to address it, and what information is needed to guide instructional design. For my project, I want to explore how teachers currently use manipulatives and what additional knowledge or skills may help them use these materials more effectively to support mathematical understanding.

The Learners/Participants Involved

The intended learners for this mini-course are elementary school teachers who teach mathematics, particularly those working with students in grades 1–5. These teachers may have different levels of experience using manipulatives and supporting students who struggle with mathematical concepts. As a math support teacher, I am interested in learning more about effective ways to use hands-on materials to support students with different learning needs. The course will be designed for teachers who want to strengthen their math instruction and develop practical strategies they can use in their classrooms.

Analysis of Gaps in Knowledge and Skills: Reality vs. Ideal

According to Shambaugh and Magliaro (1997), needs assessment involves gathering information about the learning task, learners, and instructional context in order to better understand the instructional problem. The authors also explain that designers should identify what is already known and use this information to generate goals for instruction.

The current reality I am interested in exploring is how elementary teachers use math manipulatives in their classrooms. Teachers may already use materials such as linking cubes, counters, and base-ten blocks, but they may have different levels of knowledge and confidence in selecting materials, connecting them to mathematical concepts, and using them to address student misconceptions. I would like to learn more about these current practices through a literature review and, if possible, a survey or conversations with elementary teachers.

The ideal situation would be for teachers to understand why and when to use specific manipulatives, how to connect concrete materials to drawings and mathematical symbols, and how to use questioning to encourage students to explain their thinking. Teachers would also be able to recognize when students are using manipulatives meaningfully rather than simply following a procedure without understanding the concept.

The gap I hope to address is the knowledge and skills needed to move from simply providing students with math materials to intentionally designing learning experiences that support deeper mathematical understanding. The needs assessment will help me identify what teachers already know, what they need to learn, and how the mini-course can be designed to address those needs.

Existing Efforts to Address This Gap

There are already efforts to support mathematical understanding through hands-on learning, including the use of manipulatives, visual representations, and small-group instruction. Teachers may use curriculum materials, professional development, and instructional activities to incorporate these strategies into their classrooms. However, the availability of manipulatives does not necessarily mean that teachers have the knowledge or skills to use them effectively.

Intent Statement

The intent of my mini-course is to help elementary teachers develop the knowledge and skills needed to use math manipulatives intentionally to support students’ mathematical understanding. Through the course, teachers will learn how to select appropriate manipulatives, design hands-on activities, and use questioning and assessment to identify student thinking and misconceptions. Teachers will also have opportunities to apply what they learn by creating a math activity that connects concrete representations to drawings, numbers, and mathematical symbols.

Following Shambaugh and Magliaro’s (1997) needs assessment approach, I will use information gathered about the problem, learners, and instructional context to guide the development of my course goals and learning activities. By addressing these needs, the mini-course will support teachers in creating more meaningful math learning experiences and helping students develop a deeper understanding of mathematical concepts.

Analysis of the Learner and Context

Who Are the Participants?

The intended learners for my mini-course are elementary school teachers who teach mathematics, particularly those working with students in grades 1–5. The participants may include new teachers, experienced teachers, and teachers who provide math intervention or support. They will have different levels of experience using math manipulatives and teaching mathematical concepts.

Prior Experiences, Knowledge, and Skills

The participants may already have experience using common math manipulatives, such as linking cubes, counters, base-ten blocks, and number lines. They may also have experience teaching addition, subtraction, place value, and other elementary math concepts. However, their knowledge and confidence in using these materials may vary.

Some teachers may already use manipulatives regularly, while others may primarily rely on worksheets, textbooks, or direct instruction. The mini-course will build on the knowledge teachers already have and introduce ways to use manipulatives more intentionally to support conceptual understanding.

Participants may also have experience working with students who have different learning needs, including students who struggle with math concepts or benefit from visual and hands-on learning. These experiences can help teachers connect the content of the mini-course to their own classrooms.

Instructional Context

Teachers will be able to access the course online and work through the materials at their own pace. The course will include instructional content, examples of math manipulatives, practical teaching strategies, and activities that allow participants to apply what they learn.

The learning environment will be designed to support independent professional development. Teachers may complete the course at home, during a planning period, or in another setting where they have access to a computer and the internet. The course will be organized into short sections so that teachers can learn the material without needing to attend a traditional in-person professional development session.

Time and Resources

I envision the mini-course taking approximately 45–60 minutes to complete, although the exact time may change as I develop the lessons and activities. Teachers will need access to a computer or other internet-connected device to view the KNILT materials. They may also benefit from having access to math manipulatives, such as linking cubes, counters, base-ten blocks, or number lines, so they can practice the strategies introduced in the course.

Additional resources may include sample elementary math lessons, videos or images demonstrating the use of manipulatives, and opportunities for teachers to create their own hands-on math activity. These resources will help participants connect the information from the course to their own classroom instruction.

Learning Environment and Support

The mini-course will provide teachers with opportunities to learn independently and apply new strategies to their own teaching. Participants will be encouraged to reflect on how they currently use manipulatives and consider ways to improve their instructional practices.The course will be designed to be practical and accessible for teachers with different levels of experience. By including examples, demonstrations, and an opportunity to design a math activity, the mini-course will support teachers in developing the knowledge and skills needed to use manipulatives more effectively to build mathematical understanding.

Performance-Based Objectives

After completing this mini-course, learners will be able to:

Explain how math manipulatives support conceptual understanding and help elementary students make connections between concrete materials and abstract mathematical concepts.
Identify and select appropriate manipulatives, such as linking cubes, counters, and base-ten blocks, based on specific mathematical concepts and student learning needs.
Demonstrate how to connect concrete manipulatives to visual representations, numbers, and mathematical symbols to support students in developing a deeper understanding of mathematics.
Recognize and analyze common mathematical misconceptions and identify ways to use manipulatives and questioning strategies to address student difficulties.
Design a hands-on elementary mathematics activity that incorporates appropriate manipulatives, encourages students to explain their mathematical thinking, and supports conceptual understanding.
Evaluate a sample manipulative-based learning activity to determine how effectively it supports mathematical understanding and identify opportunities for improvement.

Task and Content Analysis

To achieve the performance-based objectives of this mini-course, participants will need to develop an understanding of how manipulatives support mathematical learning and how they can be used intentionally in elementary classrooms. Participants may already have experience using materials such as linking cubes, counters, base-ten blocks, and number lines. However, they may have different levels of knowledge and confidence in selecting appropriate manipulatives, connecting them to mathematical concepts, and using them to address student misconceptions.

This mini-course will build on participants' existing teaching experiences and introduce strategies that can be applied to their own mathematics instruction. The learning content will be organized into four units that move from understanding the purpose of manipulatives to designing and evaluating hands-on mathematics activities.

Unit 1: Understanding the Role of Manipulatives in Mathematics

Prerequisite Knowledge and Skills:

Have a basic understanding of elementary mathematics concepts, such as addition, subtraction, and place value.
Be familiar with common instructional strategies used in elementary mathematics classrooms.
Recognize that students may have different learning needs and levels of mathematical understanding.

Learning Content:

What math manipulatives are and examples of commonly used materials.
The importance of using manipulatives to support conceptual understanding.
The difference between memorizing mathematical procedures and understanding mathematical concepts.
How hands-on learning can help students make sense of mathematical ideas.

Learning Activities:

Read a brief introduction about the purpose and benefits of using manipulatives in elementary mathematics.
Explore examples of common math manipulatives and how they can be used to represent mathematical concepts.
Reflect on how manipulatives are currently used in their own classrooms and consider how these materials support student understanding.

Unit 2: Selecting and Using Manipulatives Effectively

Prerequisite Knowledge and Skills:

Understand the purpose of manipulatives in supporting mathematical understanding.
Recognize that different manipulatives can be used to represent different mathematical concepts.
Have a basic understanding of elementary mathematics learning objectives.

Learning Content:

How to select appropriate manipulatives based on mathematical concepts and student needs.
Examples of using linking cubes, counters, base-ten blocks, and number lines to teach elementary mathematics.
The Concrete-Representational-Abstract (CRA) instructional approach.
How to help students connect hands-on materials to drawings, numbers, and mathematical symbols.

Learning Activities:

Examine examples of different manipulatives and identify which materials would be most appropriate for specific mathematical concepts.
Watch or review an example demonstrating how a teacher can move from concrete manipulatives to visual representations and abstract mathematical symbols.
Complete a short matching or scenario-based activity in which participants select appropriate manipulatives and explain their choices.

Unit 3: Addressing Mathematical Misconceptions Through Manipulatives

Prerequisite Knowledge and Skills:

Understand how manipulatives can represent mathematical concepts.
Be familiar with common mathematical difficulties experienced by elementary students.
Recognize the importance of questioning and observing students during mathematics instruction.

Learning Content:

Common mathematical misconceptions involving addition, subtraction, and place value.
How manipulatives can help teachers identify and address student misunderstandings.
The importance of encouraging students to explain their mathematical thinking.
Questioning and observation strategies that help teachers determine whether students understand a concept.

Learning Activities:

Review examples of common mathematical misconceptions experienced by elementary students.
Analyze a classroom scenario involving a student who is struggling with a mathematical concept.
Identify an appropriate manipulative and develop questions that could help the student explain their thinking and develop a better understanding.

Unit 4: Designing and Evaluating Manipulative-Based Mathematics Activities

Prerequisite Knowledge and Skills:

Understand the role of manipulatives in supporting conceptual understanding.
Be able to select appropriate manipulatives for specific mathematical concepts.
Understand how to connect concrete materials to visual representations and mathematical symbols.
Recognize how questioning and observation can help identify student understanding and misconceptions.

Learning Content:

How to intentionally incorporate manipulatives into elementary mathematics activities.
Strategies for aligning manipulatives with mathematical learning objectives.
How to include opportunities for students to explain and demonstrate their mathematical thinking.
Ways to evaluate whether a manipulative-based activity supports conceptual understanding.

Learning Activities:

Review an example of a hands-on mathematics activity and evaluate how effectively it supports student understanding.
Design a short elementary mathematics activity that incorporates appropriate manipulatives, connects concrete materials to mathematical representations, and encourages students to explain their thinking.
Reflect on how the activity could support students with different learning needs and identify possible improvements.

Overall Learning Progression

The four learning units are designed to build on one another. Participants will begin by exploring why manipulatives are important for developing mathematical understanding. They will then learn how to select and use appropriate manipulatives and connect hands-on materials to visual and abstract representations. Next, participants will examine how manipulatives can be used to recognize and address mathematical misconceptions. Finally, participants will apply what they have learned by designing and evaluating a manipulative-based mathematics activity that could be used in their own classrooms.

By completing these units, participants will develop practical strategies for using manipulatives more intentionally and supporting students in developing a deeper understanding of mathematical concepts.

Curriculum Map

References and Resources

Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380–400. https://doi.org/10.1037/a0031084

OpenAI. (2026). ChatGPT Curriculum Map [Generative AI image]. https://chatgpt.com/

Perkins, D., & Blythe, T. (1994). Putting understanding up front. Educational Leadership, 51(5), 4–7.

Shambaugh, N., & Magliaro, S. G. (1997). Mastering the possibilities: A process approach to instructional design. Allyn & Bacon.

Schneps, M. H., & Sadler, P. M. (Producers). (1987). A private universe [Film]. Harvard-Smithsonian Center for Astrophysics.