1 / 12

Thinking, Wondering, and Reasoning Like a Mathematician

Thinking, Wondering, and Reasoning Like a Mathematician. 2010 CSAO Conference Linda Venenciano University of Hawaii, Manoa. Example 1. Solve: 342 -145 How would a student be taught to do this? What thinking process is demanded of the student? Of the teacher?

enye
Download Presentation

Thinking, Wondering, and Reasoning Like a Mathematician

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Thinking, Wondering, and Reasoning Like a Mathematician 2010 CSAO Conference Linda Venenciano University of Hawaii, Manoa

  2. Example 1 Solve: 342 -145 How would a student be taught to do this? What thinking process is demanded of the student? Of the teacher? Is this a problem or an exercise?

  3. Example 2 • Using the digits 1 to 9 only once, find two 3-digit numbers whose sum uses the remaining three digits. How would a student be taught to do this? What thinking process is demanded of the student? Of the teacher? Is this a problem or an exercise?

  4. Thinking Like a Mathematician • What does a mathematician do? • Investigate, solve problems, reason, prove, justify, communicate, validate through collaboration • Is their objective to get “the right answer”? • Some problems take a very, very, very long time to solve • It’s the means • Applied mathematics vs. pure mathematics

  5. Thinking, Wondering, Reasoning Describe the nature of school mathematics. How do children learn to think mathematically and problem solve?

  6. Problem Solving Tips • Patience • Try something • Draw a picture • Organize your findings • Look for patterns • Generalize • Look at simpler problems first • Wish • What if x=1? What if x=10?

  7. Characteristics of a good problem Skeleton tower example • a. How many cubes are needed to build this tower? Explain how you found the total. • b. How many cubes are needed to build a similar tower twelve cubes high? Explain how you found the total.

  8. ULS HS Textbook Selection Criteria • Mathematics meet standards and benchmarks • Learning through problem solving is included as an instructional strategy • Topics are well connected • Multiple means of communication are present • A variety of instructional strategies are used • Multi-dimensional assessment techniques are available • Professional development support is available • Modern instructional technology is integrated • Appropriate balance between concepts and skills • Well developed formative and summative assessment • Multiple representations are addressed and the connections between the representations are made explicit

  9. Instruction • Interactions to build understanding • Promote productive problem solving processes • Prompt students to go beyond finding the right answer • Broaden student participation • Expand student engagement

  10. Resources • SUPER-M project • http://www2.math.hawaii.edu/superm/ • NSF Graduate STEM Fellows in K-12 Education • http://www.gk12.org/ • Math Teachers’ Circle Network • http://www.mathteacherscircle.org/ • Curriculum Research & Development Group • http://www.hawaii.edu/crdg/pd/

  11. GK-12 is an NSF-funded Program • Program Goals for Graduate students, K-12 Education, and Higher Education • Fellows have the unique opportunity to improve their communication and teaching skills through interactions with teachers and students in K-12 schools

  12. GK-12 Outreach Work • Producing an event, “Molokai Math Day” • Working with the community to develop their infrastructure and enjoy a day of mathematics activities with families on Molokai • Designing and delivering two CRDG Summer Programs courses for 2010 • International Week of Math • PD through HCTM, our own workshops, our school partners

More Related