I SPY!Looking for Rigor in the 21st Century

Mathematics ClassroomPresented by Cassandra Willis

Instructional SpecialistTitle I Mathematics

I heard it through the grapevine…What is rigor?

It is not more homework. It is not extra problems It is not finishing the pacing early!

I heard it through the grapevine…What is rigor?

And it is Not a needle in the haystack process

Its about making the main thing the main thing!

What is rigor?

Engaging Active Deep

How do we get there? Believe that all students can! Allow teachers opportunities to learn what rigor is and looks like. Learn what rigor is, is not and what is looks like.

Let’s start with testing!

What does it look like?

What does it look like?

What does it look like?

What does it look like?

What does it look like?

What does it look like?

What does it look like?

What does it look like?

What does it look like?

What does it look like?

What does it look like?

What does it look like?

What does it look like?

What does it look like?

What does it look like?

What does it look like?

•Increased focus on multistep and applied (“practical” or “real world”) problems•Testing the converse of a standard•Increased emphasis on models and multiple representations

What does it look like?

•Increased emphasis on multistep and applied problems•Probability can be represented in many ways•Increased emphasis on models and multiple representations (number lines, fraction models, operations with fractions)•Prior knowledge from earlier grade levels

What does it look like?

•Increased emphasis on multistep and applied problems•Probability can be represented in many ways•Increased emphasis on models and multiple representations (operations with fractions, integers, number lines)•Prior knowledge from earlier grade levels

What does it look like?

•Use of notation• { } empty set, • set notation (Algebra I and II) vs. interval (Math

Analysis) • x: or x| (show both to students)•Students moving from the Grade 7 SOL course to Algebra I directly – what’s missing?• Scatterplots• Solving multistep equations• Prior instruction on box-and-whisker plots

What does it look like?

•The word “prime” when talking about functions that do not have real zeros•Solving linear-quadratic and quadratic-quadratic systems (no conics)•Factoring

What does it look like?

• Intermediate answers in multistep problems may be an answer choice

•New increased emphasis on proof, including 2-column proofs•Logical arguments and precision•Equations of circles – could be given many combinations of information•Increased complexity of diagrams

What does it look like?

•Increased emphasis on coordinate geometry•Coordinate geometry could include combinations of transformations•Notation: be careful not to use classroom-specific notation like “CPCF” or “CPCTC”•Constructions

What to do what to do?

•Mathematical Problem Solving•Mathematical Communication

What to do what to do?Classrooms should have

•Mathematical Reasoning•Mathematical Connections

What to do what to do?Classrooms should have

•Mathematical Representations

What does that look like in classroom?Find the perimeter of a train of 100 equilateral triangles if the triangles are joined side to side. Each side is one inch long. Write an equation to determine the perimeter of the triangle train

What does that look like in classroom?It is night and the owls are watching in the trees.If I see 12 eyes how many owls will I find and how many pairs of eyes do I see?

What does that look like in classroom?This fall the teachers had a plant swap.We brought in plants and shared them with each other.I noticed that my day lilies were very crowded.I remembered that five (5) years ago I started with one day lily.That fall I had three plants because the original plant had two new ‘babies’.In fact every year each plant had two babies.How many plants did I have in my garden this fall (at the end of the fifth year)?

What does that look like in the classroom?

State a problem whose solution would be found by computing and permutation of 10 things taken 4 at a time. How would you change the problem so its solution would involve computing a combination of 10 things taken 4 at a time?

What immediate changes can we make?

Make certain teachers are using the Compass…

What immediate changes can we make?

•Discuss lesson plans and objectives in grade level meetings•Make certain all tests and lessons are aligned with 2009 standards•Start looking at open ended questions•Ask for help!!!!!!!!

Cassandra Willis, Instructional SpecialistTitle I MathematicsPhone 780-6418Email: cboyd2@richmond.k12.va.usBusiness as usual, is over!