Tag: mathematical mindsets

#BuildMathMinds18: How Slow Thinking, Playing and Challenge Create Mathematicians

#BuildMathMinds18: How Slow Thinking, Playing and Challenge Create Mathematicians

In the Build Math Minds Summit, Dan Finkel elaborated on this notion that “what books are to reading, is what play is to math.” And as he said this, my ears perked up, I leaned in and listened intently because this is all I’ve been thinking about for the last week as I begin to plan for next year’s inquiry maths with play as a pedagogical stance. He articulately beautifully how math thinking comes from asking questions, solving problems, playing and exploring.

So as I marinated in his words and ideas, I began binge learning all over again. Glutton for punishment?–I guess I am. But they say that when you teach others, you learn twice. So I want to share my takeaways from some of the presenters, Dan Finkel included, for the Math Minds Summit (which you should go watch right now if you read this post before August 6th, 2018). And because I know that the brain is more switched on when you present ideas as questions, my gleanings are represented in that way for this blog.

I hope it inspires you…..

During unstructured play, what kinds of questions can provoke analytical and divergent thinking?

How many? (number)

What kind? (classification)

How big? (measurement)

What if? (creativity and logic)

What makes games good to develop mathematical thinking?

  1. Anything with Dice
  2. 5 in a row
  3. Number sense cards (that show alternate variations of number patterns)
  4. Checkers
  5. Nim
  6. Anything with cards
  7. Anything that you can advance pieces on a board
  8. Games that involve making choices so that children develop strategy and thinking.

Provocations= Puzzles and Challenges

These can be concrete opportunities to explore estimation and making conjectures, but the heart of a mathematical provocation is that it must be intriguing to get the students curious and motivated to solve the problem. Consider if the provocation is going to…

  1. Allow all students to show their thinking and understanding in interesting ways.
  2. Invite conversation and collaboration among peers.
  3. Provide opportunities to assess what students know and can do mathematically.
  4. Have an ROI (return of investment) of time and resources–all the set up is worth it because of the cognitive demand and depth of learning that is going to come from this provocation.

(These 4 criteria were inspired from Jon Orr  and his work with starting a Math Fight)

These are some examples that I think were great examples:

“About” how many ketchup packets do you think can fit inside these containers?

estimate

Prompts that incite a variety of answers:

mathbefore bed

What language encourage matheI remember thinking that students should learn the way I taught; they should adjust to me. I could not have been more wrong. A great teacher adjust to the learner, not the other way around (3).pngmatical dispositions?

  • Demonstrate that wrong conjectures can be the jumping off point for refining our ideas with counterexamples which enrich our thinking and deepen our conceptual understandings.
  • Using descriptive and numerical language to highlight the math concepts  (He gave the simple example of saying “Get your 2 gloves” vs. “Get your gloves”.
  • Use language that shows that we, as adults, aren’t afraid of making mistakes, so they feel safe also.
  • Do NOT use words that suggest that you have to be “smart” or “fast” to do the math.
  • Likewise, do NOT give praise for being “fast” or “smart”.
  • Ask questions that provide challenge and make students take a position (conjectures):
    • Do you agree or disagree with this idea?
    • Why?
    • How do you know?
    • Say more about that?
    • In your own words, could you explain….?
    • Would you rather….. or would you rather……?
    • How might you represent your thinking?

What routines or thinking systems encourage mathematical conversations and develop conceptual understandings?

(Click to learn more on the links)

  • EVERYTHING WE KNOW ABOUT THIS routine: Present a problem or puzzle, asking them to….Write down, tell a neighbor, tell me EVERYTHING you know about this.
  • Number Talks: a simple problem shown that students try to solve mentally in a variety of ways.
  • Number String: a specifically structured string of number problems in which the numbers get progressively harder.
  • Counting Collections: The routine speaks for itself- students count set collections of objects. This develops a variety of counting strategies.
  • Claim, Support, Question: providing a claim (conjecture) that students have to provide evidence to support their claim. In order to deepen the conjecture, students can use counterexamples or ask questions that help develop a better math argument.
  • Two Truths and a Lie: students are presented with a math problem or graphic.  Students are instructed to create two truths and one lie about the math.  Then, students share their “truths” and “lie” and have other students decide which are the truths and which is the lie.
  • Which One Doesn’t Belong?: These are visual puzzles that have multiple answers. Click on the link to see a plethora of them. There’s also a book written by the same title.

Next week, when our 1st graders start piling into the classroom, I have an arsenal of ideas that I’ve gotten from this summit. (And it’s not even over!!) I really would invite you to check it out. I know, beyond a doubt, that our students are going to fall in love with math at an early age because they will engage in play, feel challenged at their level and construct meaning on their own timeline. I wish the joy of math for all children (and adults) out there. Don’t you?

 

10 Reasons Why I Can’t Wait to Teach 1st Grade Next Year

10 Reasons Why I Can’t Wait to Teach 1st Grade Next Year

My school year is winding down–4 more weeks left of school! (but not that I’m counting) And instead of thinking about all the great adventures we will have this summer, all I can think about is how much fun I am going to have to teach 1st grade next year. Teacher Nerd ALERT!next year After bobbing back and forth between the Early Years and 4th grade for the last couple years, I will be happy to settle in 1st grade for a while, where you get the best of the Early Years mindset (unfettered creativity and imagination) and yet starting to gain confidence and competence in Literacy and Numeracy skills, making it possible to go deep with developing their knowledge and thinking skills. Plus their minds aren’t as sullied with “can’ts” as the older grades are, making them so wonderfully teachable. Oh, the joy of learning!-for both me and them.

Here are the 10 things that are keeping me up at night that I am so dang excited to do with 1st graders:

  1. Meditation: Cultivating calm in one’s mind should be a skill taught early in life. If I was being honest, I have been a bit chicken to really make it a part of my classroom routine in a serious way. But I really intend to push myself and introduce mindfulness and meditation in a more intentional way. I think 6-7 years old can manage a brief moment of calm.   
  2. Book Snaps: Although I am not sure about introducing SnapChat to little ones, how I do love this idea by Tara Martin, in which kids take a “snap” of the book they are reading and post the questions, ideas, and quotes from the book as annotations. I think the excitement of posting these “book snaps” are a unique way to cultivate an interest in close reading when you share them in a public forum. Love of close reading–oh yeah, let’s do that!
  3. Podcasting: I dabbled with podcasting before but for the last couple months, I have taken a serious interest in it and have been working on my a personal podcast for a while. Audio content is a whole other art form so this project has really made me think a lot about creativity, word choice, and voice (literally). Which is preciously why I want to do with little kids, and I was inspired by an idea that the music teacher shared with me about read alouds. So I’m hoping to do read alouds of books and their writing and publish it to an authentic audience, all the while nailing fluency in the process.
  4. Blogging: The online world is where most of my digital natives will be probably making their greatest impact as they grow into adults. I’ve always admired the philosophy of the Writer’s Workshop as it develops the mindset of a writer. What could be more authentic and meaningful as a blog, as they articulate their ideas online?
  5. SeeSaw: I have been dying to seriously mess around with digital portfolios. Currently, we use Class Dojo, which is focused more on classroom management, but SeeSaw has oh so much more going on and has a lot more opportunity for engagement and interaction.
  6. Math Workshop: Did I mention that I like the workshop model? Ah, yes, and it works for math too! Workshop + Talk Moves + Math Tools = a deeper exploration of number concepts.
  7. Math as Art: Okay, I’m a math geek, but through a series of serendipitous events, I’ve come to see art as an integral way to show the “beauty” of math. I don’t consider myself arty, at all, but I’m super interested in how we can represent math (and science) in artistic ways.
  8. Number Talks: This is probably one of my favorite things, ever, in developing mathematical mindsets, in which students get to explore a myriad of perspectives as they look at solving a problem.  So, it creates a bank of strategies for mental math and develops mathematical fluency.  If you don’t know about it, check out the video below.

9. Design Thinking: Have you ever found that you thought you knew something but then as you start really working through it and researching it, you realize how absolutely ignorant you are. Well, design thinking has done that to me, and I want to use it more often in my classroom, not as a one-off in a STEM-like unit, but I think it can be superimposed into so many aspects of learning, even writing. I want to launch it early in my class and use it often, whether we are going through the design process or doing design sprints.

10. Writer’s Workshop: Although I am not a die-hard Lucy Calkins fan, I so do love this approach to writing because it creates “authors” with writing that is worth sharing and publishing. They get to study good writing, practice these devices, go through the writing process and get peer feedback. I think it cultivates a practice of deep reading of a text and cultivates a positive mindset about writing, dare I say a buzz about their writing. I want to remix this model a bit, with the use of technology and design-based learning through. So I reckon that this experiment will be the fodder for blogs later.

If you are a 1st-grade teacher, I’m wondering what you really love challenging your students with. What am I missing? What have you done that you think is the bee’s knees? I’d love some insight!!

Nevertheless, it is fun to sit upon the precipice of something and feel the exhilaration of possibility.

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