Passing Notes to Stay Engaged in Lecture

I was working with a class of high school Juniors (17 year olds) and there was quite a bit of lecture introducing the project (I am thinking how to revise that). I noticed two students actively passing notes back and forth. They had good technique; always looking forward during the actual note passing, using a class handout as their notepaper, and generally trying to time the crucial note pass when my eyes were elsewhere. However, I did obviously see them do it and I wondered what I should do about it.

I thought that it meant they were ignoring me, and was tempted to confront them during class. However, later when I asked a question one of the girls raised her hand and volunteered a great answer revealing she was interested in the topic and had heard at least some of what I was saying.

So I thought, maybe note passing was just her way of interacting with the lecture. I know that an active reader should always have questions and connections, which we encourage them to write in the margins (if possible). Active listening might be the same. It is just prejudice which makes me believe that since passing notes is social it must not be about the lecture. In fact I know that often personal notes are not about the lecture (as the world of notebook doodles can attest).

The social and conversational aspect of learning is so important and so difficult to achieve with 30 teenagers. Partly because they do tend to veer off topic and off task when they become social. Also because some student’s asking questions and interacting with the content can be disruptive to other students. However, perhaps passing notes could be a way to have non-disruptive peer-to-peer interactions during a presentation. Being a teacher I would want to have some way to monitor the notes or at least to establish some guidelines. If they were paper notes would I collect them at the end of class? Is that kind of thought police activity destructive to true engagement? Maybe a classroom backchannel using cell phones and twitter (or other messaging platform, a wiki, a Google doc, Moodle forum), would allow kids to interact and socialize, but in a way that was understood to be open.

Open Content-Judo Flip the Common Core Standards

Judo FlipAs educators we can decry the adoption of the Common Core standards as a homogenization of education. Or we can take this opportunity to wrest control of our curriculum from the publishing companies. Like a skilled Judo athlete we can use the power and strength of an aggressor (dominating one-size fits all standards created by non-educators) to gain an advantage. How? By working together educators can create materials to teach the common core standards: from instructional resources like textbooks and lecture videos, to formative assessments like adaptive online quizzes and rubrics, to classroom activities and projects, from 15 minute discussion starters to cross curricular, multimedia, student-led investigations of ideas. We write it all collaboratively and we make sure that it teaches the standards, because we know that you can teach the basic concepts on the standards in exciting and engaging ways even if the state only assesses them using a multiple choice test. Then we go to our state departments of education and say, “Thanks but no thanks to your approved textbooks”. The state then takes all of that textbook money and uses it for teacher professional development and student materials (including technology to access the digital curriculum).

So what do we get out of this approach? Free and open learning materials that can be mixed and matched by teachers and schools to best fit their needs, money to get digital tools into kids hands so that they can take advantage in the latest advances in learning-multimedia, interactivity, personalization, and educator control over content in spite of the attempt to teacher-proof education.

Open content already has some nascent beginnings. Now is the time to take it to the next level: The broad adoption of common core standards will give teachers across the US a common set of learning objectives, and the increase in affordable digital devices will allow us to kick the paper habit and the control of the companies with the printing presses. Can we reach a critical mass?

http://www.ck12.org/flexbook/

http://www.oercommons.org/

http://oerconsortium.org/

http://www.curriki.org/

Hard Work, Sports, and Competition

On the radio I heard a player for the college basketball team that won the NCAA tournament say, “This just proves hard work pays off”. Actually, it proves just the opposite. Let’s assume that the 64 teams that entered the tournament all work very hard. The fact that only 1 in 64 win the tournament shows that hard work does not pay off 98% of the time. Actually lets assume that the 350 division 1 basketball teams all worked hard in a season. Hard work pays off 0.3% of the time. Let us continue and assume that these students have practiced playing basketball on hard working high school teams and so only 1 team’s worth of students of the 10,000 high school teams actually won. (hard work has reached a .01% chance of winning).

Sports connected to education is a very tenuous proposition. Arguments are made for sports value as a builder of team work, character, and school spirit. Every year local schools compete in rivalry football games. Every year both teams declare they will win, every year only one team does. What if rival schools had a yearly cooperative event? What if schools took the money from the sports programs put it into arts and the two schools put on a co-production of a show celebrating talent? Some years the show would be bad, other years, when the students worked harder, the show would be better. That is how hard work pays off.

The Case Against Math

Resolved: Math education is mostly pointless and over emphasized.

Why do we teach math? We all use arithmetic and could use some knowledge of percents and fractions, but the education system seems to push a lot of abstract math. When I ask this question of educators, I often get these answers:

  • It is beautiful
  • A basic understanding is generally useful (and advanced study is required for certain professions)
  • It is mental exercise/a sign of intelligence
  • Knowledge of math can be transferred to general critical thinking

All of these might be true however, listed below are several arguments against these reasons.

Are these reasons unique enough to math to warrant the focus that our education institution places on math?

Many disciplines, e.g. music, art, dance, cooking, and computer programming,  all meet the above requirements, yet are not taught daily to all students, do not have state adopted curricula, and are not assessed as a part of school, teacher, and student success.

Do the above reasons represent how we or why we really teach math?

My observation of math education is that we teach and test the specific math functions and abilities that have little practical application, context, or critical thinking. For example, here is an example question from the California State Standards Algebra 2 test (passing Algebra 2 is required to apply to the University of California (UC) system).

This question represents a specific and esoteric application of math, for math’s sake, without context. There might be one or two fantastic math teachers who can present this kind of problem to students in a way that emphasizes critical thinking, real world application, or the beauty of the logic. However, my belief is that most math teachers present this kind of problem as an end unto itself, ie learning how to divide polynomials is the goal. So the question is, why do children (or adults) need to learn how to divide polynomials? Definitely some people do need this kind of knowledge, but some people also need to know how to modulate from Eb min to G#dom; some people need to know the difference between Hungarian and Spanish paprika; and some people need to know how to communicate with another person in a difficult relationship. Why do we teach some knowledge “just in case” and some knowledge “just in time”?

Are the above reasons, actually all true?

I agree that math is beautiful, that a general understanding is useful, and more in-depth understanding is vital for a very small percent of people. However, I disagree that math is a sign of intelligence and transferable logic/critical thinking I disagree with. I have seen students who could very easily find the 4 roots of a complex polynomial, unable to determine the correct scale for a graph for a science lab. It has always seemed to me that students leave their math brains in math class. The concept of situated knowledge is documented, and I am not sure that the case for generalizable knowledge has ever been proven. Just because math is very abstract, does not mean that it is more generalizable. As an analogy, if our goal is for students to appreciate the beauty of an ancient Greek vase, the way we go about teaching it is to break that vase into very small, comprehensible, and abstract parts. Then we teach each of these parts as if it was very important and never reference the larger goal because students are not prepared to understand the whole. Is it any wonder that students never appreciate the vase? Maybe we should approach students with the complexity and messiness we want them to be able to deal with. Perhaps the only way to teach critical thinking in complex situations (if that is a real goal of education) is to have a critical thinking class, even if the problems we present in these classes don’t have easily grade-able answers; even if the complexity scares and frustrates our students. I think we would rather have students frustrated by general complexity, than by abstract simplicity.

Are the above reasons enough to give math the heavy focus that we give it in our education system?

If you need evidence to the heavy weight that math is given, here are the percentage weights of the API (the official rating/grade of school) for California.

Subject K-5 6-8 9-12
English–Language Arts 56.5% 51.4% 36.10%
Mathematics 37.6% 34.3% 27.10%
Science 5.9% 7.1% 22.9%
History–Social Science N/A 7.1% 13.9%

(Even though Science and History are given some weight in K-8, they are only tested in 5th and 8th grade  and predominately on the 5th and 8th grade standards). The SAT and GRE tests are essentially 1/2 to 1/3 based on math.

Does math represent a third of what we think people should know? Remember, by math, I am not talking about the ability to estimate that 37%, 34% and 27% are a third. Percents and fractions are lower-level elementary math while algebra, geometry/trigonometry, and calculus are the true goals of math education. Estimation, number sense, and practical application are not the end goals of math education. Even if math qua math is valuable for all, or at least valuable enough for future academics, and all students need to be exposed to it, is it more valuable than the languages of the people of the world, health, technology, the arts, history, and science combined?

So why math?

Math is easy to test. Math is seen as a proxy for intelligence. Math is used to sort and select, ie to determine which students are good enough for continuing studies. Math has traditionally favored male students (I would argue not due to genetic reasons, but due to socialization). Perhaps math education used to focus on deductive reasoning and logic. Cultural inertia means that we have taught math and so we will teach math.

Why are you picking on math?

Science, history, English literature, world language classes, physical education classes, all share many of the same problems that math education faces. These all represent symptoms of the same disease: teaching content over skills, compartmentalizing knowledge, focusing on academic departments of universities over the real needs of our students. However, only math seems to hold the hallowed place as the proxy for intelligence. Also, many students have a very poor experience with math, which turns them off of the entire school system since math is given such a strong emphasis.

So what to do?

If we must teach math, teach it  as if math was just one aspect of the larger concepts and questions that are the main thrust of education: critical thinking, problem solving, communication, empathy, and creativity. If we must teach math, teach it through music, art, science, technology, history, cooking, construction, engineering etc. because math as an abstract system is useful to very few of our students. If we must teach math, focus less on the answers and the algorithms for specific types of problems and focus more on the questions and the processes of problems.

Caveats/Conflicts of Interest: I love math (the Fourier transform makes me laugh with joy). I am good at math. However, I don’t feel that my personal experiences in school represent an adequate reason for determining the focus of education for all children. I love learning for learning’s sake. I believe in the well rounded, academic, humanities education in which math and science are members of the humanities. I am a science teacher and technology coach. I believe that facts are important.

Content Areas
K–5
6–8
9–12
CSTs, CMA, and CAPA
English–Language Arts
56.5%
51.4%
27.1%
Mathematics
37.6%
34.3%
18.1%
Science
5.9%
7.1%
22.9%
History–Social Science
N/A
7.1%
13.9%
CAHSEE
English–Language Arts
N/A
N/A
9.0%
Mathematics
N/A
N/A
9.0%

Tech Standards

I love the concept of the ISTE NETS as very general conceptual standards that address the core skills that we should be teaching in school. However, many teachers were looking for guidance on what types of activities students should be engaging in at a particular grade level. Also we want to ensure that our graduates have experiences using certain key technologies as well as the general skills espoused in the ISTE NETS. Therefore, I created a set of standards that combine the ISTE standards with specific technology standards.

CUSD Technology Integration Standards-5 general categories with 3 strands each (Numbers match the strand to a National Education Technology standard)

  • Office
    • Documents
    • Presentations
    • Spreadsheets
  • Multimedia
    • Drawing/Image Editing
    • Audio
    • Video
  • Technology Operations (6)
    • Keyboarding
    • Computer Skills
    • Computer Science
  • Engagement (Higher Level Skills)
    • Creativity and Innovation (1)
    • Communication and Collaboration (2)
    • Problem-Solving and Critical Thinking (4)
  • Web
    • Research/Information Literacy (3)
    • Digital Citizenship/Safety (5)
    • E-Communication/ Web Publishing

These standards each have specific skills to be addressed at each grade level.

Elementary Tech Standards-Skills

Secondary Tech Standards-Skills

Tech Standards Examples chart – Some general examples of classroom use for each strand

These draft standards and skill lists are a first draft based somewhat on current practices, but are definitely on the level of a 3-5 year goal before we believe they will be met. Our teachers have had their first exposure to these standards recently, and I would love any feedback from other members of the education and technology community. Also feel free to use and re-use these standards as part of the public domain.