How Children Learn Mathematics Welcome to MAE4326 How Children Learn Mathematics

About me Former Engineer Married with 2 daughters Taught HS Math, Physics, Engineering and ACT/SAT Prep Taught in 2 states in different environments (inner-city, rural, suburban, etc.) I welcome questions More than willing to assist with your classroom or Praxis challenges Professional website: BakerMath.org

On an Index Card Write your name. Write two things that you believe are unique about you. Describe your favorite mathematics lesson, i.e. the topic, grade level, teacher, and why was it your favorite lesson. Write one word to describe mathematics.

Review Course Syllabus Office Hours Communication Attendance Policy Late Work Policy Assignments Discussions Group Discussion Boards Technology Enhancement Plan Demonstration Project Diagnostic Teaching Assignment Mini Teach Field Experience Tests & Quizzes

Group Discussion Boards Mathematical Practices Article Review Learning Center

Livetext/Falcon Online Assignments Technology Enhancement Plan Diagnostic Teaching Assignment Mini Teach

Other: Demonstration Project Design Presentation Upload into Falcon Online Discussion Area 1 Activity per Person Present activity to the class

Role of the Teacher From Lecturer to Facilitator (Coach) Pose worthwhile mathematical tasks Use of discourse Responsive (posing questions, listening, asking, monitoring) - teacher Active & Interactive (listening, responding, exploring, debating) - student Use of tools to enhance discourse Create a positive learning environment Engage in an ongoing analysis of teaching and learning.

Role of the Student Active participants in the learning process Learning by doing Collaborating with others Creating/Inventing new ways of doing mathematics Explaining and justifying mathematics

State Standards Sunshine State Standards/FCAT Next Generation Sunshine State Standards/FCAT 2.0 & EOC Exams Common Core State Standards Florida State Standards

Steps in New Mathematics Literacy All students must: Become Mathematics Problem Solvers Communicate their knowledge Reason mathematically Learn to value mathematics Become confident in one’s ability to do mathematics Identified by National Council of Teachers of Mathematics (NCTM)

NCTM Content Standards Number and Operations Algebra Geometry Measurement Data Analysis and Probability

NCTM Process Standards Problem Solving Reasoning and Proof Communication Connections Representation

Common Core State Standards, Standards for Mathematical Practice Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning

Discussion 1 Mathematics Story Assignment 1. Describe your comfort level in working with mathematics. On a scale from 1-10, rate the following: a. love for math b. Importance of math c. Your elementary math experience d. Importance of math in everyday life 2. Reflect on your own experiences as a mathematics student and think about how those experiences might affect you as a teacher.

Constructivist Theory Derivation Cognitive School of Psychology Jean Piaget (cognitive development) View Children (or learners) are not blank slates but rather creators of their own learning.

Constructivist Theory According to Piaget, knowledge can be acquired through: Assimilation – connecting current knowledge to prior knowledge Accommodation – creating a space for new knowledge

Constructivist Theory Knowledge is actively constructed by each person’s experiences. ~Constructing knowledge requires reflective thought.~

Constructivist Theory Some Principles: Exploration & discovery Social interaction & collaboration Problem-solving Hands-on Reflection Understanding why

Behaviorist Theory Contributor View Burrhus Frederic Skinner, leading behaviorist View Students are trained step-by-step, to repeat behaviors that lead to a desired result. These behaviors are constructed by the teacher

Behaviorist Theory Emphasizes the role of materials, the learning environment, and learning systems Deemphasizes the role of teachers and the “thinking” activity of learning **The approach of using positive and negative reinforcements to elicit desired behaviors of students.**

Behaviorist Theory Programmed Instruction Some principles: Rote memorization Drill and practice Understanding basic skills Use of token system to reinforce correct responses.

Sociocultural Theory Influence: View: Lev Vygotsky Knowledge is socially-constructed

Sociocultural Theory Foundational Concepts Mental processes exist between and among people in social learning settings The internalization of knowledge is dependent on the learner’s zone of proximal development (ZPD) Semiotic mediation, a term that describes how knowledge is transferred from the social to the individual plane

Sociocultural Theory Learning is dependent on the learners, the social interactions within the classroom, and the culture within and beyond the classroom .

Please Note: A learning theory is not a teaching strategy but rather informs teaching.

Implications for Mathematics Teaching Teaching strategies that reflect theories: Connect new & prior knowledge Provide opportunities to engage in mathematical talk Encourage & allow reflective thought Encourage multiple approaches Treat errors as teachable moments Scaffold new content Honor diversity

Reference Martinez, J.R.R., & Martinez, N.S. (2007). Teaching mathematics in elementary and middle school: Developing mathematical thinking. Upper Saddle Creek, NJ: Pearson Prentice Hall. Van de Walle, J.A., Karp, K. S., and Bay-Williams, J. M. (2010). Elementary and Middle School Mathematics: Teaching Developmentally (7th ed.). Boston: Allyn & Bacon.

Mini-Lesson

Fibonacci Sequence Each term is formulated by adding the two previous terms 1, 1, 2, 3, 5, 8, 13, 21, 34…

Fibonacci Sequences in Nature

More Fibonacci Sequences in Nature

My Personal Favorite Fibonacci Sequence in Nature

Homework Find at least 10 examples of the Fibonacci Sequence in Nature Take a photo with you in it (Woohoo! Selfies for homework!) of the specimen Copy/Paste into a Word Document (include a description with the location found) Hardcopies are due Next class period Can work with another person for ease of photography, but each person needs to turn in their own assignment