Balomenos Lecture

1. Richard H.
Balomenos

2. Richard H. Balomenos Lecture
Dr. Anne M. Collins
Lesley University
Cambridge, MA
October 22, 2009
3. Richard H. Balomenos
Dedicated to the belief that mathematics teachers canaccomplish great things.
Promoted solid mathematics background for teachers and students.
Offered strong opinions and justified them.
4. mathematics teachers can accomplish great things if they:
Change the focus of math instruction from skill and practice to problem solving
Offer all students interesting problem situations that will:
excite them about math
embed skills and computation
provide meaning and build understanding
5. mathematics teachers can accomplish great things if they acknowledge that:
Most of the math students experience is passive and irrelevant
Most secondary mathematics involves symbolic manipulation for the sake of symbolic manipulation
6. Beauty of Mathematics
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
7. What Does It Mean to Teach for Understanding?
There are three stages of learning:
Acquisition of knowledge and skills
Make Meaning and interpretcontexts or conditions
Transfer learning to new or novel situations
8. Acquisition Meaning-Transference
Acquire Skills ( in context when it is clear they are needed)
Make Meaning (sense making why? How do you know? Can you explain your thinking?)
Transfer knowledge to realistic situations, real world
9. Teachers Teaching for Understanding
Confront students with problem solving and ask themselves if:
Their studentscan make meaning
Their students can transfer skills to problem solving?
10. Currently the Impact Mathematics Instruction Has on high school students results in:
Nearly 40% of high school graduates feel ill-prepared for college or the workplace
Most secondary students describe mathematics asboring
(Grant Wiggins, 2009)
11. Post Secondary
Up to55% of college freshman take remedial courses
Student complaint
I wasnt taught to think.
12. Reform began in earnest in 1989 with the NCTM Standards yet:
Many teachers teach as they were taught
If we continue to teach as we always have, we will continue to get the results we have always gotten
13. And what is Worse
If we do not make a concerted effort to change the way we engage with and in the mathematics we teach
we will have yet another generation of students who are math phobic, avoid math at all costs, and believe they are stupid
14. 15. Dr. Anne M. Collins Lesley University 2009
16. Dr. Anne M. Collins Lesley University 2009
17. 17
Dr. Anne M. Collins Lesley University 2009
18. solid mathematics background for teachers
The most qualified math teachers teach high school math.
The most qualified usually teach advanced placement or honor courses.
Many high school teachers and university faculty still emphasize symbolic manipulation without conceptual understanding.
19. Yet
Students who struggle are the ones that need the best teachers.
Students who struggle are the ones who benefit most from multiple representations.
Students who struggle are often supported by special educators who have little or no math background.
20. Common core Standards consist of
Standard for Mathematical Practice
Ten standards for Mathematical Content
A set of Example Tasks
21. Mathematical Practice
All students can and do:
Attend to precision.
Construct viable arguments.
Make sense of complex problems and persevere in solving them.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Make strategic decisions about the use of technological tools.
Elementary teachers must have a deep understanding of number and operations, and how arithmetic relates to algebra.
Special educators who co-teach or support students in mathematics must also have a deep understanding of math appropriate for the level of students with whom they work.
Coursework must provide opportunity to develop mastery of the math they are going to teach.
Most K-6 teachers need intensive study of number & operation, number theory, algebra and functions, informal geometry, measurement, probability, and elementary statistics.
Most secondary teachers and university faculty need to consider modes of instruction that actively engage students.
What is the mathematics that is taught in the preceding grades?
What is the mathematics that is taught in the subsequent grades?
Why does it matter?
What you learn reflects how you learned it!
Students who have one year of poor mathematics instruction may recover but students who have two years in a row of poor instruction rarely catch up.
26. 27. Dr. Anne M. Collins Lesley University 2009
31. What Does It Mean to Teachand learn for Understanding
Skill and strategy not the same
Strategy is how you use your skill set
Students should develop the habit of asking:
What kind of problem is this?
Where have I seen it before?
What are some of the strategies I can use?
32. Assessment should be relevant
33. What Does It Mean to Achieve Success
Achievement is not the sum of the drills and tests of knowledge
Achievement measures whetherstudents are able to transfer their knowledge to real life situations/problem solving
34. What Does It Mean to Learn for Understanding
Word problems require making meaning and transference
Make students work with messy data Is this linearis that point an outlier, is it an error in calculation, or is the data non linear
Transference takes meaningand skill and uses it in the moment
35. Subtleand not so subtle Messages Relayed to Many Students
Move beyond the familiar comments:
I know this math is going to be hard but I will work with you to get you through it!
I was never good at math andlook how successful I am.
You have a disability so how do you expect to do honors math.
36. EQUITY
All Can Do Mathematics and Mathematics Is For All
We all need to work togetherto provide mathematics that will enable all students to be successful.
37. SuccessWhat a Good Feeling!

Balomenos Lecture

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Transcript of Balomenos Lecture