Download Akihiko Takahashi

What Qualities are Needed for Math Teachers in the
Next Decades?
International Symposium
for Pre- and In-Service Mathematics and Science Teachers:
Akihiko Takahashi
Asia-Pacific Mathematics and Science Education
Collaborative (AP•MSEC)
DePaul University
1
21st Century Mathematics Education for All
• Understanding mathematical principles and procedures is
essential in becoming a citizen of the data-driven and
technological world of the 21st century, no matter what
industry one is in. Mathematics education is indeed a key for
human resources development and global competitiveness.
– high quality standards and assessments for mathematics
education
– teachers with strong knowledge and expertise in providing
high-quality learning opportunities for their students
High quality standards and assessments for
mathematics education
• A focused, coherent progression of mathematics learning,
with an emphasis on proficiency with key topics, should
become the norm in elementary and middle school
mathematics curricula. Any approach that continually revisits
topics year after year without closure is to be avoided.
– Focused: curriculum must include (and engage with
adequate depth) the most important topics underlying
success in school algebra.
– Coherent: the curriculum is marked by effective, logical
progressions from earlier, less sophisticated topics into later,
more sophisticated ones.
National Mathematics Advisory Panel FINAL REPORT, 2008
Mathematical Proficiency
Adding it up, (National Research Council, 2001)
• Conceptual understanding
comprehension of mathematical concepts,
operations, and relations
• Procedural fluency
skill in carrying out procedures flexibly,
accurately, efficiently, and appropriately
• Strategic competence
ability to formulate, represent, and solve
mathematical problems
• Adaptive reasoning
capacity for logical thought, reflection,
explanation, and justification
• Productive disposition
habitual inclination to see mathematics as
sensible, useful, and worthwhile, coupled with a
belief in diligence and one’s own efficacy
Common Core State Standards
(CCSS)
• To meet the global standards, U.S. schools are moving toward
implementing the core standards. (41 states will be
implementing in three years)
– The NCTM process standards of problem solving, reasoning
and proof, communication, representation, and
connections.
– The strands of mathematical proficiency specified in the
National Research Council’s report Adding It Up:
• adaptive reasoning,
• Strategic competence,
• conceptual understanding
• procedural fluency
• productive disposition
Statistics is one of the domains that some of the
curricula emphasize
• CCSS Grade 6: Statistics and Probability
– Develop understanding of statistical variability.
– Summarize and describe distributions
• CCSS Grade 7: Statistics and Probability
– Use random sampling to draw inferences about a
population
– Draw informal comparative inferences about two
populations
– Investigate chance processes and develop, use, and
evaluate probability models
• CCSS Grade 8: Statistics and Probability
– Investigate patterns of association in bivariate data.
Teachers with strong knowledge and expertise in
providing high-quality learning opportunities for their
students
• Teachers cannot teach content beyond their knowledge
(National Mathematics Advisory Panel, 2008)
• Knowing the content may not enough for teachers to teach
mathematics effectively
• Effective teachers provide appropriate supports for the
students so that they can successfully solve these challenging
problems by themselves.
• Effective teachers can anticipate that the students will use a
variety of approaches – incorrect and correct, naïve and
sophisticated.
• In order for students to learn from this experience, the good
teacher must lead students through the discussion around
comparing individual approaches and solutions.
Three Levels of Teaching
• Level 1: Teachers can tell students important basic ideas of
mathematics such as facts, concepts, and procedures.
• Level 2: Teachers can explain the meanings and reasons of
the important basic ideas of mathematics in order for
students to understand them.
• Level 3: Teachers can provide students opportunities to
understand these basic ideas, and support their learning so
that the students become independent learners.
Study of Mathematical Knowledge for Teaching
• In order to improve the teaching of math in the United States,
we need to engage students in exploring mathematical
relationships and wrestling with key mathematical ideas.
Unfortunately, it’s not possible to achieve this goal simply by
identifying best practices.
• Listening to experts during special professional development
days does not translate into improved teaching. Effective
teacher learning must be built into teachers’ daily and weekly
schedules. Schools must become the places where teachers,
not just students, learn.
(Closing the Teaching Gap, 2009)
Two major types of professional development
• Phase 1 professional development focuses on developing the
knowledge for teaching mathematics,
–
through reading books and resources, listening to
lectures, and watching visual resources such and
video and demonstration lessons.
• Phase 2 professional development focuses on developing
expertise for teaching mathematics
–
teachers should plan the lesson carefully, teach the
lesson based on the lesson plan, and reflect upon
the teaching and learning based on the careful
observation.
A framework for developing programs and resources
for mathematics teacher education
Phase 1
Professional
Development
Phase 2
Professional
Development
For becoming level For becoming level
1 Teacher
2 Teacher
For becoming Level 3
Teacher
Reviewing the
contents for
teaching
•Workbooks
•Online courses
Undergraduate
courses for
prospective
teachers
•Books
•Online resources
•Classroom videos
•Classroom
observation
Undergraduate courses for
prospective teachers
•Books
•Classroom videos
•Classroom observation
Lesson Study
Student teaching
Lesson Study
School based
District wide
Professional development
programs for practicing
teachers
•Workshops
•Summer Institute
What are needed for Mathematics Teachers
• Moving promising research results into practice
– developing skills to effectively access to the researchbased information about teaching and learning
mathematics
– Understanding how to examine the effectiveness of the
interventions
• Becoming a teacher researcher
– Developing skills to design and conduct classroom
research
– Knowing the process of publishing research articles in the
professional journals