Grades, Creativity, and Frustration

Yesterday right after school, I saw one of my prior students in the hall. After our usual pleasantries in Spanish (which, with almost all of my students, consist of only “¿Cómo estás?” and “Bien, ¿y tú?” - another thing to work on…), I asked her if she was going on to Spanish 3 next year. Her answer nearly broke my heart and actually did leave me speechless…

see full post at kellyhass.blogspot.com

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The Collective Mosaic

From The Heart of a Teacher by Parker J. Palmer:

First, the subjects we teach are as large and complex as life, so our knowledge of them is always flawed and partial. No matter how we devote ourselves to reading and research, teaching requires a command of content that always eludes our grasp. Second, the students we teach are larger than life and even more complex. To see them clearly and see them whole, and respond to them wisely in the moment, requires a fusion of Freud and Solomon that few of us achieve.

The label “Collective” is is as powerful as the name Mosaic. Despite coming second - and thus easily dropped in casual conversation - it must be strongly considered in everything we do, design, create, etc.

Our understandably limited content knowledge and ability to forge strong and loving relationships with each and every student, as mentioned in Palmer’s quote, only serves to reinforce the collective nature of, well, a Collective.

So, here’s to the crazy ones … the Collective Crazy Ones!

We Just Tweeted Something…

Huffingtonpost:

Around 20 students reportedly were suspended from McKay High School in Salem earlier this month, after they retweeted a piece of gossip about one of the school’s teachers.

According to Oregon outlet the Statesman Journal, the students retweeted a post from an anonymous, local gossip account called Salem Confessions. The Feb. 11 postalleged that one of McKay’s female teachers flirts with her students, and it mentioned the name of the teacher’s son.

Administrators at the school say retweeting the post amounted to a form of cyberbullying…

And I wonder, how will actions like this play out when students begin wearing connected technology and social media becomes more and more impactful. How, dare I ask, will schools respond? Defensively? Proactively? Or, if social media is such a deep part of their (and our) lives, will it eventually catalyze pedagogical and cultural shifts?

Define Inquiry

It’s a simple task – define inquiry…

Yet, I struggle in finding a definition that truly represents a holistic view of inquiry based learning. To me, inquiry is more than a method, more than a buzz word, more than simply asking a question. Inquiry is a feeling, an lifestyle, and a culture that is created. It evolves as time passes and morphs into different forms as curiosities rise and fall. Inquiry can be engaging, loud, and messy. It can change the way people think and the way people view the world. Inquiry inspires people to remove the old confines of how and when to learn. It allows for true out of the box thinking. Inquiry can also be very structured and methodical. Some may not see that from the outside, but behind the scenes, inquiry based teaching is incredibly thoughtful.

Inquiry is the “yes man” in a “no man” world. Inquiry methodologies encourage people to explore their ideas and when they fail – they try again. In this type of culture, it is okay to fail – as long as you reflect and try again. You will see a large increase in creativity in this culture because people are not afraid that they will lose points, get in trouble, or be ridiculed for being “wrong”.

I am in no way an expert on inquiry. I like trying new things in my classroom and finding new ways to make my students think differently. (I would love to learn how inquiry techniques are used in other disciplines… hint hint.) What I can provide are examples on how the students and I create an environment (a culture) that is conducive to inquiry. In my science room, we hold off on content for the first week. We focus on team building and collaboration. We also spend a great deal of time being silly and working on fun puzzles and brain teasers. Setting up this environment is crucial for an inquiry driven classroom. If they (and you!) don’t feel comfortable with each other then inquiry based teaching could just be an awkward exchange of looks in silence. When we know each other and feel comfortable in asking and exploring questions, we build the unit together. I am a huge fan of addressing misconceptions and exploring what the students already think and know about science. I like starting with a simple word wall. It is just a collection of ideas, phrases, and yes, words, that the students think about when I give them a topic. So, for example, my students came up with pretty predictable things for our topic/unit on microbes: bacteria, e. coli, virus, infection… Then they get into sweet things like: jock itch, toe fungus, cancer, fecal matter, pink eye, UTI’s, fermentation… These are the topics that are super interesting (and in some cases unfortunately relevant) for the students. What looks like a simple activity is really an assessment for me as the content leader in the classroom. What do my kids already know? What are they passionate about? What direction do they want to take this idea? This simple idea allows the students to build the unit. I can fit the crucial content into things they call out. (Now honestly, I might have to send questions back at them to help them get thinking or to guide them off a tangent.) So I tell them we will learn about jock itch, UTI’s, fecal matter, and pink eye. That sounds way cooler than we will learn the differences between various microbes. It makes the content relevant and more importantly, it gives them a voice in their education. I know what I need them to learn in my class but they just told me how they would like to learn it.

Okay, now the topic/unit is planned… moving on to how we approach the content. RIG’s (research in groups)is another technique I like to use to get the students thinking and researching. We already know what we’d like to learn about so we take the main questions that came up in discussions and explore them. To keep the microbe unit example going, they had a slew of awesome questions. What really are antibiotics? Where do they come from? Why does a cold suck so much? Where does mucus come from? Canker sores are herpes – fact or fiction? I do these in two different ways – depending on how the class discussion goes or how interested the students are in the questions. If there is one big question that the kids disagree on, I have the teams (collaborative tables with 4 people at them) research the same question. My only stipulation is that they must answer the question and provide scientific evidence to support their claim/answer. The groups spend time looking for answers and in the process come up with several other questions. I tell them to write them all down. We go through and present our answers and discuss the relevant content along the way. Pretty soon, the kids know the different between bacteria and viruses and also how to research, how to speak in from of a large group, how to argue a claim, how to react to set-backs, and how to ask additional questions. So I could have lectured or given a PowerPoint on the difference between bacteria and viruses but I believe using the students natural curiosities is much more powerful. #inquiryforthewin.  The other way I use RIG’s involves the teams to research different questions but they all stem around the same general topic. Using this slight modification allows for a wider scope of answers and opinions. It also tends to generate more questions that can be explored (either through research, actual laboratory exploration, or through human interactions/conversations).

Last little tid bit on how I make the science labs inquiry based. Instead of a cookie cutter lab where the students are robots following a list of commands from a company that wrote the procedure 10 years ago, I have the students create their own investigations. I might start with a guiding question (like right now in AP Biology – What factors do you think will affect photosynthesis?). I go through and show them some different methods to measure/see that photosynthesis is working, then I set them loose. They have to come up with their own hypotheses, controls, and procedures. They collect and analyze their own data. They come up with their own conclusions about photosynthesis based on their data and the data of their peers. Each group does something different and presents their findings out to the class. I’m there to help guide the students to become better scientists and to expand their content knowledge but this way, they are doing the majority of the thinking for themselves. This inquiry approach ‘covers’ scientific thinking, collaboration, data analysis, summary writing & speaking, and a great deal of photosynthesis details all in shorter amount of time than a traditional lecture and lab to confirm the lecture.

So, what is inquiry… It’s complicated but beautifully simple. It’s open but thoughtfully structured. It’s asking questions but actually exploring and creating your own conclusions. It’s collaborative, but metacognitive and personal. It’s engaging in your passions, while learning something new. Inquiry is fun(gi).

(Special thanks to Kyle & Ryan as we have had several conversations about inquiry and collaborated to make inquiry a success in each other’s classrooms.)

Futurecation and Prensky

I spent some time with Marc Prensky and some fellow teachers today. 

We were there to discuss anything education. The format was a bit hinky as we were arranged in a large circle and were asked to simply, well, ask Marc questions. 

We had an hour.

Now, to know me is to know that I can talk - especially about education. I enjoyed our discourse but after an hour’s time was just starting to get warmed up. It’s possible that the meeting could have been organized differently to make an hour feel much longer.

Here’s some feedback:

Roundtable discussion. We sat in a large circle.

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I agree with Marc that “circles encourage conversation,” but I would have loved to have been sitting at a round or oval* table. It would have been easier to take notes, doodle, live-tweet, etc. Do they make tables large enough for this group?

* and by oval I truly mean elliptical (hat tip to Karl Fisch)

Coffee talk! Coffee was there somewhere but it would have been brilliant to have it at the tables where we sat… you know, like at a coffee shop. I suppose the words I’m thinking of are ambiance and warmth.

Ask us questions. Encouraging conversations amongst educators is such an important part of professional development and growth. I would have loved it if Marc would have asked us questions and then facilitated our group’s conversations. Instead the format was long-winded and too filibuster-ish. Given a description of our collective expertise, passions and vision I think would have allowed Marc to prepare and facilitate such a discussion.

Lights! Cameras! (No) Action! I certainly value the decision to video our session. Video is a shareable medium that can propagate and go viral. There’s absolutely no doubt in my mind as to its importance and impact. I suppose by setting the scene as I described above (table, coffee, etc.) would help here, but there must be a way to make the camera and crew less obvious. People get self-conscious and seemed to either talk too much or not talk enough. It was entirely too composed in there! To borrow a phrase from one of my colleagues, we just weren’t getting “rowdy” enough.

Though I certainly appreciated the invitation and the time to gather with my colleagues (and Marc), I think it could have been more impactful with provided some purposeful planning and execution. The conversations were just getting deep when our time ended, which is why I’m craving a “Round Two” of sorts.

Though this post may seem a tad bit critical, I’m really just reflecting on the time spent with Marc and my colleagues, its overall impact, and how events/meetings like this could be conducted in the future. I’m very thankful to the people who organized today’s meeting. Like I said earlier in this post, creating conversations in educational professional development is fantastically important.

*****

Here are some points that Marc and others made that, for one reason or another, are sticking with me because I either agree, disagree or am still working to figure them out.

Content cannot live in isolation. We must recognize opportunities for multidisciplinary work and design learning with respect to such opportunities.

We are in the midsts of a digital revolution that had no specific beginning, but is truly revolutionizing society.

Nothing, not even reading, writing and math, is immune from this rapid change.

Some current reforms and legislation may be mired in “20th century” and/or “analog” thinking.

Computer science should be introduced early and in an integrated fashion with all content.

Programming languages are world languages, i.e., World Languages are not necessarily defined by physical borders.

The time-tested concept of campus education will change as eLearning technologies continue to evolve and improve. Translation: “Stand by to stand by!” and, “Fasten your seat belts!”

Marc, like others I’ve met this past year, travel the globe having these types of discussions. Globalization.

Again, thank you to the organizers, my colleagues and to Marc for the thoughtful conversations.

What is Mosaic?

With more than 100 years in education COLLECTIVELY, we know that most high school freshman:

  • are not truly self motivated to learn in a traditional academic setting. They need external srewards or punishments for motivation

  • are not oriented toward long-term goals. Instead, school forces them to focus on short term successes or goals (test, week, project)

  • do not know what they are passionate about or lack the inspiration to pursue that passion within the traditional academic setting

  • have a limited awareness of their potential powerful relationship to the larger communities in which they reside

So, IMAGINE a school setting that will attempt to create intrinsically motivated, goal oriented passionate students able to take full ownership of their education before they fully matriculate into the world of work or post-high school education.

IMAGINE a school that will focus on student “doing” and “creating” as learning. Instead of learning, then doing, our students will learn AS they build, design, produce, experiement, create, innovate and invent. A school that adopts:

  • Problem or Project Based Learning using an Inquiry approach.

  • the elimination of grades in favor of a more informative, more relevant form of narrative feedback. Feedback that describes a student’s progression toward mastery of specific content or skill standards

  • the elimination of a traditional bell schedule, term lengths and seat time. A schedule flexible enough to allow students to learn what they need when they need with the guidance and mentoring of content experts

  • small seminar classes where teachers offer skill and content specific lessons students will need to master in order to complete projects. Instead of 35 students spending 90 minutes with one teacher for 18 weeks, seminars work with small-groups in shorter periods when students and mentors identify the need.

  • a more individual curriculum based on student needs, interests and personal academic goals identified with the guidance and mentoring of content experts.

  • public displays of student learning where they design, present and DEFEND their learning

  • A building design that includes spaces for collaboration, computers, quiet reflection, to use tools for messy creations, small seminars and lectures, guided and independent labs, and presentations.

In order to accomplish these goals, IMAGINE a school that offers a solid, real advisory program where mentors assist students in

  • choosing projects that will allow them to proves mastery in all contents needed in order to earn a solid liberal arts education and ultimately a DCSD and Colorado diploma.

  • building their weekly schedules. Once Mosaic publishes the weekly schedule, mentors and students build a personal schedule based on individual skill and content needs. These seminars address the identified academic needs and help students gain mastery in skills/content needed for current project(s).

  • creating individual long-term project management skills, including: goal setting, self-analysis, and work-flow analysis.

  • communicating regularly with family regarding progress toward mastery and interventions in place to support success.

IMAGINE a school day that looks like this:

  • students arrive and review their schedule for the day

  • Because their current project, he and his mentor have identified a specific need in Math. He heads to 8550 for a 20 minute session with Mr. Justice for his seminar of Exponential Rate of Growth

  • He and his partner have blocked out early-morning to continue to test, collect and analyze data in order to identify further design changes for their invention

  • Since he plays trombone in the Jazz band, he leaves to attend CVHS Band class that meets 2A - every Monday, Wednesday and Friday.

  • Since he is coming from the band room, he decides to take first lunch and meet his friends

  • After lunch, he has scheduled a writing lab/conference with Mr. Schneider to review his research and essay plan regarding his data collection.

  • After the conference, he meets with his project partners to share new insight into their research

  • Based on weekly conference with his mentor, he moves to a 90 minute lab with Ms. Chloupek on the Zombie Apocalypse Contagion (Rate of Growth)

  • Before he leaves for the day, he drafts and publishes his daily blog. At this time, he refines his script for his groups’ weekly podcast and previews his schedule for tomorrow.

Notice a few things:

  • He know when, where and WHY he travels from place to place, teacher to teacher and content to content

  • Parents will know exactly what he is doing through his own words, teacher narratives and public displays of learning

  • He has time for collaboration, experimentation, reflection and production each and every day

  • He is guided by a mentor and several content experts

  • He is learning specific skills and content WHILE he collaborates on a long-term, interdisciplinary project

  • He is free to take advantage of CVHS life - lunch, electives, sports, clubs

As we attempt to fulfill our school’s Mission Statement, these are our plans. We know the hard work starts now as we continue to present Mosaic to students and parents, design and refine project ideas, create and submit a budget, modify the physical space, research and choose the best method for digital portfolio creation and curation and narrative feedback - and continue the difficult job of navigating the never ending minefield that is our colleague negativity.

Any thoughts or suggestions? Thanks,


Michael

Student Perspective on the State of Education

Here’s a provocative, five-minute video wherein a student from Knox County, Tennessee addresses his school board. Here are some quotes that stuck with me… please consider watching the video embedded below.

Rigorous is a buzzword.

These subjective, anxiety-producers do more to damage a teacher’s self-esteem than you realize.

Erroneous evaluation, coupled with strategic compensation, presents a punitive model that - as a student - is like watching your teacher jump through flaming hoops to earn a score.

… teaching is interaction.

Education is unlike every other bureaucratic institution in our government. The task of teaching is never quantifiable.

Everything is career and college prepatory. Somewhere our Founding Fathers are turning in their graves… pleading, screaming and trying to say to us that we teach to free minds - we teach to inspire, we teach to equip. The careers will come naturally.

Haven’t we gone too far with data?

Ethan’s closing remarks are evidence of a deep thought process that he undoubtedly went through as he prepared his comments. He says that fools complain about the state of affairs without suggesting improvements. He then strongly urges the board to study and research his comments before continuing their course of action.

What a wonderful example of a freed mind and I can’t help but wonder: What career will come naturally for Ethan?

Hard Knock Life?

From a recent email:

Thank you for all your hard work during term one.  Congratulate yourself for everything you have done - creating your e-portfolio, formulating your goals and professional growth plan, developing performance task assessments, posting your grades, establishing your club, participating in STOMP and/or Showdown, mentoring an intern and/or colleague, taking tickets at an athletic event, conferring with parents at conferences, participating in safety drills. You have all been very busy and deserving of a relaxing fall break to re-charge for next term. Enjoy your family and friends and bring balance back to your life.

Me: Oh, and for teaching kiddos. :)

*****

I did all of this stuff AND even found time - with the help of my chemistry students - to add another fire drill to the list.

It was a nice and well-intended email. I just thought this list was funny (and kind of pathetic).

From someone with the perspective of a student, teacher, coach, and administrator in my district. Times are so heated and political right now. (Originally shared on Facebook)

From someone with the perspective of a student, teacher, coach, and administrator in my district. Times are so heated and political right now. (Originally shared on Facebook)

Spirit of the Law vs. Letter of the Law - Thoughts on Teacher Evaluation

In 2010 the Colorado State Senate passed Senate Bill 191, which, among other things, mandated a new system of teacher and administrator evaluation. As part of its reform initiatives, my district modified the SB 191 mandates and tied them to a pay-for-performance program.

Now, I tend to be an optimist by nature, but this post is going to highlight a few of my concerns (now that the reforms are being initiated). Please forgive my pessimism, err, I mean professional criticism. From my brain to yours:


Not all evaluators are created equal.

Five administrative evaluators at my school from five wildly different backgrounds that have wildly different abilities to observe, communicate, coach, and judge teachers effectiveness. This wouldn’t be an issue in a perfect and ideal world, but we - of course - do not live in a such a place.

Word has already began to spread around my building as to who was rated Highly Effective, Effective, and so on, with conversations (and sometimes debates) as to why one teacher was rated HE over another.

"HE was rated highly effective? Wow, I want his evaluator."

I’ve also heard such questions and comments from parents and, alas, students.

(Exasperated sigh.)

This can’t be healthy in the long run. 

Teachers are bound to do what students do when they encounter a teacher they don’t want. They’re going to do whatever they can to request another evaluator. 

Mark my words.


A body of evidence can be faked.

I’m still a tad bit fuzzy on this, but the idea of some sort of ePortfolio keeps coming up. Apparently we’re to record Professional Growth stuff and are encouraged to begin documenting “evidence” that can be used to indicate whether we are Highly Effective, Effective, etc.

See, I’m all for teachers blogging, networking, and collaborating with each other. I’ve been a huge supporter of ideas like the 180-Project (though I have yet to initiate my own). The thought, however, of having to curate some sort of collection to show an evaluator misses the mark entirely for me.

I think evaluators should know what’s going on in classrooms without having to visit an ePortfolio … and that teachers should not have to rely on some sort of self-promotion to make a mark. What’s to stop a teacher from giving some sort of silly assignment and then simply taking pictures to post in their collection along with smartly written descriptions that say all the right things in order to impress an evaluator?

Now, don’t get me wrong, I think an ePortfolio that supplies links to authentic student products is different. But will an evaluator take the time to visit these links to ascertain their validity?

To me it kind of reeks of more bureaucracy and less opportunity for meaningful feedback, which is opposite of what I think an observation should provide.

I suppose some sort of peer-reviewed ePortfolio may receive less criticism from me, but now we’re talking time and energy most of us simply don’t have - unfortunately. Mandating portfolios seems like a symptom of a larger issue: administrators are already overburdened and to bandaid this teachers must curate their ideas to prove their own effectiveness, which, depending on the level of scrutiny, may be exaggerated.


The playing field is certainly not level.

I’ve taught 8 different courses in 7 different classrooms in my time at my current school. The reasons for this are complex - some stemming from choices I made to help smooth other teachers’ schedules; some stemming from a “somebody needs to do it” rationale. Regardless, I’ve traveled and challenged myself with multiple courses.

Several of my colleagues have taught as few as two courses and have not traveled. They have amassed tremendous resources (some would say “hoarded”) and have grown rather comfortable with their situations. Sure, a few have continued to push and challenge themselves by learning new approaches, but most have “gotten better” by becoming more efficient and entertaining.

What’s my point?

A portion of our CITE and therefore our pay for performance is affected by students testing. Is it apples-to-apples when a teacher travels from classroom to classroom while another doesn’t? Furthermore, at our school students select from one of four Academies. Might it matter if one science teacher has primarily Science and Engineering students and another has Visual and Performing Arts students? No doubt it will, but by how much is not known.

Bottom line: how can this NOT create an environment that pits teacher against teacher based on classroom and course assignments and student enrollment?


Forget micromanagement… it’s time to introduce a new term: nanomanagement.

Micro means 1/1,000,000th, it’s the scale of microbes and cells.

Nano means 1/1,000,000,000th, it’s the scale of molecules and certain wavelengths of  light.

Nano, my friend, is smaller than micro.

What happens if a school’s evaluators judge a large number of their teachers as Highly Effective relative to other schools? What will eventually raise district alarms? Surely there will be disparity from one school to another, but what will result in “reassessment” of a school’s evaluations? I suppose the term I’m dancing around is “quota.” 

It’s one thing for building-level administration to micromanage classrooms, but I think this system will result in more and more district-level management of classrooms, heretofore referred to as nanomanagement. Not only will nanomanagement frustrate building-level educators, it may also result in ineffective communication when principals are, for whatever reasons, not as informed as their teachers. Think about it. Suppose I attend a district-level training and am told new information, which I pass along to my colleagues. If my principal doesn’t hear the same information because he wasn’t at the training, then we may have an issue. How much tolerance will we all have for ambiguity and multiple answers to the same question of protocol?

*****

Okay, I suppose I feel better now. Like I said, I just felt like getting a few things off my chest. I hope I’m terribly wrong about this stuff.

Good talk…

An Educational Death Valley

Sir Ken Robinson gave a recent TED Education Talk in which he compared the current state of education in the United States to life in harsh Death Valley, California.

Talks like this can be frustrating because of their theoretical and lofty perspectives and opinions. They often make teachers nod in agreement, but leave us confused as to our next steps to “change education.”

This said, I actually enjoyed this SKR talk. He made some points that are sticking with me … they’re points I’d like to share:

"If you sit kids down hour after hour, doing low-grade clerical work, don’t be surprised if they start to fidget."

"Teachers are the lifeblood of the success of schools."

"Teaching, properly conceived, is not a delivery system."

"Investing in professional development is not a cost, it’s an investment."

"There’s wonderful work happening in this country, but I have to say it’s happening in spite of the dominant culture of education - not because of it."

"If we all did that [Alternative Education] there would be no need for the alternative."

"The real role of leadership in education, and I think it’s true at the national level, the state level, and the school level, is not - and should not be - command and control. The real role of leadership is climate control."

Here’s his talk … check it out:

What ideas and opinions resonate with you?

From Vodcasting to TED…

In 2009 I attended a training on how to “vodcast” content. Our hosts were two teachers from Woodland Park High School, Colorado, Jonathan Bergmann and Aaron Sams. They taught us how to record video and audio … and how to edit and upload to various services.

Anyway, quite a bit has happened since our time together in the WPHS library: the term “vodcasting” was replaced with “flipping;” Jonathan and Aaron published a book on the topic and on their reflections (both have subsequently moved on from teaching at WPHS); Sal Khan, with the help of Bill Gates, forced himself into pedagogical conversation by producing and propagating thousands of video lectures; and a California-based teacher who also attended the training, Ramsey Musallam, recently gave a short-form TED talk where he explained his embrace of the following ideas:

  1. Curiosity comes first
  2. Embrace the mess
  3. Practice reflection

You don’t need to read Bergmann and Sams’ book or watch any of Khan’s stuff … but you should watch Musallam’s talk. He did a great job; watching and listening was well worth 6 min and 30 sec of my life. 

See, what Ramsey did so nicely was he described his transition away from simply flipping lectures and pseudoteaching and into a more pure and natural and humanizing form of teaching and learning - one designed around the aforementioned three ideas. Well done Ramsey!

Caffeinated Collaboration

ACT testing was today and I, for once, did not have to proctor the exam. I essentially had the morning off from teaching and student contact. Upon learning this a friend and colleague of mine (@robhazle) invited me to “geek out” with him at a local coffee shop.

"Let’s drink some java and build some Arduino boards.”

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Intrigued by hanging out with him AND messing around with Arduino product, I logically agreed.

We spent about two hours messing with LEDs, resistors, circuits, and C programming. He explained, I listened; he asked, I gave feedback. Yet, despite the technical nature of our conversation, we were able to relate the Arduino-related content to teaching, our school’s engineering program, and to student learning.

We spent quite a bit of time discussing robotics, literacy (via technical reading strategies); biochemical/cellular analogies to programming, board construction, and output; and mathematical overlays of programming.

As he programmed and discussed pulse-width modulation and the nature of binary code, I couldn’t help by daydream a bit about the connections between his words and several mathematical concepts.

I was essentially asking myself (and him) these questions:

How can programming and related skills be used to bolster students’ learning of mathematics?

Who is doing this?

Which schools are doing this?

See, I’ve had so many conversations recently about designing multi-disciplinary projects and creating learning environments that encourage transference of content from one broad area to another. The one area that seems to frustrate such conversations is mathematics.

This frustration has often been likened to a thumb that juts out away from the other fingers.

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I attempted to capture this comparison in a previous post.

At this time, however, I’m left pondering these questions:

How can we use ideas like programming and board construction to better integrate mathematics with other topics?

How can we bring that thumb in a bit?

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Clearly I have more questions than answers, but I can’t help but think that in this world of #globalmath and Professional Learning Networks, PLNs, many creative and responsible ways to integrate and mature math education are possible … and well within reach.

(Thanks to my youngest son for lending a hand with this post.)

Special Spatial Thinking & Analysis

As I’ve taught some Earth/Space/Environmental Science this semester, I’ve made an effort to incorporate some Geographical Information Systems (GIS) technology to add both depth and relevance.

We began by using some investigations designed by Al Bodzin of Lehigh University designed to investigate tectonic activity as related to plate boundaries, earthquake and volcanic activity, and plate motion.

Bodzin and his group designed six investigations that I used (and modified slightly).

Each investigation had both a student guide and investigation sheet that students used to explore the maps.

Here are some images from the investigations:

World Earthquakes (identification of plate boundaries):

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Age of Oceanic Crust:

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Mid Atlantic Ridge

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Relative Plate Motion

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North American Plate Motion

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San Andreas Fault Zones

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Subduction Zone Depth - Aleutian Islands

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You may notice in the images that students were able to explore, measure, zoom, scale, and manipulate the data behind the images. This, I found, led to relevant and deep inquiries into tectonics driving forces that shape our planet.

Additionally, I was able to demonstrate real-time data acquisition and inclusion by downloading a USGS csv file for the world’s earthquakes (M2.5 and greater, last seven days):

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The data file was then easily overlaid onto an ArcGIS map to create the following map:

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The real power behind this technology and my students’ investigations is the highly visual and customizable results that the maps yield.

For next steps my students will compile their own data sets and overlay them onto maps. Their data will cross location (latitude and longitude) with weather, temperature, and environmental data as preliminary steps in larger investigations into Earth patterns and energy distribution.

I appreciate the ease with which I and my students can utilize GIS technology. I think the following image (via @josephkerski) effectively summarizes the power and scope of GIS:

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Hopefully I can share some of my students’ work in the creation and overlay of their own data.

Until then, here are some examples of multi-disciplinary uses of GIS.

"There Is No Center, Man."

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Almost 20 years ago, while exiting an Allman Brothers Band show, I had an interesting conversation with a good friend. This wasn’t your typical conversation. During the show, I had ingested some…let’s call it recreational pharmaceuticals…and found myself on a different plane. Though I don’t remember what started the conversation, I do remember what I said and why.

I told my friend, “There is no center, man.” As one would expect, he had no idea what I was talking about. I explained to him that if you marked two points and used a marker to draw a line in the center, you didn’t really mark the center. After all, if you zoomed in on that mark, you’d see that it had a width of a couple millimeters. I continued, “If you draw a smaller line with a pencil, you could still zoom in on that mark with a magnifying glass and see that it still has a width.” This discussion continued much longer than it should have.

I suppose a little explanation about my past is in order. I wasn’t very academic when I was young. In fact, I was more concerned about where the next party was than I was about doing my homework and going to class. I was decent at math, but once I finished algebra 2, there was no way I was going to venture into trig and calculus. That was the really hard math…or so I thought.

What does a conversation have to do with learning math? Quite a bit, actually. Our discussion about “the center” was actually describing a limit which is one of the first things learned in calculus. Admittedly, it wasn’t the most eloquent description of a limit nor was it even 100% accurate, but it was an idea about a concept. I had never taken calculus, nor did I know anything about calculus for another 15 years. But that concept made sense. Fast-forward 15 years…Now I’m an electrical engineering major who spends most of my time knee-deep in calculus and differential equations.

One of the reasons for so many people struggle in math is that it requires a level of abstract thought that other subjects do not. That alone will limit the number of people who will excel at math. However, that isn’t the only limiting factor. There is a problem with the way math is taught. There are two parts to learning math; 1) learning the rules, formulas, derivations, proofs, and various other problem solving techniques, and 2) learning the concepts. Too often, the focus is placed on the former.  Most algebra students never venture into calculus for the same reasons that I didn’t. They fear that it is a difficult math reserved only for the brightest. In reality, it is one of easiest of all the mathematics.

That leaves us with a few questions that should be answered about why we teach math the way we do. Why don’t we offer a conceptual math class? I’ve seen conceptual physics classes. Surely, the same could be done for math. Your first calculus really only deals with 3 concepts; limits, derivatives and integrals. Better yet, why don’t we just start introducing some of these concepts in lower level classes and reduce the fear of higher math that students have. All three could very easily be introduced geometry, algebra and trigonometry from a conceptual viewpoint. So why don’t we? Until we make mathematical concepts more real and understandable, potentially good math students will continue to shy away from higher level math.