Teacher Tech blog with Alice Keeler

Paperless Is Not a Pedagogy

Alice Keeler

From @mathdiana: Have Students Talk About Math

diana herrington
From @mathdiana: Have Students Talk About Math

diana robots

Diana Herrington Impacted Many

Diana Herrington was my co-author of “Teaching Math with Google Apps,” mentor, and friend. She is probably the most influential person in my life for an impact on my teaching and pedagogy. We nerded out together for two years to write this book. We would get together to write and it would take at least 2 hours before we would actually start on the book because we were sharing ideas and creating activities for her to use in her math class. They would try them out and we would add them to the book.

Diana Will be Missed

Sadly, she suddenly passed away this last week. Her dream was to start a scholarship, in her memory an endowment is being set up to provide scholarships at Fresno State where Diana taught after her retirement of 30 years teaching high school. You can contribute to the endowment at http://gofundme.com/dianaherrington.

Include Your Passion in the Math Lesson

Diana was always passionate about students being curious and seeing math in the world. She was an avid wildlife photographer and would use these photos in her math class. She had a knack for having students relate what they were learning to the real things she had interacted with on her last trip. By using her own photography in her math classes she was personalizing the lesson, it was something she had experienced and was sharing with her students. Her students get to know her better and apply their learning to real contexts; win!

Have Students Explore and Talk About Their Ideas

One of the biggest themes we talked about over these last couple of years was about students talking about math. Not just doing math problems but understanding them. Collaborating. Evaluating what the students know instead of what they do not know.

Using Desmos, Diana would ask “What does a Sine function do to a circle?”
Diana Herrington Sine to a circle

Working in small groups students would investigate these “What if” questions. Students were working in small groups. Rather than her telling them, she had them explore and discuss. Students used Google Slides to record their exploration and discussion. She designed her math lessons NOT so much to be about HER TALKING about the math, but rather to pose interesting situations that would get the students talking and discussing the math.
what if the sine graph

One thing that particularly fascinated Diana was she would add Sine to the circle formula in a way that caused it to “poop out a circle.” I of course for the life of me can not remember how she manipulated the below equation so that it pooped out the circle. She sure did enjoy it when it did though! Students could then talk about how they thought that might happen. Build their curiosity around math.
add sine to the circle formula

Math conversations

Link to template

Her and I created a template around her idea of students having math conversations with her rather than cranking out math problems. Instead of doing 30 problems per day each week, she would let the students choose 3 problems. She then invested in providing feedback to help develop their thinking and understanding of the math concepts. She had back and forth conversations rather than grading the steps and correct answer. This allowed students to take risks in trying harder problems. When we take away the risk of failure of getting the wrong answer, students can explore the ideas and concepts to deepen their understanding. Students initially chose the easy problems but then once they realized they would get feedback to help them, 100% of Diana’s students would choose the hard problems.
diana conversations

alice diana cathy in new york
You would be hard pressed to find a picture of Diana not smiling. She loved her students, teaching, and math. This is me, Diana and our friend Cathy in New York city after we presented at the Google Office on “Teaching Math with Google Apps.”


I found a few of Diana’s quotes on Twitter:

  • “I teach students not math” @mathdiana #googlemath #mathchat
  • “I prefer to call it a task not a test” – @mathdiana
  • .@mathdiana doesn’t assign math problems, the students get to choose. #googlemath #mathchat
  • .@mathdiana got a 95% passage rate on AP calc test when she stopped giving algorithms and only gave 3 problems a week. #googlemath #mathchat
  • “here are 3 problems, put into wolframalpha.com, get steps, analyze and discuss, figure out algorithm” @mathdiana #googlemath
  • Wolframalpha.com shows all the steps. What do you do??? Ask different questions! @mathdiana #googlemath
  • When @mathdiana changed to less homework her students understanding went up!! #googlemath ditch the busywork!
  • “have students create their own guiding questions” @mathdiana #googlemath
  • Explaining your work is NOT stating the what the symbols mean. #mathchat #googlemath @mathdiana
  • Student says “You’re always trying to get us to explain why not just solve it.” @mathdiana #googlemath #mathchat
  • @mathdiana even gives choices on the test. Choose one problem from each section!
  • Something @mathdiana does is has kids, pencils down, discuss quiz/test in groups before they take it.
  • I use templates, but I also don’t use them. @mathdiana mostly has them go from scratch. They decide how to organize ideas
  • .@mathdiana gave a test with no questions. Seeing the student creativity and thinking that resulted is AMAZING! #mathchat #googlemath
  • what can they look up? What challenging Q’s can you ask them and they discuss in small groups and use @Desmos
  • .@mathdiana shares how she always gives students choices. On test here are 9 questions, choose 5. #googlemath
  • Doing math on Google Slides has kids go SLOWER so they can THINK more @mathdiana #googlemath alicekeeler.com/googlemath
  • Trip math – determine the ratios for the wolf’s face. Are they the same as your pet’s? @alicekeeler dropbox.com/s/9c40ib12e0k7… (Side note: Diana took that picture of the wolf!)
  • “Technology allows us to spend our time doing mathematics differently” @mathdiana #googlemath
  • On Google Cardboard math teacher @mathdiana says “Can you imagine this as a station in your class, they can get real world experiences”
  • “All great teachers are great storytellers” @mathdiana #googlemath
  • “My lesson starts with a story” @mathdiana #googlemath
  • Hanging out with @mathdiana again today. Pondering how do we get assessment closer to what the student actually knows? #googlemath
  • @PearDeck is awesome for the teacher who wants to have an interactive class” @mathdiana #googlemath #mathchat
  • “Mathematics + Modeling = Meaning” @mathdiana #googlemath
  • Appreciate @mathdiana telling me not to use the word “average” on my rubric. If we should not average grades, we need to use different words
  • “Starting the period looking at homework is starting your day looking backwards” @mathdiana #googlemath
  • Instead of calling it homework @mathdiana calls it “conversation” and uses Google Slides
  • Remember to assess the work not the student! #googlemath
  • Goal is to have students ask significant questions rather than being given questions @mathdiana #DOKchat #googlemath
  • It is so much easier to test DOK1 and DOK 2. It is also hard to test creativity and collaboration. #googlemath @mathdiana
  • When you structure out a process for students you’re denying the student the opportunity of DOK 2 and DOK 3 @mathdiana
  • Compliance is not the definition of a good student. @mathdiana
  • Take a selfie with where you find math outside. #mathchat @mathdiana
  • Overriding question is instead of “Solve a problem” is “Compare problems” #mathchat @mathdiana
  • Don’t ask what the answer is, ask about the process. Use Google. Use Wolfram. Critically analyze. @mathdiana
  • Kids are not numbers. If what you know about a kid does not match their grade or other data. Assess differently. @mathdiana
  • Instead of algorithms in elementary school, focus on grouping to build number sense #googlemath @mathdiana
  • Kids right now think if their answer is correct they should get an A… but are they getting to the understanding level? @mathdiana #DOKchat
  • If you’re only asking students DOK level 1 questions, how can you expect more than level 1 answers @mathdiana
  • Instruction that empowers begins where students are and gives students opportunities to move forward #edchat, #ccss, @alicekeeler
  • When teaching don’t forget the power of Socratic questioning! #CCSS, #edchat, #ngss
  • 5E 5:Evaluate – be sure to embed within Engage, Explore, Explain and Elaborate – not stand alone.#CCSS, #NGSS, @alicekeeler
  • I learned from @mathdiana that you can change your lessons to start the next lesson half way through class & finish the first half next day
  • 5E 4: Elaborate: Challenge, extend conceptual understanding and skills. Give new experiences for plowing deeper #NGSS, #CCSS
  • 5E 3: Explain: give students time to focus on their learning experiences and show their conceptual understanding #NGSS, #CCSS @alicekeeler
  • 5E-2: Explore.Give time to provide a common base of experiences for your lessons concepts, processes, & skills #CCSS #NGSS @alicekeeler
  • First E: engage – story telling and personalizing activities will help engage students #CCSS #NGSS @alicekeeler
  • Remember #CCSS practices are for students and 5E’s are for teachers #NGSS @alicekeeler
  • Science should be the focus of education and everything else can come along with it. #mathchat #scichat #edchat
  • Don’t be afraid to let Ss try and fail, it through failure they will learn. #EdChat


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