Category Archives: authentic learning

Unauthentic, Imaginary World Math

Photo by Cowboytoast

“Real world” and “authentic” are two of many educational buzzwords overused right now. What if instead of making sure that everything has a truly “real” context we give students a creative opportunity to explore the “unreal.”

The inspiration for this post comes from a new blog by Randall Munroe, author of xkcd, called What If?. In this blog he answers hypothetical questions by doing the actual math to answer them. So far he has shown things such as how much force does Yoda have? and what would happen if you gathered a mole (unit of measurement) of moles (the small furry creature) in one place? These questions are not real or authentic but the math and science is.

But these questions are fun and interesting! Students love to talk about fantasy and science fiction such as zombies and vampires.

So why not expose your students to a few of these kind of questions and have them try to “prove” their answer. Afterwards show them what Randall Munroe came up with. Then have students come up with their own questions and write out their reasoning and solutions. This activity would tap into their creativity but also demonstrate their mathematical computations and more importantly their mathematical reasoning. It also would be a literacy task in math. Finally and most important in my opinion it may also be an avenue to engage a student’s passions in math class that Jeff de Varona has been asking about.

Unions

I read this post at the Cooperative Catalyst by Educational Revolutionist and left the following comment:
I think you are confusing two separate issues: unions and learning. The purpose of unions is to protect the rights of workers in regards to wages, benefits, working conditions, etc. Union dues are paid by teachers to protect their rights and wages. Unions are not directly designed to promote learning or guarantee student rights. Unions are part of the democratic “checks and balances” against big business. Review the history of Carnegie and other robber barons. Sure they donated lots of money to libraries to and created education institutions. Sounds alot like Gates, Broad, and crew to me.
But as Mary Beth has pointed out, positive working conditions and benefits leads (but does not guarantee I admit) to better learning situations for students. These benefits lead to more qualified teachers entering and staying in the field. Other rights such as planning time lead to better learning opportunities. As my dad always quoted a friend who owned a used construction equipment business said, “I can’t afford a $7/hour mechanic. I need a $20/hour mechanic.”
Unions do fight for more funds for education all of the time. Are they self-interested? Sure, but the money goes to many things in schools also.
Lastly, I agree it would be incredible if teachers would rally, protest, and boycott against NCLB, RTTT, and standardized testing too.

BTW “Get up, Stand up” by Marley came up on my Itunes shuffle as I wrote this. #karma

Real Reform Goes Backwards

I for one am tired about hearing about broken public schools. Are they perfect, of course not. Neither is any other human institution. But what really disturbs me is that the people who want to “fix” public education have the worst ideas ever. They want to make schools more like business and hire head-hunters (superintendents) to fire the bad employees (teachers). Then the head-hunters move on to work for Fox news or some think tank. These people do not truly care about children but about money. Therefore their goals are to get rid of the evil unions that protect teachers’ benefits so they can hire cheaper teachers (outsource them just like the manufacturing industry in this country). Standardization measured by tests is the magic cure!

The problem is that schools are not factories and should not be treated like them. And most importantly students are not widgets that can be taught by anyone using the same script. These reforms disrespect both teachers and students by treating them as all the same. Just put the student in the proper machine (program) and out they pop at the end- educated (able to pass standardized tests). But students need relationships to grow and learn. Schools should be more like families than factories.

I think real reform starts by going backwards to a “classic” liberal arts education. In Ancient Greece students were discipled by the master as part of a community. Relationships were an important part of education. They learned by asking questions. They studied logic, poetry, geometry, and exercised all as one experience. They were not divided by age and subjects were not compartmentalized. There was not classwork and homework. All of life was learning, one integrated experience.

By caribb

Students today need to be given time to think, deeply. They need to play, ask questions, discover, solve real problems, and discuss. They do not need to memorize facts for tests. They need to think critically from multiple points of view. Students need to be given choice in what to learn and how to do it. Schools need more individualization and less standardization.

What can we learn from the Ancients? That living is learning and relationships matter. We need less federal bureaucracy and more local control. We need schools that look different because the communities they serve are unique. If we truly teach students to think and learn on their own and in community with each other they will do amazing things. We need science, math, and arts all mixed together. I believe that we should give students freedom to be creative and to engage in ideas with each other. We should scrap textbooks (this form of standardization has dominated even longer than the state and national tests). We should teach from real world problems and current events (we have plenty of them to choose from). Students should engage in real questions and work for real solutions. We should use hammers, nails, wood, computers, dirt, flowers, paper, cell phones, microscopes, cameras, and animals. Students should perform labs where the teacher does not know the answer. Students should study current events and then research the history to understand why things are as they are now. Students should use math to calculate solutions to world poverty, lack of clean water, and adequate food.

So what is the role of the teacher in all of this? To guide the learner and challenge them with new ideas and experiences. Most students are not self-motivate learners by themselves (because schools have bored this out of them); they will need mentors and guides to show them how to learn and to challenge them with new ideas. Master learners (teachers) should create fascinating learning opportunities as starting points and then encourage students as they pursue deeper concepts. Too many teachers use curriculum, standards, and textbooks as a crutch and rarely present students with authentic learning. Real reform happens when we abandon the pre-packaged education being sold by textbook companies and start the adventure of giving students great learning experiences.

So what’s your excuse? Reject standardization now. You may not be able to change the structure of your school schedule or the the architecture of the building, but you can change the way your classroom works. Don’t know how to start? Start by talking to your students. Find out where their interests are and build from there. Start by talking about the news and the issues in the world. Ask students what they can do about it. Put away the textbooks and engage with your learners. You might be surprised by where you end up.

The Alchemist and Louis L’Amour

By Alexandre Baron

Last weekend I read The Alchemist by Paulo Coelho for the first time. Yes, I know it is not new by any means and I would guess that many of you have read it long ago. There are many layers that one can read into the story but I would like to point out two that struck me.

I think most people would say that the overall theme of the story is pursuing one’s passions and dreams. The obvious question to me is “do we allow space in schools for pursuing dreams?” It seems to me that we are too busy covering curriculum and meeting standards. I am sure that I have said it before, but I hate standardization. The reason is that standardization drowns out passion and crowds out dreams.

The thing that struck me most about the book was about the channels of learning in the book. Santiago learns in many ways: reading, from experts (the king Melchizedek, the gypsy, the crystal shop owner, the Englishman, the leader of their desert caravan, and finally the Alchemist), from experiences, from following his heart, but most of all from nature. He learns from watching his sheep and camels. He learns from the desert. Contrast Santiago to the Englishman who primarily learns from books. I think the Englishman represents Western text-based learning whereas Santiago is a more ancient, Eastern, holistic learning from nature. Santiago learns by living life and observing life and nature everywhere. Western schools need to be more like Santiago.

Santiago also reminds me of my favorite childhood author, Louis L’Amour. He was a western writer and I loved his stories. In his memoir, Education of a Wandering Man, L’Amour details his “education.” Much like Santiago he left home when he was 15 and explored the world. He had jobs as a boxer, sailor, lumberjack, elephant handler in a circus, skinner of dead cattle, assessment miner, a tourist guide in Egypt, and a tank officer during World War II. He sailed the world and was shipwrecked in the West Indies. The other thing that L’Amour did was read-all of the time. Let me share some quotes from his memoir:

This is a story of an adventure in education, pursued not under the best of conditions. The idea of education has been so tied to schools, universities, and professors that many assume there is no other way, but education is available to anyone within reach of a library, a post office. or even a newsstand…


Somewhere along the line I had fallen in love with learning, and it became a lifelong romance…


this book is about education, but not education in the accepted sense. No man or woman had a greater appreciation for schools than I, although few have spent less time in them. No matter how much I admire our schools, I know that no university exists that can provide an education; what a university can provide is an outline, to give the learner a direction and guidance. The rest one has to do for oneself.
If I asked what education should give, I would say it should offer a breadth of view, ease of understanding, tolerance for others, and a background from which the mind can explore in any direction.
Education should provide the tools for widening and deepening of life, for increased appreciation of all one sees or experiences. It should equip a person to live life well, to understand what is happening about him, for to live life well one must live with awareness…We can only hope they come upon an issue they wish to pursue.

By Sandy Redding



To me this is another example of how all of our ideas to “change” education are really not new. Leading thinkers understood this years ago before computers even existed. I can’t help but think that L’Amour would find even less use for schools as they still exist today with the easy access to knowledge through the internet. Lous L’Amour was a self-made man in many ways, but he understood that learning is available for anyone who passionately pursues it.

My favorite quote is his reasoning for dropping out of school and leaving home: I left for two reasons, economic necessity being the first of them. More important was that school was interfering with my education.


He goes on to explain how the factory model of school would not let him skip basic classes and take higher classes that he was more interested in. So he dropped out and pursued his own learning. He later says, that dropping out is a good option only for those who are willing to read hundreds of books on their own. Certainly does not seem to be watering down learning, does he?

How can we create a climate that encourages students to dream and pursue passions rather than “interfere with their education?”

PS: I was very surprised to hear my pastor tell this story to close his message today. It sounds to me like “The Alchemist” used this as the basis of its plot.

How I laid out the square

Here goes my attempt at explaining how we laid out a square parallel to our school around a circle with diameter of 21′. I must confess that I did the math and started by having some students help me in class. I ended up having two students stay after school with me for about an hour to finish the layout.
First,I may have been unclear in the previous post but the circle already existed that the square needed to go around. So we measured 12′ 6″ off the building in two spots outside of the circle to establish the east line of the square parallel to the building. We put stakes in and ran a string line. Next we measured over 21′ from that line to establish the west side of the square also parallel to the building. That was the easy part. The tricky part was finding the corners.

(The building is on the east side and west is up on this sketch)

Our reference points were the furthermost northern and southern points of the circle. These points are the midpoints of the north and south sides of the square. But how did we establish  another point to create a line that it is perpendicular to the east line? If you are thinking Pythagorean Theorem that is part of it, but how do you find the corner? You guess, of course. Mathematicians, in the real world sometimes you have to estimate.

We multiplied a 3-4-5 triangle by 3 to get the dimensions 9′-12′-15′. We measured 12′ off from the east string in line with the midpoint. Then we held a string from the east string to the west string so that it barely touched the stake and we “eyeballed” it square with those lines. We marked the intersection between this string and the east string with a sharpie on the east string. We measured over from this mark 9′ and put another mark on the east string. Next we measured from this mark to the stake (the hypotenuse) and it should have been 15′. Of course we guessed on our corner point so we were off one inch and it measured 15′ 1″.  We corrected this by shifting the corner and this point north 1″. Now the hypotenuse measured exactly 15′ and we put a stake in at the northeast corner.

Now it gets easier. We pulled a string from the established northeast corner to the west line so that it barely touched the stake at 12′. This allowed us a very good estimate of the northwest corner. Next we measured over 21′ from both northern corners on our string lines to establish the two southern corners.

Our last step was to measure the diagonals which should be congruent. We ended up about an inch off so we double checked our overall dimensions and found one stake was leaning in so it was not quite 21′. We straightened it and our diagonals were within 1/2″.

The next day we measured over 2′ 6″ from all four sides of our square and pulled lines to find their intersections which gave us the four corners of our outer square. I really do not think that this problem was solvable by my 8th grade class but I wish I would have taken the time to walk them all through it.I think it was a great opportunity to show my students that math does apply to real problems in blue-collar jobs not just at universities or in a lab somewhere.

PS If I was doing it over I would have just “picked” center point on the east line pulled off the building where it touched the circle. Then I could have measured 10′ 6″ both ways and established both of the east corners and used Pythagorean theorem to find perpendicular lines off from both corners. It would have been much easier 🙂

Warning: The grade you have received may not reflect your actual level of learning in this class.

As some of you know this is my first year teaching math. I am currently teaching one section of 6th grade math. The rest of my assignment is 6th, 7th, and 8th grade technology which I have taught for six years. This new math class is the source of my focus on grades and grading. In my district we have standards-based report cards and in math we have district tests for our required assessments. For this post I will focus on my technology class and assessment (I will save math for the next post).

My Technology class flies under the radar. We have standards that reflect what the class was like five years ago but not what it is today. I and my fellow middle school technology teachers use project-based learning and computers to challenge kids with fun and relevant learning. I truly have more freedom than almost any other teacher in my district to teach whatever I want however I want. I am accountable to my principals who are happy to see children “doing” creative things. We build pop bottle rockets, balsa towers, hot air balloons, pneumatic devices, and egg drop vehicles. We use Lego Robotics and some math software games. Starting last year students blogged and use Google Docs. This year we are using programs such as Google Sketchup, Pivot, and Scratch.

I grade of course in Technology because I have to but my grades are either a rubric of checklists or once in a while based on reaching certain levels. So many of my grades reflect effort of students to complete the projects rather than measure learning. I am ok with that I guess.

For example some excellent students attempted some unique balsa tower designs (the picture is one of them) that totally failed when tested. By the way, most of the class voted their towers to be the strongest before we broke them. They did not receive an A but I would argue that they learned and taught the rest of the class more about good design that anyone else. Why, because they took a creative risk and tried something the rest of the class was unwilling to do. We do not have time or $ for materials to have students build multiple towers to improve their designs which would be the best way to show their level of learning.

Even more difficult for me was when my students made their own Pivots, Sketchup, and Scratch program. We created rubrics together as a class and then I made a grading form in Google that the students embedded on their blogs.

How does one grade creativity? What makes my opinion more valid than anyone else’s?

Therefore I was just going to count the students’ assessments of each other. This did not work out as planned as too many of them did not grade each others’ projects because some were completed late and some did not take the rating seriously. Basically I question the whole point of this grading as a waste of my time.

My ideal system would be to share these tools and projects with students and have them complete them as creatively as possible to the best of their ability. Their “reward” would be the learning that they experienced as a class. Would they all learn the same things or even the same amount? No, just like now they would learn based on the amount of thought and effort they put into their work. If they slacked off then they would learn less; if they worked hard then they would learn more.

I really don’t know how I can accurately measure their actual learning anyway. Grading feels like a game to me and some of the greatest projects like this and this happened for no grade or extra credit. I fail to see how the “grades” that I assign to them contribute to their learning experience and oftentimes do not adequately reflect their actual learning. I also know that grades do not motivate my at risk kids at all, and they motivate the “top” students just to perform for me not to actually learn.

The ultimate thing that matters to me is that students are challenged, given a chance to be creative, and explore in a hands-on way math, science, and technology. The rewards are internal for the students who give their best. Those who just go through the motions miss out no matter what their report card says.

Next post I will explain the conflict I feel comparing this class and grading to my math class.

Twitter addict confession

Why am I addicted to Twitter? It’s not the links. They’re great, but I love the conversations…
I can control my use of Twitter. Really I can. But last night was an example of how powerful of a conversation tool it is to me.

First, I watched an interesting discussion that Jon Becker (professor at VCU) had with plugusin (teacher in North Carlina) over the “validity” of a survey that plugusin created and used. Now I was not very interested in the survey itself, but in the discussion of what makes something “valid.” I would have to say that I sided with plugusin as far as twitter and social networking giving voice to teachers working in the field vs. professors writing for peer-reviews journals.But I must confess I am not an expert on what makes something “valid” so when Sylvia Martinez (a leading educator from LA) asked Jon to explain this more I joined the conversation and asked too. Jon patiently answered our questions. The thing I know and respect about Dr. Jon is that he is not condescending or narrow-minded about the equalizing power of social media. 

Meanwhile Jane Vanhof (choir and ELA teacher from my school!) and Ira Socol ( from Michigan, too) joined the conversation too. The end result is that Jon Becker decided to do a session on “What makes a survey valid” open to anyone who wants to join in (Here is the signup for time).

At the same time I was asking questions of some experts from my PLN about educational history (Teaser: stay tuned over break for some posts about grading) including Ira, Shelly Blake-Plock (Maryland Latin and history teacher), and Andrew Watt (classical history teacher in Connecticut). During this multitude of conversations Tomaz Lasic (an excellent teacher from Australia) tweeted to Ira and asked him to quick Skype into his class that was in session. Ira did and re-joined our conversation a few minutes later.

Wow! There is no way this is possible ten years ago. I would have to enroll at VCU and sign up and PAY to learn from Jon Becker. I would still not be able to attend faculty meetings with him, which is what it feels like as I “watch” conversations he has will leading educators from around the world. I have personally met only two of these people (Jane and Ira about two weeks ago) but yet I can learn from them anytime, anywhere around the world. And added onto it  is the ability for Ira to off-the-cuff join into a classroom discussion on the other side of the world at a moment’s notice.

I have never been so motivated and excited about my own learning. And I am working out methods to share this with the other teachers and the students in my building. I am truly amazed at the knowledge and GENEROSITY of the people in my PLN. It really is about the conversations and the giving. Thanks to all in my PLN, and of course I would highly recommend following all of the educators mentioned here.

Why am I addicted to Twitter? It’s not the links. They’re great (especially the ones to thought-provoking blog posts), but I love the conversations …
                                                               with some of the greatest minds in the world.
                                                                Thanks

Wood chips

I should have wrote this before my last post to better describe how my math class has been going. We are currently working on a basic geometry unit of area, perimeter, volume, and surface area. I was excited because this would be “easy” to teach with out a textbook.


I started off by explaining a problem I had of needing to know how much wood chips I needed to cover some landscaping that I did with a class last year. We discussed what we needed to know to figure this out and then went outside and measured the circle. They told me we needed to know the length and width of the circle so I had them measure where they told me those were. I did not try to correct their improper terms. We came up with 7 meters and 6.9 meters. One student noticed that they were approximately the same. We ran out of time for the day.

The next day we started in class and discussed the wrong use of terms. I had them search and find the area of a circle and we talked about what the formula means. Then I asked which of our measurements was right. They argued that 7 meters was correct because it was a whole number. We finally concluded that we did not know which one was right and that we had to go outside and take more measurements and then average them. We also talked about the fact that the circle was eye-balled when created and not perfect.

We ended up solving the problem and then solved two more wood chip problems for some rectangle gardens. Through out these lessons I asked lots of questions and guided their learning but did not give out any information. The students either came up with the answers themselves or surfed the web for them.

My evaluation of this teaching method was that I did not see the high engagement that I had hoped for by the class. My top students were with me and the bottom students seemed to be daydreaming or not really participating. I don’t have a great story of the student who always fails getting excited and being successful.

Next I needed to cover parallelograms and triangles which are harder shapes to find in the real world. So we did some visual proofs together in Geometer’s Sketchpad so they could play around and see why the area formulas work.

Again I have to give the district unit test so I gave them some practice problems with area and perimeter of parallelograms and triangles. They were totally lost. They could not remember the formulas or even use them when I gave the formulas to them. I ended up going around the room and individually teaching how to use the formulas.

We measured a bunch of food boxes and found their surface area and volume. I demonstrated how to use the formulas on the board and the majority of the class still needed me to re-teach individually.

So in response to the comment from Matt Townsley on last post about teaching at a deeper level. I have tried (I am not giving up!) but in the end I have to prepare the students for the district test. That is why I found ThatQuiz to be a useful tool for students to check their work on the basic problems that they need to know. I know it is not technology integration but doing the same old thing just on the computers. I do think the immediate feedback to students of whether or not they found the right answer is helpful. And unfortunately these are exactly the kinds of problems on the required tests.

All right push me back some more readers 🙂

Students say using technology to cheat is not cheating

E-school News reports today:

A new poll conducted by the nonprofit organization Common Sense Media suggests that students are using cell phones and the Internet to cheat on school exams. What’s surprising, however, is not just the alarming number of students who say they cheat, but also the number of students who think it’s OK to do so.

According to the poll, more than a third of teens with cell phones (35 percent) admit to cheating at least once with them, and two-thirds of all teens (65 percent) say others in their school cheat with them.

Of the teens who admit to cheating with their cell phones, 26 percent say they store information on their phone to look at during a test, 25 percent text friends about answers during a test, 17 percent take pictures of the test to send to friends, and 20 percent search the Internet for answers during tests using their phones. Also, nearly half (48 percent) of teens with cell phones call or text their friends to warn them about pop quizzes.

First of all, where are the teachers in the classroom administering the tests? I think cheating is not that easy if teachers are paying attention while they administer tests. Surely you would notice if they have out an electronic device. Some readers are quick to blame the technology and say “why are phones in school” and that they should be banned. Cheating has been around for ages before we had cell phones. Don’t blame phones for students behavior. Cell phones have a very useful place in the classroom as mini-computers that can be used for research.Reading a text message is not that much different than reading a note. Teachers watching for phones out during a test is no different than watching to see if they have a “cheat sheet” on a piece of paper.

More importantly teachers should re-evaluate their tests. If tests are really at high-level thinking requiring analysis, evaluation, synthesis, and application then they should be “cheat-proof.” It is much easier to cheat on multiple choice or fill in the blank than on a test that actually requires thinking, interpreting, and students writing their own opinion. I agree with Alan November who said that tests should be open Internet. But it requires a new way of thinking for teachers and students. This open test would actually be more difficult because it would require higher level thinking rather than just rote memorization. Students would have access to all of the “facts” on the Internet, but then would have to use them to answer a more difficult level of questioning.

I personally lean toward no traditional tests, but use projects, blogs, and other forms of writing to assess student learning. For example after my students build and launch hot air balloons made of tissue paper, they must write a letter to Leon Gambetta explaining to him how to escape from a siege of Paris (1870). In the letter they must explain how to build a hot air balloon and why they fly. My 8th grade students write evaluations of all of their projects on their blog explaining their experiences for each project. Of course if it was up to me I would eliminate grades all together but that is another discussion.

Finally also disturbing to me is that students do not view this as cheating. Morals are in decline in our country and many students will do whatever it takes to get ahead just to get a good grade. I often ask ethical questions as “opening” writing assignments to students and many of them see little wrong with cheating, stealing, or lying if they think that they will not get caught. Many students admit they would take a stolen ipod from a friend or lie to get out of trouble and see nothing wrong with it. Therefore we need to teach students why cheating is wrong on top of monitoring them from doing it.

In summary, authentic learning experiences with authentic assessments with open resources makes cheating impossible. So what do you think?

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