Saturday, April 10, 2010

Math


These are the questions the Wyoming math consultant recommended asking of any curriculum you might be interested in purchasing OR you might be creating.

Suggested Questions to ask of a math curriculum:
  • Is there an obvious emphasis on the grade level critical areas? (70% emphasis, 20% rethink and link, 10% sampling)  
    • Idea:  Look at table of contents - does it match the percentages?
    • Is the emphasis throughout the year and not just in one chapter?
  • Is the vocabulary aligned to CCSS?  
    • "There are some specific changes that have been made in the name of mathematics."  
    • Ex:  Number form is now "base-ten numbers", Word form is now "number names"...
  • Is there a focused use of manipulatives? 
    • A one day focus or in picture only will not suffice.  
    • At all levels, manipulatives should be used and used often.
  • Are there HCT with multiple entry points? 
    • See Questions Below
    • Exploring different entry points is key to the math practices.
    • Students should be asked to "make sense of problems and persevere in solving them" daily.  
    • They should be exposed to problems that last across class periods.
  • Are students exposed to the math practices on a daily basis?
  • Is time for reflection woven into each class period?
  • Is mistake analysis an integral part of the curriculum?
  • How are students asked to show/share their thinking?  
    • How are they pushed to explore multiple representations or mutliple solution paths?
  • Is formative assessment a key component?
  • Is talk/collaboration a daily component?  How does is it in service of learning?

Instructional/High Cognitive Tasks

Research indicates that student learning is increased when teachers regularly engage students in cognitively demanding tasks. Teachers must recognize, however, that there are many factors that contribute to the overall effectiveness of using high level tasks with their students. These factors should be considered so that teachers carefully select tasks and use them appropriately with their students. Below are a series of questions to consider for teachers using instructional tasks in their classrooms: 
1. What are the mathematical goals for using this task? 
  • Which standards does the task target?
  • Which Standards for Mathematical Practices will my students experience by working on this task?
  • How does this task build upon prior knowledge?
  • How will I know that students have met the mathematical goals?

2. Have I worked the task in order to anticipate possible solution paths that my students may take?
  • Do solution paths include a variety of representations and/or strategies?
  • What are common misconceptions students may have when working on the task?

3. How will I maintain the cognitive demand of the task?
  • Does the task have multiple entry points to provide access for all learners?
  • Does the task allow my students to explore, investigate, and make sense of mathematical ideas on their own?
  • Does the task provide personal challenge and productive disequilibrium for all students?
  • Am I using Accountable Talk to assure that all students’ voices are heard and are actively engaged in the task?
  • How will I respond when students struggle or have difficulty starting the task?
  • How can I advance the thinking of students who finish the task early?
  • Are students required to justify and defend their solutions?
  • What questions will I ask students to assess their learning and advance them toward the mathematical goals?

4. How can I summarize the learning during the whole group discussion?
  • How will I select and sequence the solution paths to leverage and advance student thinking about the mathematical goal(s) of the lesson?
  • How will I help students make connections among students’ solution paths and mathematical goal(s)?
Teachers using high level instructional tasks in their classrooms should follow the launch–explore -summarize lesson structure. It is recommended that teachers give students a regular diet of high level tasks, while also recognizing that there are other productive mathematical activities to use with students. 


From February Studio, these are our big questions/outcomes:
  • What does it look like to be fluent?
  • Scaffolds....Have I exhausted all strategies? What are all the tools that can be scaffolds? How can technology serve to scaffold (and push) learning?
  • How do I create application opportunities?  Is this the same or different than HCT?
  • CAS vs SpEd vs RtI vs Extended Day:  Who is filling the holes?  Who is supporting Tier 1?
  • Will vs Skill conversation:
    • How do we increase "will" when the "skill" is lacking?  
    • How do we increase "will" when the skill is there?
  • What are our student needs?  Which students have these needs?  We are discovering that we cannot rely on labels to know who has the needs.


 Tasks:



 Exploring Free (DG approved) Resources:

  1. WYOMING STANDARDS - standards broken down, Go To released items and math assessment descriptors
  2. Inside Mathematics - 6th, 7th, 8th grade lessons and resources including student work, classroom videos, etc...
  3. Think Math - 
  4. MAP - especially valuable for algebra
  5. Revisit Conceptua - (Jill for passwords)
  6. Revisit National Library of Virtual Manipulatives
  7. Balanced Assessments task bank - from Harvard Grad School of Education, developed a large collection of innovative mathematics tasks for K-12, along with scoring rubrics.  The library of more than 300 mathematics assessment tasks developed during the project remains freely available through this website.
  8. The Math Forum - has rich problems, a feature called Ask Dr Math, a teacher-to-teacher network, and PD.  Hosted by Drexel Univ.
  9. Educational Development Center - framework for big ideas and essential questions - Mark Driscoll.  (More information than units, Algebra Habits of Mind)
  10. Other..
    1. Videos from Khan Academy - Bill Gates' favorite teacher!
    2. Complex Instruction Website - hosted by Stanford University. *Links to curriculua in different subject areas as well as classroom video examples.
  11. FlowingData - and Information is Beautiful - two very cool sites for statistics.
  12. Interesting Blog - Number Warrior
  13. Algebra in the World - a number of problems for Algebra class!

Tasks/Assessment:

Flipping the Classroom & Workshop:



 Models/Manipulatives:
Math Anxiety:
CCSS - Math
PAWS Rubrics:
  • Recollection (compare/contrast), 
  • Connection (multiple representations), 
  • Reflection (understand and interpret)
  • Accuracy (use the */symbols to calculate), 
  • Appropriate (How appropriate is the use of the concept, skill, properties, and relationships to investigate and solve problems?), 
  • Adequacy of communication?
Books/Units to buy?
  • Making Sense author:  http://www.stenhouse.com/html/mathsensepodcast.htm?r=n263
  • MINDS ON MATH...
  • Marilyn Burns - About Teaching Mathematics:  A K-8 Resource (2nd Edition)
  • EQUALS Investgations Units - Lawrence Hall of Science, Univ of CA, Berkeley.  "...Rich curric on important topics.  The problems are engaging and have multiple points of entry.  The units lend themselves to collaborative learning environments."  **Would have to be purchased**
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