Math – sonya terborg

Pictures Pack A Punch

02/26/2015 Sonya terBorg

If you are ever in the market for an infographic for kids, go to Pinterest and do a search for “infographics” “kids”. Find one to use was no easy task – there were so many great ones to choose from!

I am a little one-track minded at the moment with the PYP Exhibition about to start at our school. With that in mind, I decided to pick out a few infographics to support the Exhibition – but for different reasons.

1.To showcase what might be going on with our students

The exhibition can be stressful for us as teachers, but also for kids. I liked this infographic because it identifies potential stressors, offers kid-tested solutions for resolving the stress (and reminding teachers to integrate opportunities for things such as movement, music, and time outside during the school day), and it gives parents some tips on supporting their child. It is fairly accessible, graphically, although still contains a lot of text which could be challenging for those without English as a first language.

2. To show how infographics can be created in “real life”:

Infographics-In-Real-Life-1-620x460 — Image Credit

This is from a Portuguese website in which ‘real life’ photographs are taken and edited to become infographics. I really like this idea of mixing the concrete materials with the data visualisation. This is accessible for kids and a great way for them to showcase statistics that they have gathered over the course of their inquiries.

3. To show how two things can be compared

Many times, the students will end up comparing two different things. I really liked this infographic that uses direct comparison and photography to showcase the data. Again, I think that the ideas in this infographic are ones that could be replicated by our students in order to share their own data. I liked that for this example (owning a cat or a dog) it was an idea that was accessible to the kids at their level while still be sophisticated in design and depth of information shared.

4. To show how to use everyday objects to visualize data

I really like this idea of taking something like Lego or other toys and using them to convey a message. The possibilities for arranging legos and photographing them (or just displaying them during the exhibition) are endless. This is definitely something that I think if you shared this picture with kids, they would very quickly and very easily make up their own designs with the information they have from their research. And they look cool too!

5. To show the key points of Infographic design in an infographic.

This little set wouldn’t be complete if there wasn’t a ‘how to’ infographic! I like this one for the clear and simple way that it outlines the key features of a good infographic and gives a few pointers about fonts and colors. I also like that it references adding the sources from where you got your information. This isn’t perhaps the MOST kid-friendly but I think it does a good job of outlining some of the key points – until you get one of your expert infographic groups to make their own Infographic on Infographics!

Innovation, Inquiry, Math

A Geometry Inquiry with Attitude

04/02/2014 Sonya terBorg

One of my concerns is that math in my classroom is not as inquiry based as I would like it to be. My students and I just began a unit on Geometry. I gave the pretest and for the most part, students had a spattering of knowledge and the test was completed with much hair pulling and cries of “Man! I KNOW this….but….I forgot!”. When we went over the paper, I could see a collective “aha” from the majority of the students as they started to dust off the vocabulary sitting at the back of their minds. So, what to do?

I did some scouring of the internet and came up with a couple of really interesting reads: Angle Measurement – An Opportunity for Equity, and Inquiry Maths: A Parallel Lines Inquiry.

After reading these articles, the next day my students and I sat with the pretest and pulled the vocabulary from it. They spent the lesson with math dictionaries, math tools, the Khan Academy, and various math text books from the classroom shelves in order to create an understanding of what these terms meant. They found all these connections that I wanted them to know but didn’t want to just tell them: that perpendicular lines were also intersecting lines but not all intersecting lines are perpendicular. Same with equilateral triangles and isosceles triangles (all equilateral triangles are isosceles but all isosceles are not equilateral). Some asked if they could work on their “Math Dictionaries” at home. Others took screen shots of Khan Academy videos and added their own notes. I told them they were preparing for an inquiry and they needed to be well equipped!

The next day, we discussed the idea of using math as a language. I drew a rectangle on the board in purple marker. If this were to be described using the English language, I would call it “Purple Box”. If it were to be described using Math language, I would call it “A rectangular quadrangle with interior angles of 90 degrees each (right angles) formed by a set of horizontal, parallel line segments and a set of vertical, parallel line segments. They got the idea.

I told the class that this was an open, collaborative inquiry. That meant they were free to consult any source they needed in order to extend their inquiry and that the work was collaborative in that I wanted them to build off each others ideas. I have 18 students (I know, I am blessed!) and so I printed off 9 pictures (3 of each image) so that children had a choice of where to work in the small room. I also wanted to be able to have them come together with other groups during the next lesson to share and compare their findings. Before I showed them the images, I shared the Success Criteria for the lesson:

Here are the images I used, the first one from the Parallel Lines inquiry and the second and third from another Inquiry Maths Inquiry:

My students were shown the pictures, reminded of the Success Criteria for the lesson, and were off! It was fascinating. They partnered up in a similar fashion to the day before when they were creating their vocabulary understandings and quickly started to use their knowledge to describe their image. I “casually” asked if anyone wanted a protractor (YES! YES! YES!). As I wandered around I saw children reading, questioning, measuring and using their math language to describe the image in front of them. “Can we draw on it?” Yes! For one group who had the star shaped image, this led to some pretty crazy coloring/marking which to my naive eye looked more like silly scribbling than serious math but I let them keep going. One group started talking about symmetry and I found some mirrors and laid them on their table which started another investigation into where that line of symmetry actually was.

This was supposed to last 15 minutes but it was clear they had more than 15 minutes of math language in them! As the end of the lesson neared, I asked them to briefly group with the other people who had the same image to get an idea of what others had done. Cries of, “I was going to do that next!”, “I hadn’t thought of that!”, “I forgot to put that, too! ” and “Where did you get a mirror from?!” were heard around the room.

I have a really great class of kids but like all kids they need to be asked to think about why they do what they do and how they are behaving. As a PYP school, we offer a values-laden curriculum so teaching about attitudes is part of what we do. We are currently working on the culminating project of the PYP – the Exhibition. It requires a lot of group work and one of the things I am noticing is that students need more than to be physically placed in a pod of four students, for group work to be successful. We have been looking at the type of attitudes we expect to see at our school and I wanted them to see the connection to this in math class so I gave them the following exit slip for the lesson:

Their comments were so insightful:

curiosity…because I wanted to see just how much I could write in math language

confidence…because I knew I knew a lot about this and I knew I could describe the picture in a lot of details

respect…because I listened to the ideas of the person I was working with and also added my ideas

and the student that I thought was goofing off:

creativity…because I was able to add really colorful and interesting designs to our star and it looked really good and then it also helped my group see patterns within the star and we were able to add a lot more information

I think the students were not the only ones learning something today!

To download a PDF of the lesson plan and materials used today, click here

Math, Mindset

More on Mindset

02/13/2014 Sonya terBorg

A couple of weeks ago, I posted about developing a growth mindset , in particular in math class. Engage their Minds chimed in with more great resources for developing a growth mindset. It’s something that clearly people are thinking about.

One of the ideas I had was to follow in the steps of the Khan Academy and add an inspiring quote or statement to printed papers I gave my students to encourage them as they learned. I was going over the types of fraction work my kids needed and was about to print some customised worksheets for them to practise from Math-Aids.com when I noticed that at the end of each worksheet is a box for you to add instructions or other text. What a perfect spot for a growth mindset quote!

And then I thought, why not let the kids create both their own learning pages and add their own words of encouragement? So I did. And they were great!

Give it a go!

Learning, Math

Failure is a Prerequisite…And 2 Math Gems

01/30/2014 Sonya terBorg

Have I mentioned I love Gaping Void? Good.

Here is one of their latest posts:

The cartoon was accompanied by the text: “it’s something we tell our children every day”.

Do we?

Sometimes I wonder.

My kids use Khan Academy for math. At the moment we are working on fractions (fourth graders) and we have just started to move into unchartered waters for some students. They are unsure. They don’t know what they are doing. They are scared to fail. I can see it in their hesitation, their avoidance of tasks that are deemed “too hard”. So, what to do?

Today, I decided to show them the coaches report that I generated for the links we are working on at the moment. It looks like this:

For those of you who are unfamiliar, red means “struggling”, grey is “not yet started”, the pale blue means “practiced”, slightly darker blue means “level one”, darker still means “level two”, and the darkest blue is “mastered”. When I pulled this graph up, there were a few gasps around the room. Struggling! Red! Oh no! I got everyone’s attention on the board and said, “There are some people I am very concerned about according to this graph. Do you know who they are?”

Of course, “the red people” was the chorus around the room. When I asked why, the response was that those people were not doing good, that they didn’t know, that they were failing.

No, I told them. They are not the people I am concerned about. I am concerned about the grey people – the ones who are yet to try. If you are in the red or in the blue, I know how to help you, how to move you on from where you are at. If you won’t try or haven’t tried, how can I know how to help you? You might fail, yes. But you might succeed too. And I know that if you do move to the red, you won’t be there for long because “failure is the prerequisite for learning”.

I promised you “2 math gems” = and here they are:

Gem #1

If you are at all like me, you have written a test for students that requires them to show their work. Well, last weekend, I read this article that invites students to choose whether or not they show their working. The ideas behind this option are sound and really made me question why I ask this of my students and wonder what the consequence is on thinking in my students. The author, David Ginsburg, goes on to suggest mixing up the usual “show your thinking” question with a different take on the format: He suggests giving students a completed equation and asking them to explain why it is or is not correct. This naturally means they have to explain their thinking.

Gem #2

Via one of my favorite blogs, Engage their Minds, I was introduced to the math version of Would You Rather…? It is awesome – and just happened to have a fraction problem up today which suited us perfectly.

A quick run-through of the site shows me that some decent math skills are required but there is also the element of personal choice BUT you must explain your choice MATHEMATICALLY (not just based on personal preference). It is really cool – check it out. I can see kids making these for each other too. And if you have younger kids, Terri from ETM, has created some Would You Rather questions for Valentines Day with a slightly lower level of math skills needed. Check it out!

Math, Mindset

Developing Growth Mindset in an Inquiry Based Math Class

11/25/201311/26/2013 Sonya terBorg

I have been researching the use of ‘good’ questions in math via the book Open-Ended Maths Activities by Peter Sullivan and Pat Liburn. This book challenges teachers to think more deeply about math questioning and about providing students with opportunities to show the depth of their thinking. It places math understanding on a continuum and allows you to really see the thinking process that children go through when solving problems. The problems differ from ‘regular’ math questions in that the focus in not necessarily on THE right answer, but more on the process of problem solving, predicting, refining thinking, justifying decisions and creating own like problems.

The three main features of a ‘good’ question:

They require more than remembering a fact or reproducing a skill
Students can learn by answering the questions, and the teacher learns about each student from the attempt
There may be several acceptable answers

In partners, we started with this question:

We will take a look at the different strategies people used and then move on to a more challenging question. As children work, I am looking at the following behaviors (not all at once, but throughout the process):

works cooperatively
works independently
makes a plan
keeps trying
when stuck, tries something different
discusses work with others
uses materials when useful
draws diagrams when necessary
concentrates on the task
asks questions
organizes information systematically
explains and displays ideas clearly
looks for all possibilities
able to generalize
accepts assistance from others
is confident
uses a range of mathematical strategies

After the kids finished their work, I scanned it and shared my thinking with them as I went through their responses. This was probably the most valuable part of the lesson – and the part where we begin to put into practice the idea of growth mindset. By actively illustrating what I am thinking and where I see the next steps for all groups of children, it promotes the idea of deeper learner for all. What I like about this approach is that there is feedback that is applicable for all students and everyone can see something that they can look to improve on during the next question. We did this on our smart board with the whole class. Here are samples of some of the feedback I gave my students:

Our next step was to stay in our partnerships (mixed ability) and tackle a few more questions of increasing difficulty. Each time, I scanned their papers and we discussed and gave feedback as a group. Toward the end, the students were very adept at indicating the strengths of the teams and offering suggestions for growth.

We have now moved on to applying our problem solving strategies to a weekly math challenge. A math challenge is a problem that is designed to last more than one lesson before a solution is found. It is a chance to show what you know about math, to make predictions, to create your own problems, and to share your reflections on yourself as a mathematician.

Each week, we will have a new math challenge. It can be solved independently or in a small group. It can be done at home or at school. It has a due date (usually will be on Friday), and it is designed to help students apply what we are working on or skills that have been focused on in class already.

Each math challenge comes with the same list of ten criteria. Each of these criteria is equally important. Students are challenged to respond to each of the criteria to the best of your ability. These criteria will be the same each week.

Here is our first question:

You might notice the quote at the bottom of the question slip. After reading the work of Carol Dweck on establishing a growth mindset, I then saw that the Khan Academy have also utilized this research and have found a way to improve student performance via one simple trick: adding a growth mindset inspired quote to their math pages. This is just one way of reminding students or drawing their attention to the fact their brains are capable of growth and new learning.

We just started this today and worked on it for about fifteen minutes. The kids were super excited and it was great to see them tackle this problem with such a high degree of independence.

After setting this up, I was reminded of a post I read recently about additive grading. I am now rethinking how I am going to grade this to some degree. But that’s for another post…

Learning, Math

Struggling…

09/12/2013 Sonya terBorg

Today we were looking at the Khan Academy website. The coaching dashboard allows me to see where the students are at in their learning. It provides the following categories:

As we were looking at this, one student mentioned that they didn’t want anyone to know if they ever were in the struggling category. The student was embarrassed to think that others would find out that they were struggling with a concept.

This reminded me of an article I had read recently, which I encourage you to read. It brings up the idea of struggle and the cultural connotations around this word. Depending on how you view struggle, changes the way you deal with struggles that you come across in your learning:

Obviously if struggle indicates weakness — a lack of intelligence — it makes you feel bad, and so you’re less likely to put up with it. But if struggle indicates strength — an ability to face down the challenges that inevitably occur when you are trying to learn something — you’re more willing to accept it.

As we discussed this further, I shared with the students the idea of peer coaching. In previous classes, I have had a “Can Help/Need Help” board where students have been welcome to add their name to either side depending on if they feel confident in sharing their knowledge with others, or if they would like a classmate to work with them. This is just one strategy that will be used in the coming year to help further our learning.

What does struggle mean to you?

Math

Get Started: Khan Academy

09/01/201308/31/2013 Sonya terBorg

Starting at a new school means re-evaluating the things I “used to do back at my old school”. One of these “used to do’s” is the Khan Academy, which aside from sporadic usage by some teachers, is relatively new to our Junior School.

As I began looking over the (recently updated) Khan Academy website, I was once again blown away by what an awesome tool this is for teaching math. I put together a packet of information for my team as we begin discussions on the role the Khan Academy will play in our classroom. The majority of the packet comes from me pulling from the mountain of resources available on the Khan Academy website. There is a ton of stuff there to help you get started on your Khan journey. Try clicking here for a good place to begin.

The packet I put together contains links to KA materials on their website as well as some materials that I downloaded from the website and (confession time) reformatted so the packet would look more organised.

One of the things I like the most about the Khan Academy is that it (in its own words) elevates the role of the teacher:

Teachers are critical in a Khan Academy classroom

Teachers provide the human element to inspire, motive and guide students through their learning paths. There are some people who believe that technology in education diminishes the importance of teachers. In our experience, nothing could be further from the truth. The fantastic teachers we have seen implement Khan Academy are bright, innovative, creative, and they take their classrooms to new heights. They realize that technology is a tool to help make classrooms more personalized, more mastery-based and more individualized.

Shifting from lecturer to domain expert, master coach, and mentor

In a personalized, mastery-based learning environment, the role of the teachers is elevated. Responding to the needs of many learners goes beyond classroom management and a lesson plan. Teachers must be responsive to the data and must problem solve for every learner individually.

Technology allows the role to evolve to allow teachers to minimize time grading homework or giving the same lecture, and instead use real-time data to ensure time is used most effectively. Khan Academy provides the tools so you can do what you went into teaching to do – to personally interact with and provide guidance to every student, and to engage students in collaborative activities and interactions. Technology will not replace teachers, but empower you to be great mentors to your students.

We are about to have a back-to-school night and later a parent information session regarding the use of the Khan Academy and this will definitely be information I want to share with my parents. It has also reminded me that I need to be on the lookout for really good collaborative activities and interactions in math for my students. Which is where YOU come in! Please share your gems for thought-provoking, discussion based problem solving for math in the comments box below. I need your help!

For the Khan Academy packet I put together for my team, click here.

Brain Research, Math

How To Learn Math

08/18/2013 Sonya terBorg

Thanks to my new colleague, I learned of a free class offered online by Stanford titled How To Learn Math.

I started the class and am on to the third lesson. Each lesson comprises of short video clips with questions in between. Your submissions are peer reviewed and you play your part in reviewing others responses to the same questions. Some of the submissions are self-reviewed – more of a reflection on what you have just watched in the video.

The following ‘definition’ of a mathematician was given in one of the readings that does not use the word ‘numbers’ but paints a different picture of the way in which a mathematician ‘works’

A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. ~Paul Lockhart, A Mathematician’s Lament

The above quote made me think of one of my favorite mathematicians (after Sal Khan, she is my favorite!) – Vi Hart. I think to begin a year with some of her videos is to expose your class instantly to whole new mindset on math.

The first lesson also talked about the power of direct feedback and with prefacing your feedback (critical commentary on learning) with the statement: “I am giving you this feedback because I believe in you”. Research showed a greater acceptance of the feedback and improvement by the student when they felt that the teacher believed in them. The suggestion is not to preface every comment with this statement but rather to recognize the power of relationship, honesty, and trust between student and teacher.

The second lesson spoke of math and mindset and taps into the work of Carol Dweck on the subject of mindset. Again, research shows that three weeks is the time period it can take your brain to develop new pathways when learning something new. This was interesting to me as I am sure that before the three week period is up, I will often convince myself that I am not an X person, or I can’t possibly do Y. Armed with this information, I hope to look into hanging in there a bit longer when I next tackle something new.

I have until the end of September to complete the eight session course. I am motivated by what I have learned thus far and by the fact that I know some of my colleagues are also doing the same course. The format is easy to follow, the information interesting, and the chance to get feedback on ideas from like minded students, teachers, and parents who are also doing the course is fascinating.

If you are interested in this free open learning opportunity, click here for more information. As I thought about extending my own learning and in light of the day looming near in which students are about to return to school, I found this poster which sums up my feelings on learning and what I want to foster in my class this year – which is why learning is something I am choosing to do now.

21st Century, Innovation, Math

Reason #4565 Why I Love the Khan Academy

04/03/201204/03/2012 Sonya terBorg

I couldn’t have said it better myself! This is what I want to keep on an index card to pass out to those people who either have never heard of the Khan Academy (seriously?) or who scoff at it’s relevance or purpose in our education system. In fact, I just may whip a few up when I finish this post! Leave a comment below if you want me to send you your own!

“This has absolutely nothing to do with replacing teachers. When we talk about getting lectures out of the room, that’s because we think we can move teachers up the value chain. That they are better off forming the bonds and connections. That’s what you need a human being to do and for a really great teacher to do. Khan Academy takes some of the more traditional stuff off the plate and now, all of a sudden, the classroom becomes a richer and more stimulating experience.” ~ Sal Khan

For more of Sal’s comments, click here.

Design, Innovation, Math

The Best Way To Teach Math

03/21/201205/01/2013 Sonya terBorg

I read an article that expressed extreme dislike (understatement) for the Everyday Math curriculum. This is the same curriculum we currently use in school and was the same I used in my last school, as well as another of the schools I have taught in.

Do I love it? No. Do I loathe it? No. I actually find it to be quite adequate as a basis for developing math skills within a class of students IF you make a few adjustments and additions to support student learning. Having taught in one school where your progress through the math book was monitored on a day by day basis with repercussions for not being in line with ‘state expectations’, I know that words like adjustments and additions are challenging if not impossible to entertain. If you are fortunate enough to work in a school that allows you the freedom to teach and facilitate learning amongst your students AND uses the Everyday Math curriculum, here are some points I have picked up along the way…

If you teach in an IB school, you are going to be asked to look for ways to authentically integrate data handling, measurement and geometry into your units of inquiry. This is difficult but not impossible to do if the basis of your math program is EDM. I haven’t done it yet, but I would love to sit down and look for the connections between these areas of math and our units and pull them into their own ‘math unit’.

Again, for IB school teachers, you are not expected to integrate number, pattern and function into your units of inquiry. Think of these components of math as the ‘alphabet’ – addition, subtraction, multiplication, division, fractions, decimals, percentages…these all should be taught in their own right and EDM provides multiple ways of sharing the ‘why’ behind these processes.

Use your discretion! As a teacher, you can decide how you present the content to your students. I find the EDM methods for some things quite confusing. I also find some of them really help me explain the ‘why’ to kids who then really get it. If I have kids who are already solid in a method that works for them, great! Just like we make kids eat a balanced diet, I ask my kids to at least follow along but the freedom is theirs to use whichever method works for them -mostly it is the one they are comfortable with but sometimes they will change it up and go with something new that makes even more sense to them.

Play the games – or at least some of them. They are great for engaging discussion and when disagreements arise, perfect grounds for ‘forcing’ kids to demonstrate and explain their understanding of a concept.

Don’t start at the very beginning of each lesson. It is just a guide, a plan. It doesn’t say that if you don’t follow it precisely, the world will end! There is actually a lot of good problem solving and analytical thought required in much of the enrichment and study link pages. Flip things around and have students work collaboratively on these in class when they are supported by yourself and other students and can engage in discussion.

Use the Khan Academy! It is brilliant. I can’t figure out why more people don’t use it. I have had a few parents say they don’t like it. That they don’t want their child sitting in front of a computer and “can’t they just have a worksheet for once?”. Seriously? Who doesn’t want quality online support by way of the videos, hints that show the ‘how’ of solving a problem, instant feedback on their work and some really fun badges! If you assign Khan videos/exercises for homework, your students are prepared for the more analytical problem solving challenges at school that ask them to apply their understanding. We are fortunate, here in Boise, to have Sal Khan coming to town to share his thoughts on the changing face of education. Educators were asked to share their experiences with the Khan Academy – here is an excerpt from my letter:

I never liked math as a kid. As a teacher, I love it. I love the mystery of it, the methods and the madness! I am really grateful to Sal and his Academy for helping me develop a greater love for math. I love that my kids get the chance to challenge themselves and review their work on a regular basis. I love that the videos really explain the concepts in a clear way. I love that I have more time for doing and less need for telling. I love that I can see my kids whiz off into the math matrix with a huge interest and passion for developing their math skills. It is “cool” to love math in my classroom and I have had kids log on each week, on average, for about 2 and half to 3 hours between Monday and Thursday nights. The “requirement” is 15 minutes a night.

I think my own classroom math program could do with some work. I would like to be a little more dedicated to integrating with our units in a more meaningful way and relying less on the unit tests at the end of each unit of work in the EDM book. I would love there to be a few more hours in the day so we could play more of the games together. Perhaps these could also become homework tasks? What I would also like to do is to focus more time and importance on remembering to talk math with kids. This article reminded me that more important than which book or website your ideas come from, make sure you are engaging kids in math related discussions – even (or especially) when it is not ‘math’ time. A great way to do this with kids is to tap into the booming market of infographics. They are everywhere and are a perfect way to bring math into the discussion. Take a look at these as examples:

I see two uses for these – discussion and inspiration for creation. I can already hear a few cries of ‘but we don’t have the technology to do that!”. Who says you need technology to make an infographic? Ultimately, it is a graphic that shares information (we used to call those ‘charts’ or ‘diagrams’ or even ‘graphs’ when I was at school). There are people in the wings, ready to launch infographic capabilities to the masses: here are ten sites you could use, a great resource called visual.ly, or five kinds of infographics and free tools to make them. (I can see another post coming soon after I try some of these out!).

Until then, take a leaf out of the book of this Portugese design firm, who created the following ‘low tech’ infographics that are awesome and totally do-able in any classroom and would again, encourage and stimulate mathematical conversations both in their construction and sharing:

What works for you in your math classroom? Or as a parent, what works for you at home?

I know people may have extreme feelings towards Everyday Math, and if I were given no leeway in how to implement in my classroom, if I were not allowed to supplement where necessary (in my professional opinion) and to skip parts that seem somewhat pointless, then I might have some of those feelings too. Words like accountability and consistency are just the words that got Everyday Math its stronghold in many schools. In order to have a prescribed set of units of work, complete with tests that even a muppet could pick up and spew forth over the the classroom, schools needed to subscribe to ‘something’ – and Everyday Math has become that ‘something’ for many schools. What is missing – and can’t even be found by substituting the Khan Academy (gasp!) – is good math teaching. I am not sure which comes first but if teachers were more confident in teaching math, pulling from a variety of resources to create a balanced math diet, student performance in math would rise, parents anxiety about their child’s level of achievement would dissipate and administrators would breathe, have confidence in their faculty and let them do their job.

Am I going to throw my hands up in the air and rage against the Everyday Math machine? At this stage no. Am I going to blindly plod through each page in the text (do I even have to answer that one?). Ultimately, I trust that educators and administrators and parents can work together for the greater good – the kids.

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Teachers are critical in a Khan Academy classroom

Shifting from lecturer to domain expert, master coach, and mentor

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