1. How Children Learn Mathematics
Welcome to MAE4326
How Children Learn Mathematics

2. 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.

3. 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

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

5. 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)

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

7. NCTM Process Standards
Problem Solving
Reasoning and Proof
Communication
Connections
Representation

8. 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

9. 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.

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

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

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

13. 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

14. 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.**

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

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

17. 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

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

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

20. 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

21. 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.

22. Mini-Lesson

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

24. Fibonacci Sequences in Nature

25. More Fibonacci Sequences in Nature

26. My Personal Favorite Fibonacci Sequence in Nature

27. 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 and the Fibonacci Number represented)
the document to
Can work with another person for ease of photography, but each person needs to turn in their own unique assignment (NO “double-dipping”!)