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Teachers You Remember
Who made an impact on you?
Why do you remember them?
Math EngagementCreating a Student-Centered Classroom!
Henrico County Public Schools
August 2012
What is your name? Where do you teach?
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Introductions
Our Goals Learning about different instructional
methods to create a student-centered classroom.
Examining practices for maintaining productive mathematics discussions.
What is your definition of a “problem”?
A question to be considered, solved, or answered.
A situation, matter, or person that presents perplexity or difficulty.
If students know the answer, it is practice.
What is our goal as mathematics teachers?
Teach kids how to use their critical thinking and reasoning skills to adapt and overcome in unfamiliar settings.
What will tomorrow’s jobs look like?
Do we over teach to our students?
No Pain, No Gain Pertains to learning mathematics as well Let kids struggle to make sense of the
mathematics
Problem/Project Based Learning
Simpson Park
Work individually at first.When told, discuss with elbow partners.
What questions arise in your conversation?
Does the problem challenge students to use higher-level critical thinking skills?
Are there multiple ways to solve this problem? Is it accessible to all students?
Is this a practical and worthwhile task?
What might students struggle with? Does the problem promote mathematical
communication? This would be an appropriate problem if you
were studying… or if you have already studied…
Is this a practical and worthwhile task?
In what situation would this task be used? In which grade level would you use this task? How would you adjust it for another grade
level?
Is this a practical and worthwhile task?
What kind of learning experiences will prepare students for the 21st century?
Research tells us that complex knowledge and skills are learned through social interaction.
This is difficult to do in the classroom daily due to curricular demands. The key is to maintain the right balance.
Productive Classroom Discussions How do you make student-centered instruction
more manageable? Creating discussion-based opportunities for
student learning will require learning on the part of many teachers.1. Identify cognitively challenging instructional tasks
(Setting Goals for Instruction).
2. Support students as they engage and discuss their solutions (Select Appropriate Tasks).
Lesson StructureTo foster reasoning and communication focused on a rich mathematical task, use a 3-part lesson structure:
1.Individual thinking (preliminary brainstorming)
2.Small group discussion (idea development)
3.Whole class discussion (idea refinement)
Organizing High-Level Discussions: 5 HabitsPrior to the lesson,
1. Anticipate student strategies and responses to the task
Key Instructional Questions (for the teacher) What might students struggle with? What are common misconceptions?
While students are working,
2. Monitor their progress,
3. Select students to present their work, and
4. Sequence the presentations to maximize discussion goals
Organizing High-Level Discussions: 5 Habits
Key Instructional Questions (for the teacher) while students are workingIf a student is struggling, what are good questions to ask?Am I soliciting multiple solutions from students?How is the students’ work informing my lesson planning?
Organizing High-Level Discussions: 5 Habits
During the discussion,
5. Ask questions that help students connect the presented ideas to one another and to key mathematical ideas
More on 5 Habits can be found in: “Orchestrating Discussions” by Smith, Hughes, Engle, & Stein in Mathematics Teaching in the Middle School, May 2009
Organizing High-Level Discussions: 5 Habits
Practicing: AnticipateWork on the following geometry task and think about possible student strategies/solutions:
Triangle ABC has interior angle C measuring 105°. The segment opposite angle C has a measure of 23 cm. Describe the range of values for the measures of the other sides and angles of triangle ABC. Explain your reasoning.
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Practicing: Select and SequenceLet the provided samples work on the triangle task represent the work your students observed while monitoring their work.
1.Select 4 to 5 students who you would call on to present their work.
2.Sequence these students to optimize the class discussion of this task.
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Practicing: ConnectingFor the student work you selected and sequenced,
3.Identify connections within that work that you would hope to highlight during the class discussion.
See file TriangleProblem.gsp for model of triangle activity in Sketchpad.
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Thinking About Implementation In order for students to reason about and
communicate mathematical ideas, they must be engaged with high cognitive demand tasks that enable practice of these skills.
BUT! … simply selecting and using high-level tasks is not enough.
Teachers need to be vigilant during the lesson to ensure that students’ engagement with the task continues to be at a high level.
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Factors Associated with Lowering High-level Demands
Shifting emphasis from meaning, concepts, or understanding to the correctness or completeness of the answer
Providing insufficient or too much time to wrestle with the mathematical task
Letting classroom management problems interfere with engagement in mathematical tasks
Providing inappropriate tasks to a given group of students
Failing to hold students accountable for high-level products or processes
Factors Associated with PromotingHigh-level Demands
Scaffolding of student thinking and reasoning Providing ways/means by which students can
monitor/guide their own progress Modeling high-level performance Requiring justification and explanation through
questioning and feedback Selecting tasks that build on students’ prior
knowledge and provide multiple access points Providing sufficient time to explore tasks
Revisiting Simpson ParkSOL 8.10 – The student will
a) verify the Pythagorean theorem
b) apply the Pythagorean theorem
From a planning perspective, is this sufficient?
Teachers need to examine the Curriculum Framework!
Solve practical problems involving right triangles by using the Pythagorean theorem.
Is this a high level task?A 12-foot ladder is leaning against a brick wall. The top of the ladder meets the wall 10 feet off of the ground. How far is the bottom of the ladder away from the base of the wall?
Think about the Task Analysis Guide from the Math Assessment session.
Blended Learning Refers to mixing different learning
environments. Combines traditional face-to-face classroom
methods with computer-mediated activities. The flipped classroom is a form of blended
learning.
Project Based Learning articleGetting Started with Project-Based Learning (Hint: Don't Go Crazy)http://www.edutopia.org/blog/project-based-learning-getting-started-basics-andrew-miller
Flipped ClassroomPete Anderson’s website:http://geometryonline.pbworks.com/w/page/54592258/Purdue%20University
Performance Task Ideas(some aligned to Common Core Standards) Project Based Learning - http://www.bie.org/ Math Capstone Course -
https://sites.google.com/site/mathematicscapstonecourseunits/home/
Smarter Balanced Assessment Consortium - http://www.smarterbalanced.org/
Illustrative Math Project - http://illustrativemathematics.org/ Calculation Nation - http://calculationnation.nctm.org/ Minnesota STEM - http://www.scimathmn.org/stemtc/ Learn Zillion - http://learnzillion.com/
PBL Creation Pete’s examples – 4 D’s
Tiling a Patio See handout.
Math Rigor, Assessments & Engagement Five goals – for students to
become mathematical problem solvers that communicate mathematically; reason mathematically; make mathematical connections; and use mathematical representations to model
and interpret practical situations
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Narrowing Achievement Gaps Ask high-level questions of all students Consistently provide multiple representations Facilitate connections Solicit multiple student solutions Engage students in the learning process
Narrowing Achievement Gaps Promote mathematical communication Listen carefully to your students’ words and
learn from them Provide “immediate” feedback on all work Give students challenging but accessible tasks
Real-World Problems + Group Learning = A.P. Calculus Success Bridging the Achievement Gap http://www.nytimes.com/schoolbook/
2012/07/30/real-world-problems-group-learning-a-p-calculus-success/
No Pain, No Gain If you are more tired than the kids, it’s not
because you are old Make kids estimate/predict and think before
calculating Don’t ask questions that solicit one word
answers Let kids struggle to make sense of the
mathematics40
Key Messages We must not solely focus on multiple-choice assessments We must provide students with rich, relevant, and
rigorous tasks that focus on more than one specific skill and require application and synthesis of mathematical knowledge
We must connect mathematics content within and among grade levels and subject areas to facilitate long term retention and application
We must reflect on our own teaching and resist the urge to blame students
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Be the teacher that makes students remember you.
Closing Thought
