- a sign that she is not learning the concepts of math in class. It may be taught in the same way that I taught grammar years ago, workbook style, algorhythms, repetition and little meaning.
- the assessment was inadequate in measuring the learning that his daughter had achieved in the classroom. I have had great success with teaching math using open ended, "conceptual math" (Dan Meyer et. al.), yet it has become obvious to me that the way I assess learning will have to change along with the more patient, creative approach to learning math concepts. It is my sincere hope that the changes I have made in my math classes will eventually result in my kids out- performing others on provincial assessment or, at the very least, improving their test scores drastically.
Friday, December 31, 2010
Wednesday, December 29, 2010
- Ask yourself each day, “Was what the kids did with computers today good?" "Did it include higher order thinking and was it a transformative use of technology?"
- Remember that quality work takes time. The structure of the classroom and the timetable will need to be changed.
- Shun ‘software du jour. Have an all encompassing goal like "students will learn to think".
- Stop using computer time for non-computing activities. Use the encyclopedias in the library if you need to.
- If a kid is breathing, she has probably surpassed the NETS. Real change occurs when you have one achievable, measureable goal, not a shopping list (much like the curriculum?!).
- Commit to the entire writing process for digital products. Great digital products like movies and slide shows are based on great writing.
- Stop integrating someone else’s curriculum. Commit to your goal (perhaps to have the kids learn to think) and stick to the course, don't deviate for every holiday theme.
- Not with my computers you don’t! Demand that appropriate, engaging and transformative technology use is a requirement in your class and in everybody else's too.
Sunday, December 26, 2010
1. Confusing difficulty with rigor.
2. Mistaking process for understanding.
He adds that:
He goes on to say that: ."
Wednesday, December 22, 2010
I decided I would gather data for a presentation I am doing on higher order thinking in math and writing (or any other subject). I created my own google doc that I hope you look at and add the ways you ask your students to be knowledge producers in your classroom. Help me out with my presentation and pass it on!
Saturday, December 18, 2010
- formulation of problem is more important than solution to problem
- pseudo context or pseudo problems, insulting to students
- we are fixated by problems on dead trees
- images used to convey problem should contain structure, steps and hook
- the hook should be up front
- roll of tape question, no one doesn't know how to start
- have more demanding questions
- build a culture of curiosity
- most traditional problem solving is impatient problem solving, banging numbers together to get to one right answer
- new problems should focus on objects of perplexity that pose questions to the viewer
- photo from the movie "Holes"- the movie, shovel deep and wide. How much dirt? How long? Let them ask the questions. ( see Dan Meyer's blog)
Friday, December 17, 2010
He begins by saying that many of us have it wrong. We are talking about changing schools. What is really happening is that the way everybody is learning is changing. When he was in Saskatoon at the IT Summit he said that if we did nothing else and didn't feel ready to change our classrooms, we needed to begin to be a 21st century learner ourselves.
1. Share a Vision- our vision is that all students will use technology to be knowledge producers
2. Your School Should Be a Change Agent- our school is a technology school within the division
3. Analyze Data- we are collecting data based on our objective
4. Introduce Students to Their Data- students in my room are aware of our schools objective and the data collected
5. Increase Rigor- we are learning about rigor and the levels of rigor
6. Teach Students the levels of rigor- we are teaching our kids the levels of rigor (Bernajean Porter)
7. Expectations- we try to keep our expectations are high
8. Teach Students How to Learn- there is a lot of talk about meta-cognition and think alouds
9. Teachers as Learners Environment- the PLC's are dedicated to making teachers learners
10. Teach Smarter and Not Harder- it is hard to teach smarter, it is a process of change
As I wrote all of the comments for our school, I realize that I have salted in a heavy dose of optimism. Perhaps I'm too easy on our staff?
How does your school rate on the list?
Wednesday, December 15, 2010
His second post is about comparing items in the grocery store. He provides many photos which will create great opportunities for your kids to do higher order thinking in your math class.
If you are new to his ideas, you can read more on my posts about math and/or Dan's work. Basically, his idea is that in math problem solving we pave the road to the answer and don't allow deep, divergent thinking about the process of problem solving. From my experience, even when teachers try to provide more open ended questions, students ask them for more information and the teacher can't resist and begins to pave the road again by giving hints or teaching convergent techniques.
As Conrad Wolfram says, let them struggle, hear about their process and give them a little technique (not too much). I would highly encourage you to look into the work of Dan Meyer, Conrad Wolfram, Alfie Kohn and Paul Lockhart. I have blog posts on all of them and links to their work.
Enjoy continuing the math-makeover!
From time to time, I hear that the university community isn't embracing 21st century tools and skills. This video certainly doesn't support that idea. I love it when he says it is not enough to just present the numbers, he wanted to engage his audience and present some ideas through data. I've definitely got this video on my delicious account for when my class is looking at data management.
Not sure you caught that? As I wrote the last sentence I realized that great math is not isolated topics and isolated lessons. I will plan to use this video to encourage my students to report their data in a creative way for their critical thinking projects. (In case you are wondering, our current class critical question can be found on our water wiki. The critical question can be found at the bottom of the page.)
Saturday, December 11, 2010
I plan on having my kids find sports stadia/arenas on google earth and then describing how big they are. I will tell them they have to describe their size in three diferent ways. I may teach them how to use the ruler tool on google earth.
I may follow through with further study of how the building was constructed or to compare it to other sports arenas. I would use higher order thinking questions such as "which building ws the hardest to build?" or "which building has the most impact on it's community?"
It's going to be a blast!
One of the beautiful ideas of 21st century learning is the idea of sharing. How cool is it that Kim attneds a conference in Japan, takes notes and makes them available to me (and everyone!). I plan to use many of the links from her google doc.
This reminds me of a class activity we did the other day. We are developing a list of research and critical questions on the topic of water with our partners in Puerto Vallarta, Mexico. Six pods of students took a half an hour of class time to create a google doc. It was imperfect, a bit disjointed and unformatted. After we were done a student stayed back from recess to format the document and to add more questions to guide our research. I did not ask her to do this, for her it was fun. Felt a lot like wikipedia to me, for that matter, we could have used a wiki.
Thanks a million Kim, I'll do the same for you when I am lucky enough to be at a conference!
Wednesday, December 8, 2010
One of the sites on the OER list is mathalicious. Wow! I can't believe this stuff is out there. If you are a classroom teacher this is just too juicy. As Alan November once said to us, "This stuff is low hanging fruit!" These resources "can" fit so well with what Dan Meyer, Paul Lockhart, Conrad Wolfram, Alfie Kohn and many others are saying about learning math. These multi-media activities are truly impressive, engaging, creative and are aimed at middle years to high school students.
Notice I said can fit so well. If you take a look at the activities they are very engaging and well put together. An example is the tunnel digging activity for ratio and proportion. If you take a close look it is really just traditional problem solving questions put in an engaging way. All the information is given, as Dan Meyer says, the way is paved for them to find the answer, no deep thinking is needed about the processes involved. For my taste, the questions give too much information for them to be process oriented, creative problem solving opportunities. For example, the simple question I would ask is "How much dirt would have to be removed to dig the tunnel?" I would not mention volume, I would not give numbers. As Paul Lockhart says, "let them struggle, then give them some technique, but not too much".
They also give links to favorites of mine like HippoCampus and the Khan Academy.
Among the other OER resources listed are:
Our school's main PD focus is to have our students understand and perform better in math. Everything I read these days is about higher level thinking and creating as integral processes in learning mathematics. My "community of interest" group's goal is for students to understand and use higher order thinking as learners (and to be knowledge producers).
For a long time, I had described this as teaching thinking rather than researching or following directions. Turns out that in 1956, Bloom had this cased for us. This year has been a very rewarding year for my students and I because for the first time ever, it is a clearly stated goal in my classroom to learn how to think in every single thing we do!
I was sent these links by a good friend Judy Byers. She is a very important part of my PLC. Check them out!
Saturday, December 4, 2010
If you can't read the whole thing (25 pages) I would suggest you move to his conclusion where he gives a scathing description of math education as it is in most schools.
His main idea is that math education is broken and not worth fixing. The patient is dead. Math needs to be recreated, not revived. He says students claim "..math class is stupid and boring...they are right...". Math is taught as a paint by number method void of imagination, creativity and discovery. Students are never allowed to create or think. Traditional math is about following directions, not creating directions. His main claim is that none of us recognize math as an art.
Math reformers claim for testing and/or higher standards will fix the problem. Lockhart says they are all wrong. He gives solutions:
- thinking rather than following directions
- math need not relate to real life, sometimes it's beauty is in it's complete irrelevance to real life
- give them a problem and let them struggle with it, don't show them how to solve it
- give them some technique to solve the problem, but not too much
- play games, teach them chess and go, hex and backgammon, sprouts and nim, whatever, make up a game. Do puzzles.
- expose them to situations where deductive reasoning is necessary.
- don't worry about notation and technique.
- help them to become active and creative mathematical thinkers
- don't get caught up in the vocabulary (ie. quadrilateral)
- story that matters, not the ending
I have been in love with teaching math for my entire career. I feel like I have many things right. Thanks to him I have a more accurate road map for the learning of math in my class. I can hardly wait to get back into the classroom and to share this with my colleagues.
- Deeper understanding of content
- Greater motivation for learning
- Development of learners' thinking and learning abilities
- Development of learners' attitudes toward thinking and learning and their alertness to opportunities for thinking and learning (the "dispositional" side of thinking)
- A shift in classroom culture toward a community of enthusiastically engaged thinkers and learners
These are the stated goals of the blog "Visible Thinking".
On their blog there is an assessment tool for thinking classrooms. The criteria from the tool are below (see the assessment tool for complete viewing).
1. In this class, the work students are doing is connected to big or important ideas in the subject area.
2. In this class, the work is focused on developing well articulated understandings. It is relatively evident what understandings are to be developed as a result of doing the work.
3. In this class, a few topics are explored in depth rather than attempting to cover or touch on many.
4. In this class, the work is purposeful and has meaning for students. It is not just work for work’s sake.
5. In this class, students find the work engaging and worthwhile. Engagement is intellectual as well as social and/or physical.
6. In this class, there is a level of meaningful choice embedded in the work that allows students to have real ownership of the work or helps to personalize it.
7. In this class, the work challenges students in some way, by pushing their thinking in new directions or asking them to reexamine ideas or beliefs.
8. In this class, the work asks students to generate original ideas, explanations, solutions, responses, or findings.
9. In this class, the work has depth and regularly goes beyond the level of knowledge/skill building.
10. In this class, students’ thinking is made visible through the work/discussion/ reflections they do so it can be discussed, shared, examined or reflected upon.
11. In this class, patterns of thinking/habits of mind are on display. It is possible to identify the types thinking that students are engaged in and must do to be successful with the work
12. In this class, there is adequate time for thinking, to prepare responses, and express ideas.
I apologize for copying and pasting another's work. I think this is an amazing assessment piece which I am going to have my students fill out on our classroom. I also have an intern (not exactly and independent source) and I will ask him to assess our class as well.
Look forward to the results in a future post!!
I had a volunteer in my classroom and he was busy in the back of the room trying to solve the toaster quesstion. Notably, I did not even speak during or after the toaster math video. Part of the appeal of such questions is that the kids have to figure out the question themselves. Check out the first link for the toaster math video and the second for possible solutions. Keep in mind that one of the big ideas is that there can be many solutions (divergent thinking).
One particular student, who has a real mental block about math, exclaimed, "we should do math this way every day!" after we finished the first three activities. I look forward to many challenging lessons addressing the conceptual foundations of math instead of the computational barrage typical in our classrooms.
I think that I choose to be connected and creating, a producer rather than a consumer. My theory is that kids in my class are very similar, that is if they are guided towards areas of interest (choice!). My oldest son is a very good athlete yet never liked organized sports with a top-down structure (ie. a coach). He skateboarded and snowboarded for hours each day (and still does) alone and with his buddies. They would jump, somersault, spin and crash, often filming it and posting it to youtube. In a small way, I believe this is the new generation's way of creating instead of consuming.
Back to my theory, people who blog, twitter and build learning communities on-line watch TV less. TV is passive, TV is for consumers, TV is asocial. Creating and collaboration is more rewarding, and more fun. What do you think?
Wednesday, December 1, 2010
"....good schools promote displays of incompetence (strange as that may sound) in order to help students find their way to competence".
Alfie Kohn is also quoted by Joe. He says:
"teachers who want to encourage intellectual growth give students time to be confused and create a climate where it's perfectly acceptable to fall on your face".
These quotes make me feel really good about my classroom. Every single day I talk about the cool things we try and every single day I admit that I am failing to some degree. I love to toss around the big ideas in my head and try like crazy to incorporate them into my classroom. Some days it matches what is in my head and some days doesn't.
As I reflect on the importance of failing for teachers and for students, I am happy to say that my classroom looks very different from what it looked like five years ago. I need just a little more time....
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