Manipulatives – Making Math Fun Dr. Laura Taddei

Learning Outcomes Discuss ways to enhance children’s natural interest in mathematics and disposition towards mathematics Actively engage in mathematical concepts, methods, and language through a range of appropriate experiences and teaching strategies Develop, implement, assess and modify curriculum and lessons using the PA Learning Standards

Math and Anxiety Abbreviated Mathematics Anxiety Rating Scale (A-Mars) Questionnaire Abbreviated version of Mathematics Anxiety Rating Scale How do you feel about mathematics? Gresham (2007) conducted a study on pre-service teachers level of anxiety regarding mathematics

Bruner’s Theory Applying Bruner’s theory of developing conceptual knowledge before procedural knowledge – discovery learning Using manipulatives and other materials – make concepts more concrete and meaningful Data revealed a statistically significant reduction in math anxiety when Bruner’s theory was implemented (Gresham, 2007)

How to Relieve Math Anxiety Use manipulatives Encourage small group discussions Journal Writing Literature Based Math Activities

Young children learn by being actively involved To be good or proficient at mathematics, children must know more than the content. Children should be given opportunities to communicate and connect knowledge to other mathematical ideas and to other subject areas, represent their understanding, solve problems and reason, and demonstrate a disposition to think flexibly

Process Standards Problem solving Reasoning Communication Connections Representation Process Standards from NCTM

Identify the Process Standards Please watch the video and identify process standards (as identified by the NCTM) being used. Math Instruction in a Seattle Public School

Teacher’s role in the classroom When watching this video, how do the teachers describe their role in teaching math in the classroom - Everyday MathEveryday Math

Manipulative Small Group Activity You will be working in small groups with a hands-on math activity After completing the activity, please identify what your group decides is the goal of the activity (what is the big idea), the grade level this activity would be appropriate for, and at least five ways you could implement the process standards. PA Common Core Standards for Math

Helping Children Problem-Solve Understand the problem Experience with material Prior knowledge Planning how to solve it Prior knowledge Carrying out the plan Modify Try again Reviewing the solution

Promoting Reasoning Skills Ask question that require investigation and reasoning. Are you sure? How do you know? Why do you think …? What else can you find that works like this? What would happen if …? I wonder how this could be changed? What would the pattern be …? What if …? I wonder why …? Perhaps it’s because …?

Promoting Communication Skills Teacher’s can verbalize and restate mathematical concepts and process and ask questions to help children clarify or extend their ideas Also to help give them a lot of opportunities to talk with and listen to their peers

Promoting Connections The overall goal is understanding: if they can see how it is related or connected to other things they know

Promoting Representation To encourage flexibility in mathematical representation use – pictorial (drawings, maps), graphical (bar graphs made from stacked objects, timelines, pictographs), and symbolic (tables, prose descriptions).

Encouraging Innovation Ryshke, R. (2012) What schools can do to encourage innovation: can-do-to-encourage-innovation/ can-do-to-encourage-innovation/

Provide Opportunities to talk about Mathematics Build In Opportunities for Reflective Thought Encourage Multiple Approaches Teaching should provide opportunities for students to build connections between what they know and what they are learning. Engage Students in Productive Struggle Allow students the time to struggle with the mathematics they are exploring.

Treat Errors as Opportunities for Learning Scaffold New Content For concepts completely new to students, the learning requires more structure or assistance, including the use of tools like manipulatives or more assistance from peers. Honor Diversity Each learner is unique, with a different collection of prior knowledge and cultural experiences. Since new knowledge is build on existing knowledge and experience, effective teaching incorporates and builds on what the students bring to the classroom.

Questions These questions should be used as a guide to facilitate the discussion. However, please feel free to add/modify questions as needed.

What can we do or do we do to encourage innovation for faculty and students?

Techniques What are you doing that works? What innovative techniques do you use to improve student learning? How do you encourage innovation in your students?

Innovation can include “fun, creativity, diversity, collaboration and the ability to trust intuition” (Reimers- Hild & King, 2009). “One of the most essential elements of innovation is risk taking” (Reimers-Hild & King, 2009).

What kind of technology do you use and how has this impacted student learning? What are some ways to be innovative without the use of technology?

Create Communities of Learners How can we or how do we create collaborative communities of learners?

“When faculty talk with colleagues about teaching strategies and challenges, it helps to create an atmosphere in which it feels safe to try new methods and take risks as an educator” (Simmons, 2012) how-colleges-can-encourage-professors-innovate- teaching how-colleges-can-encourage-professors-innovate- teaching

Challenges What are some challenges you face? How do you overcome these? What are some barriers to student learning? How do you overcome these barriers?

“Research recognizes that some of the most effective leaders are truly passionate about what they do and have a genuine interest in helping their constituents or followers” (Reimers-Hild & King, 2009).

“Innovation is about coming up with new ideas, products, collaborations, services and solutions that can be implemented and used” (Reimers-Hild & King, 2009).

What “new ideas, products, collaborations, services and solutions” can come out of this discussion? What support do you need to move forward? How can we follow-up on this discussion?

Questions or Comments Please contact Laura Taddei at if you have any questions or

Resources Enterprise School (2011) provided an article An Entrepreneurial Development Framework for Higher Education Institutions. Extracted from Reimers-Hild & King (2009). Six questions for entrepreneurial leadership and innovations in distance education. Online Journal of Distance Learning Administration. Extracted from Ryshke, R. (2012) What schools can do to encourage innovation. Extracted from Simmons, E. (2012) Rewarding Teaching Innovations. Extracted from