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BODO HEILIGER

MY MUSINGS ON TEACHING AND LEARNING
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It's Okay To Not To Be A Super Hero

1/5/2020

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We have been rolling with Continuous Learning for six weeks. There have been amazing challenges and struggles; however, what has remained constant has been the amazing resilience of our faculty and staff. How teachers have completely transformed their learning environments into their homes absolutely astounds me.  They go above and beyond in every aspect of teaching and learning, and I know we will never know all their sacrifices. 

As a parent of six-year-old twins and their principal, I witness the impact of the policies and procedures that I help to create and implement. And, it's hard for everyone. Hard for the teachers. Hard for the kids. Hard for Ann, my wonderful partner. And, hard for me. 

Over the past couple weeks, I began to realize that it's okay not to be a super hero. And, I decided to write a letter with the Head of Early Childhood to our community letting them know that's it's okay not to be perfect right now. 
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  • It’s okay to not get everything done
  • It’s okay to do it your own way
  • It’s okay to miss a class
  • It’s okay to break a rule (both adults and kids)
  • It’s okay to take a break 
  • It’s okay to play
  • It’s okay (and good for kids) to be bored
  • It’s okay to let your kids watch T.V. 
  • It’s okay to not be okay
  • It’s okay to share how you’re really feeling with your kids and with us
  • It’s okay to email us
  • No one is judging you
  • Be kind to yourselves and your families
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Whose Questions Do We Value?

27/1/2016

 
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What a powerful statement: “The questions a student asks after reading a text are a better assessment than the questions a student can answer.” When I think about David Pearson's quote, I wonder what it means for our classrooms. What does it mean for our assessments? How can this change the roles of the student and the teacher? ​
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When I was a kid in the late 80s and early 90s, Pizza Hut had a computer-based (Apple IIGS) reading incentive program—I just Googled it and it's still around—which offered free personal pizzas if you correctly answered seven out of ten comprehension questions. Well, I was incentivised! Every recess, I sat down at the Apple IIGS and started taking those tests. Well, by the end of Grade 4 and Grade 5, I ate a lot of pizza, but I didn’t read any books. I just kept taking and retaking the tests until I got the questions correct. And, voila, free pizza! No Comprehension Necessary.
Do comprehension worksheets allow for students to share the thinking they had while reading texts? Usually not. Do they celebrate student thinking? Nope. Do they actually keep students accountable? Not really. Do they actually improve student learning? “No. There has never been one study that has ever proven that a comprehension worksheet has ever improved a students’ ability to read" (Steph Harvey). If they are ineffective, what can kids do instead? Read. That’s what kids should be doing, reading! However, the common response is there’s no time. So where do we find the time? By uncovering our benches.   

Guarding Benches

Previously I have posted about Debbie Miller’s analogy in her book No More Independent Reading Without Support  that teachers guard benches, and they often hold onto the things they’ve done for years without thinking deeply about the purposes. She relates this to soldiers in Eduardo Galleano’s short story, Bureaucracy 3:
At a barracks in Seville, in the middle of the courtyard of that barracks was a small bench. Next to the small bench, a soldier stood guard. No one knew why the bench had to be guarded. It was guarded around the clock—every day, every night, and from one generation of officers to the next, the order was passed on and the soldiers obeyed it. No one expressed any doubts or every asked why. If that’s how it was done, there had to be a reason.  
And so it continued until someone, some general or colonel, wanted to look at the original order. He had to rummage through all the files. After a good bit of poking around, he found the answer. Thirty-one years, two months and four days ago, an officer had ordered a guard to be stationed beside a small bench, which had just been painted, so that no one would think of sitting on wet paint (1992, 64). 
The bench was guarded for over thirty years without ever knowing the purpose! How many things do we do in schools and have no idea why we do them? When you think about teaching, can you think of some benches we have, things we’ve always done just because we’ve always done them? ​
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Rather than spending hours figuring out different literacy centers activities where the kids produce sheets and sheets of paper that require very little cognitive demand and often ends up at the bottom of a trashcan, perhaps the kids could spend that time reading and writing down their thinking about a story. Rather than having students fill out comprehension worksheets (shut-up sheets), perhaps the kids could be taught the art of discussion and engage in a thoughtful discussion about a story while being videoed so they can reflect on the depth of their discussion and thinking. 

Valuing the Thinking of Our Students

Over the past ten years, I have embraced the idea of celebrating kids’ thinking, and I have tried various ways to make their thinking and understanding visible. The ultimate goal of a teacher should be to understand a child’s thinking about a text, and how he or she developed that thinking. As inquiry-based teachers, we should teach the reader, not the reading, so that students can seamlessly transfer the skills, strategies, and concepts of reading from one text to another. So, what does that look like? I walked into a Grade 1 classroom and saw exactly what David Pearson expressed: student thinking being valued while providing authentic assessments of understanding. 

The students were sitting on the floor closely clustered around Ms. T who was reading, What Do You Do With an Idea by Kobi Yamada. Teachers and students were equipped with Post-it Notes, clipboards, and pencils. Conceptually, this book is quite difficult; however, what this book does do it push kids to question. In a nutshell, it is about a boy who has an idea that follows him around and grows and grows as the boy’s confidence grows until one day when…(read the book :-)) 


The students’ questions were exploding out of the room. As Ms. T read, students wrote and drew pictures of their questions, teachers scribed, and everyone turned and talked about their thinking. All thoughts were valued, and the students' thinking showed us their understanding, misconceptions, and overall comprehension. 
Students asked:
  • Why is the idea following him? 
  • Why does the idea have legs?
  • Is the idea inside an egg?
  • Why did they say it was a stupid idea?
  • Why is he keeping the idea to himself?
  • Why is he walking away from his idea? 
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When kids ask questions, they immediately want to answer them. They are fully invested in the reading process. So, Theresa masterfully then asked the students to discuss these questions in small groups.
 
Why is the idea following him? 
  • "Because it wanted a lot of attention."
  • "Because he wanted to be friends."
  • "Because [the idea] wants the boy’s imagination to grow."
  • "Because [the boy] was safe with [the idea]."
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When you walk into this classroom, you immediately realise that celebrating student thinking is of paramount importance. Kids were learning, thinking, and understanding, and time was not wasted. How can we ensure that what we value are students’ questions rather than those prescribed or ones we think are important, because in reality, they’re not important to the students. 

The Power of Our Words

1/12/2015

 
Think about these questions: 
  • What does it look like when a student's behavior is rude?
  • What does it look like when a student's behavior is mean? 
  • What does it look like when a student's behavior is bullying? 
During a recent staff meeting, our assistant principal asked us to discuss these questions. She based her presentation on the Huffington post article, Rude vs. Mean vs. Bullying: Defining the Differences by Signe Whitson. In this article, Whitson argues that we need to make sure that we define these words in order to understand their differences. How we define a child's behavior is supremely important; therefore, having a common understanding of the definitions is the first step. Here's how Whitson defines each: 
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  • Rude: Inadvertently saying or doing something that hurts someone else.
  • Mean: Purposefully saying or doing something to hurt someone once (or maybe twice).
  • Bullying: Intentionally aggressive behavior, repeated over time, that involves an imbalance of power.  
​As our discussions evolved, we reiterated the importance of naming behaviors rather than labeling children. Instead of saying, "John, you're being rude", say, "John, what you said was rude." This led to much deeper discussions about the power of our words, something that I have been fascinated by over the past several year. Recently, I have been collaborating with a few teachers on their language. We’ve transcribed lessons and are analysing the language being used. It’s been a wonderfully enlightening process to read what has been said in a classroom, as it provides a great deal of insight into teaching practice.
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We have been referencing The Power of Our Words: Teacher Language That Helps Children Learn by Paula Denton. She believes that languages “molds our sense of who we are; helps us understand how we think, work and play; and influences the nature of our relationships (Denton, 3).” I’m sure that all of us agree, too! Therefore, she states that the goals of teacher language should be to:
  • encourage habits and strategies that lead to learning
  • help children learn from each other
  • influence children to use language skilfully themselves
  • develop self-control
  • build a sense of community in and out of the classroom

She provides many ways to support the development of these goals; however, the three that connect the most with this week’s staff meeting are to be direct and genuine; mean what you say; and use statements rather than questions. 

Be Direct and Genuine
Denton states that when trying to get several students to listen to a direction, many of us use the phrase, “I like the way Sam is sitting quietly”; however, statements like these have inherent problems of extrinsic motivation and often do not produce the desired effects. The first problem is that students should not sit down on the rug so they gain praise from the teacher, but should sit down because it’s a time to learn and because they recognise their place in the learning environment. The second problem is that this language actually is “trying to manipulate the the other children to do what [the teacher] wanted without [the children] being conscious of [the teacher’s] control over them (Denton, 15).” In reality, many kids would rather carry on with their discussions than worry about sitting properly so the teacher would praise them. Instead of using this language, gain the attention of the entire class using a common signal and then state something like, “Come to the circle and take a seat now.”

Mean What We Say: Following Through on Our Words
We have to follow through on our expectations. If we expect students to be silent in the hallways, then we cannot permit any talking. If we expect quiet voices, we have to hold them to this expectation. Say only what you can and are willing to follow through on.

Use Statements Rather Than Questions
Denton continues to share the importance of using statements rather than questions. Often children hear, “Could you all go back to your seats now?” and while most of them will realise that this is really not a question, the statement is not clear. What should be said is, “Everyone go back to your seats now.” This is clear, honest, direct, and gives the kids only two choices, to go back or not go back—only one is not acceptable. Here is a list of some alternatives to try instead: ​
10 Rhetorical Questions to Stop Using in the Classroom by Blair Turner
This past week, through the wonders of social media, 10 Rhetorical Questions to Stop Using in the Classroom & 10 More Effective Alternatives by Blair Turner came to my attention. This humorously written article provides many alternatives to the questions we often use with our students after a student has been rude, mean or bullying.

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As you read through her list of ten questions teachers should never say, think about how many you might have said (I have said many):
  1. Why would that be okay?
  2. Is this funny to you? Oh, you think that’s funny? Do you think this is funny?
  3. Is this how we act in room 123?
  4. Are you really still ______ after we just talked about it?
  5. How many times have I said________?
  6. We’ve been learning about ________ for over two weeks, and NOBODY can answer my question?
  7. What. Are. You. Doing?
  8. Do you know why you’re in trouble? Do you know why you’re speaking to me? Do you know why you’re going to the office?
  9. Are you listening? Were you listening?
  10. Do you want to go to recess today?

Head to her blog to read about the alternatives. To read more about positive teacher language, here are some other articles and blog postings from The Responsive Classroom website:
  • Encouraging Words
  • Want Positive Behavior? Use Positive Language
  • Responding to Misbehavior
  • Keeping Routines Crisp
  • Encouraging Words
  • Naming What Children Can Do
  • Sometimes Less Is More
  • Teaching Without Rewards
  • Envisioning Language: Naming Positive Identities

Banned  Books  &  The  Rights  of  the  Reader

2/10/2015

 
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www.bannedbooksweek.org
During a recent cross-curricular planning meeting discussing an upcoming unit on the impact of technology on our lives, we began to discuss the concept of censorship with regards to access to information. We questioned our school's policy on internet controls and the filters in place to keep our students "safe". In order to push the depth of our students' thinking we came up with a provocatively debatable question. 
Should access to information be controlled?
As Banned Books Week comes to a close, I thought this was quite a powerful and pertinent question; books, once considered one of the highest forms of technology, continue to be censored and banned. But, why? 

During our school's past two Teacher Talks, where teachers present workshops on areas of interest,  our Deputy Head of School and Junior School Teacher Librarian both alluded to the concept of censorship. Our teacher-librarian shared the amazing wealth of information, access to books and technology, and how easily accessible they all are just from the JS Library Blog.

This past Thursday, our Deputy Head of School  spoke about the Self-system Theory, which emphasizes how motivation for students relies on three basic psychological needs—competence, autonomy, and relatedness.
  • Competence: student’s need to feel capable of academic work
  • Autonomy: student has a feeling that he or she has some choice and ability to make decisions
  • Relatedness: a student feel socially connected to teachers and peers
Sitting in the library listening to the teacher talk and looking around the library, I saw how well our library fosters student autonomy. When you walk in, you always see such wonderful displays of books. Recently, I walked in and saw this unassuming collection of books. Within this collection of books, one has been on the American Library Association Top 10 Most Challenged Books  across the United States since its publication in 2005. Can you guess which one?
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Yup, it’s And, Tango Makes Three. This adorable true story of two male penguins at the Bronx Zoo who father a baby penguin named Tango has been banned not only in countless schools and counties, but in other countries, as well. 

But, at Munich International School, And, Tango Makes Three sits front and center asking students to check it out. 

Censorship of books is not new and won’t stop in the foreseeable future, but to what degree do we unknowingly ban books for our students? When we’re in the library with our students, do we subconsciously or consciously ban books our students want to read because the books are too hard or too easy or they’ve read those books before or they’re only reading fiction books? 

I hope not at all. Libraries should be sanctuaries of freedom, openness, expression, and comfort. If you walk a little further into our library, you’ll see The Rights of the Reader Poster by Daniel Pennac on which he states that every reader has certain inalienable rights. 

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 I’ve been wondering, how do we support these rights? What do these look like in the Junior School? How do we provide choice? How do we foster student autonomy? How often do we allow students to stop reading books? How do we foster a love of reading? 

These questions are supremely important because as Daniel Pennac writes, “What we need to understand is that books weren’t written so that young people could write essays [or answer comprehension questions] about them, but so that they could read them if they really wanted to.”

Let’s make sure we’re helping them really want to read.

And, on a lighter note, if you question the technological impact of books, watch an oldie but a goodie:

The  POWER  of  "YET"

11/9/2015

 
Welcome Back Sesame Street
My last memories of watching Sesame Street involve me sitting in my friends’ living room silently detesting a show I once loved but now believed was too childish. Big fluffy animals singing silly songs about letters and numbers weren’t cool anymore. I was now eight-years old and the messages being sent abruptly stopped resounding within me.

It’s taken twenty-eight years for me to be reconnected with Sesame Street. YouTube has taken over the world of online videos and finding ways to quietly engage our 21-month old twins has led us to the Sesame Street YouTube Channel. This has led us to creating a playlist of famous musicians rewriting their own songs as“educational." From Usher to One Direction to Elvis Costello, many musicians have performed on Sesame Street. They are cute, educational, and quite catchy. Best of all, my kiddos love ‘em.

One song, however, has deeply reverberated with me, and over the past few weeks I have reflected on its message and connection to teaching and learning. The Power of Yet by Janelle Monae melodically brings up the important message of fostering a growth mindset.

You try to add but the numbers came out wrong
You tried to sing but you didn’t know the whole song
You tried to cook but it didn’t taste right
You tried to dunk but you didn’t get enough height
You just didn’t get it yet,
but you’ll make it soon I’ll bet.

It’s the power of yet.
We Often Forget About "Yet"
Mark Hecker, founder of Reach Incorporated, says that we often forget about “yet”.  In one of the most powerful TedTalks, he shares how the most disadvantaged have always been judged only by what they have done before and what they cannot do now. Rarely are they ever seen as what they can do or what they haven't done, yet. I began to think about teaching and how often our language focuses on the now rather than the then. How can we shift our language, so rather than saying, “Johnny does not know his 8-times table,” to saying, “Johnny knows his 5-times table and does not yet know his 8-times table?” This minimal shift changes what we are saying to children and parents from what is to what could be.

Growth Mindset
Carol Dweck, the guru of growth mindset research and Professor at Stanford University, states that “just the words "yet" or "not yet," give kids greater confidence, give them a path into the future that creates greater persistence…[E]very time they push out of their comfort zone to learn something new and difficult, the neurons in their brain can form new, stronger connections, and over time they can get smarter.”
When Do We Forget Yet? 
At what age do we stop saying, “….yet”? We always say it about babies as I have recently learned in my conversations with other parents that always end with “….yet”.

“Are they sitting up, yet?
“Have they started crawling, yet?”
“No, they are not talking, yet.”
“Are they eating solid foods, yet?”
“Yes, they are walking, but they’re not running, yet.”
“Are they only taking one nap, yet?”
“Have they stopped breast feeding, yet?”
“No, they are not sleeping through the night, yet.”

When and why do we stop asking and answering using, “yet”? We often hear students saying, "I can't..." How can we teach ourselves and our students to say, "...yet." Dweck believes that we can begin by “praising wisely, not praising intelligence or talent. That has failed. Don't do that anymore. But praising the process that kids engage in: their effort, their strategies, their focus, their perseverance, and their improvement. This process praise creates kids who are hardy and resilient.”

Many teachers in Grades 3 and 4 at Munich International School have begun the year focusing on the growth mindset and the power of yet using Jo Boaler's Week of Inspirational Math from Stanford University’s YouCubed Project. Within this week, students learn important growth mindset messages that help them develop confidence, try harder all year, persist with open and difficult problems and embrace mistakes and challenges. "All tasks are low floor and high ceiling – they are accessible to all students and they extend to high levels." This is one amazing example of how we can push our students to recognise the importance of developing a growth mindset. Here is Day 1's video on growth mindset: Day 1 Growth Mindset 

I was fortunate to observe several of these lessons and the discussions were extremely powerful. The learning experiences were challenging for all, but the results help set the stage for a year of deep understanding of mathematics. When students begin to think about their understanding of mathematics based on their experiences with it rather than their ability, they recognise that we can all learn not just mathematics, but all subjects. This past week was the beginning of something important. Below are some photos from the week of inspirational math:

Transcending  the  Classroom  Walls

4/9/2015

 
Meaningful Homework?
Since the beginning of school, I have been a part of many discussions across grade levels about the value and purpose of homework. Using our homework policy as a guide, teams have developed homework that helps consolidate learning, is rooted in inquiry, allows for a degree of choice, and integrates IT in transforming how homework is communicated and completed. 

At the end of last school year, I posted about Dan Meyer’s work on how to engage students in inquiry-based mathematics through open-ended problem solving. This past week, the Grade 2 team put this into practice while inquiring into how they can organise numbers by using a big bag of Gummi Bears packets. Following this lesson,  they created a video of the lesson and posted it on their blogs to support parents in understanding what is going on in the classroom; allow students to articulate their learning; and create engaging ways to extend learning beyond the classroom. 

This led one student bringing in several boxes of Hubba Bubba for the class to explore just as they had with Gummi Bears. Below shows the progression of the lesson they developed using Dan Meyer’s Three Acts of a Mathematical Story:

  • ACT 1: Engage All and Lower Barriers to Entry
  • ACT 2: Determine and Overcome Obstacles
  • ACT 3: Resolve Conflict and Extend
Act 1: Engage All and Lower Barriers to Entry
They presented the students with a visual that pushed students to question, wonder, and had very few words. It was something that connected to the students and would engage them in mathematical thinking that they might not have thought of before.

Students in Grade 2 were asked to pose questions about this box of Hubba Bubba. Rather than just posing the question yourself, students are able to formulate their own thinking, which also greatly increases engagement.
  • How many packs are in the box?
  • How many pieces are in each pack?
  • How many pieces are in the box?
  • How many pieces can fit in my mouth?
  • What flavor is the gum?
  • Are all the flavors the same? 
  • Am I going to get a pack?
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The teachers then asked students to share their questions and then focused on the question that will help support the standards they are focusing on as a class. “Great. Love these questions. I hope we get to all of them. Here’s one I’ll need your help with first: How many pieces are in the box? Now estimate and give an answer that is too low and an answer that is too high." This allows all students to focus on developing their estimation skills and gives access to all students.
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ACT 2: Determine and Overcome Obstacles
Students began to figure out what they need to know and solve the problem. “What information would be useful to know here?" After students have listed all the information they need in order to solve the problem, they document their exploration to answer them. 

"How big is a piece of gum?"
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"How many pieces are in a pack?"
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"How many packs are in the box?"
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"How can we easily organize these to count?" 
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"How else can we group these?"
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Students then took time to organise their mathematical thinking on paper.  
ACT 3: Resolve Conflict and Extend
The students then were shown the original box, again and discussed and reflected on how they solved the problem.  Whose estimates were the closest? How did they figure out their estimation? How did students solve the problem? Are there any other questions that weren't answered? 

"Yes, you can each have a pack of gum." :-) 

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The Messages We Send

2/9/2015

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Over the past several years, I have been fascinated by the power of our language on our students. While researching articles on learning through play, I stumbled across this article, Why Does Gender Matter? Counteracting Stereotypes With Young Children. The authors, Olaiya Aina and Petronella Cameron, forced me to think about the language I have used with students and how it affects gender stereotypes. They state, “While unintentional, a teacher’s inherent biases can perpetuate unfair stereotypes and may be manifested in discriminatory classroom practices,” (Aina and Cameron, 13). I began to wonder if my classroom environment was becoming like Toys R Us.
What I’m thinking about…

  • How do we allow children to combat stereotypes and foster independent thought?
  • Are we continuing to create a gender divide within academic disciplines?
  • Do our classrooms favour one gender over another?
  • Are the stories we read perpetuations of stereotypical gender roles? If so, are we educating our kids to recognize them?
  • How often do we say, “Boys will be boys,” “Boys and girls,” “Oh, she’s such a good girl…?”
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Neuromyths

1/7/2015

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This week, I wanted to share the work of Harvard Professor, Bruno della Chiesa, an educational neuroscientist. His presentation focused on how neuroscience is dispelling many of the ingrained myths we believe about learning. He spoke about the perpetuation of these myths due to the environments in which people live and the perspectives of those cultures. He calls them neuromyths – false beliefs about how the brain works and how people learn.

NEUROMYTHS

  • The Stupid Myth: We only use 10% of our brain anyway. This is completely untrue.
  • The Dubious Myth: Men and boys have different brains from women and girls. Completely false. There is no scientific backing to show that men and women have different brains. We are raised and trained to become men and women. That’s how our brains are shaped. Individual differences in talents certainly exist, and every student has a profile of strengths and weaknesses, but no evidence suggests that these profile are biologically limited by gender. These differences in performance are based on societal influence.
  • The Dangerous Myth: There are critical periods when certain matters must be taught or learned. There is no time to lose as everything is important about the brain is decided by the age of three. False. There are sensitive periods, which are windows of opportunity, but not critical periods. IT IS NEVER TOO LATE TO LEARN ANYTHING.
  • The Commercial Myth: Brain-based product/method—Improve your memory—Learn while you sleep. This doesn’t work.
  • The Funny Myth: I’m left-brained and she’s right-brained. WRONG. There is no such thing as a right brain or left brain. The danger is that we lead to stereotyping students’ capabilities and limitations, perpetuating, for instance, a child’s difficulty in maths. “It’s wrong to imply that strengths and weaknesses come from the dominance of one hemisphere and are resistant to good teaching and learning” (p.11). “When you clash with your spouse and you compromise by saying, “I’m right brained and he/she’s left brained” you know it’s BS.”
  • The Political Myth: A child’s brain can learn only one language at a time.There is no evidence to prove this. It has nothing to do with the capacity of the children. We have colonial pasts. That’s why we don’t do well with foreign languages. When you raise children bilingual, they might realize people outside of them are not
  • The Worst Myth: Some people are good at learning and some others are not. This sentences a person to a lifetime of negative self-perceptions.
  • Additional Information:
    • What Does the Brain Have to Do with Learning. Phi Delta Kappan, May 2011, p. 7-13 .
    • Brain Research, Learning, and Emotions
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Three Acts of a Mathematical Story

27/5/2015

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Problem Solving in Mathematics
Recently, the teachers at MIS watched a TedTalk by Dan Meyer on teaching mathematics: Math Class Needs a Makeover. 
Over the past several weeks, the math curriculum team has been working to put together guiding principles for how we teach mathematics based on much of his work of focusing on teaching math reasoning and patient problem solving. While researching, we came across some more of Dan Meyer’s work on engaging students in inquiry-based mathematics.

He has developed a model that he uses with students in Grades 5-12; however, it could be adapted to the younger grades. He calls it the Three-Acts of a Mathematical Story.

Act 1: Engage all and lower barriers to entry.
Present a visual that pushes students to question, wonder, and has very few words. It should be something that connects to the students and will engage them in mathematical thinking that they might not have thought of before.  Students are asked to pose questions based on these visuals. Watch this Act 1 using what we all love to pop: Bubblewrap, and allow your brain to wonder.
After watching, ask students to share their questions. Then focus on the guiding question on the standards you are trying to accomplish. “Great. Love these questions. I hope we get to all of them. Here’s one I’ll need your help with first.” Tell students you hope we’ll get around to answering all the questions on their list.

  • Guess how long the other bubble wrap pieces will take to pop.
  • Give an answer you know is too high.
  • Give an answer you know is too low.
Act 2: The protagonist/student overcomes obstacles, looks for resources, and develops new tools. This is the guts of modeling right here.

  • What information would be useful to know here?
  • What information doesn’t matter?
  • Look to the primary sources for answers and ask for guesses first.

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Act 3: Resolve the conflict and set up a sequel/extension.
Show the students the answers. Show the same visual but now with the answer. Ask students to see if their questions were answered. Whose answers were the closest? How did they guess? Allow time for discussion and reflection. Here are the videos below revealing the answers to the large and medium sheets of bubblewrap:

Large Bubblewrap
Medium Bubblewrap
Dan uses these bubblewrap sheets during breaks for himself and believes they’re soothing. He has developed these problems for high school and middle school students by examining the world through mathematical glasses. There are many other examples that involve Starburst (candy), caffeinated drinks, taco carts, sugar in soda, cutting Lucky Cow cheese evenly, which are all part of his Bank of Lessons from his blog: Dan Meyer Blog.

Where can we find more examples like this for Junior School students where students can engage in authentic, real-life inquiry? And, can we make our own?

All resources retrieved from Dan Meyer's Blog and used through his Creative Common license agreement. blog.mrmeyer.com/
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Concept-based  Mathematics

28/1/2015

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YouCubed:  Mathematical Fluency Without Fear 

Over the past several years, Jo Boaler, Professor at Stanford University, has developed YouCubed, a website dedicated to promoting inquiry- and concept-based mathematics instruction. In her most recent publication, Fluency Without Fear, she posits that a focus on fluency in mathematics is important; however, fluency is often misinterpreted as rote memorization of math facts without any number sense.
  • “High achieving students use number sense and it is critical that lower achieving students, instead of working on drill and memorization, also learn to use numbers flexibly and conceptually. Memorization and timed testing stand in the way of number sense, giving students the impression that sense making is not important.”
  • “When we emphasize memorization and testing in the name of fluency we are harming children, we are risking the future of our ever-quantitative society and we are threatening the discipline of mathematics (Boaler, pg. 8).”
Fluency Without Fear provides many concrete activities students can engage in to expand their conceptual understanding of number sense. Take a look at the end for some easy and ready-to-use activities for your classes, such as:
  • How Close to 100?
  • Pepperoni Pizza
  • How Many Are Hiding?
  • Shut the Box
Conceptual Learning: Number
Hear Jo speak about the importance of conceptual-based mathematics teaching and learning for all our students, particularly with our students who struggle the most.

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