Still a work in progress…

My introduction to blogs came when I was in high school. They were of the livejournal variety: diaries with their content broadcast to the world (or several of its inhabitants at least) rather than kept privately in a locked drawer. While curiosity drew me to the blogs, it was frightening to become¬† aware of the thoughts and emotions of friends and acquaintances, especially when I was present at the time of the events they discussed. The comment feature on these public diaries was rarely used for anything other than to say “hi.” Meanwhile, the comment section for the online newspaper articles that I read was used regularly but was equal in terms of usefulness to that of the blogs. I began ignoring the comment section of these articles not long after I discovered it. The comments were frequently extreme, hateful, and attacking in nature. It was disheartening to think that people actually felt and talked in this manner, most likely empowered by the anonymity of being an internet commenter.

Over the past couple of years, I have begun to read blogs discussing education and, more specifically, math education. I have been surprised to discover blog comments that actually formed productive conversations (although they still sometimes contain subtle and not-so-subtle personal attacks). The challenge is forcing myself to actually sit down and read these blog entries and the ensuing comments. The mental exhaustion resulting from a day of teaching (and all the other challenges that a school day brings) can be difficult to overcome. Yet, one advantage of blogs and online presentations over in-person professional development sessions is that you can experience them when you are most up to the task. One of these newly discovered blogs that I have been following is that of Dan Meyer. I have found great value in both the entries and the comments that follow, especially since there is a fair amount of overlap between the content in Mr. Meyer’s class and the 8th Grade Math Georgia Performance Standards.

Following the administration of the state standardized test at my school, I have had more flexibility to try teaching in a more “high-risk, high-reward” manner. I utilized several of the ideas from Dan Meyer’s “What Can You Do With This?” blog entries, including “What Can You Do With This: Italian Job,” “Who Cares? – The Wager,” “What Can You Do With This: Water Tank,” and “What Can You Do With This: The $6400 Question.” My focus was on better engaging my students and giving them problems without a clear, easily obtainable resolution. Real-life problems can rarely be solved by looking at an example problem and following the exact same procedures. So why were we taught this way as students? Why do we continue to teach this way now that we are educators? Just look at the accepted observation that there is no one-size-fits-all reform strategy in education as a real-world example. Every school has a different student population and unique challenges to overcome.

One day I introduced a lesson based on a challenge presented by Dan Meyer (The Wager from “Who Cares?”). I played about 20 seconds of a video clip created by Dan Meyer of a transparent tank filling up with water at the beginning of class. I asked each group of students to predict how long it would take to fill the tank. Their guesses ranged from ten minutes to a few hours. The fill/drain a water tank problem is a pretty easy, if unexciting, application of linear equations to a real-world situation. Yet, by allowing the students to actually see the tank and having them make a prediction, the plan was to engage the students in the process of discovering the answer. After the students made their predictions, I abandoned the water tank problem and moved on to something completely different. In each one of my classes, eventually a few of the students made a comment along the lines of “you never told us how long it took to fill the tank.” Sometimes the comment came only a few minutes after we had moved on. Other times, it came much later. More convincing evidence of the students’ level of engagement in the exercise came at the end of the lesson when I played the rest of the video. With their focus on the screen, you would have thought they were watching a summer blockbuster at the movie theater, not a tank filling with water in a classroom.

I used the engagement of the students to invest them in solving a problem that involved some critical thinking. When we revisited the problem, I avoided the temptation to hold the students’ hands through writing a linear equation to represent the situation. Instead, I simply asked them to come up with a justified answer to the question of how long it would take to fill up the tank. Some students’ answers included a rate of change and/or linear equation. Most of the answers didn’t. All of them experienced the struggle, including failure, that it takes to solve a real problem, and the first group was able to make a connection between the content covered earlier in the year and a problem they had not seen before.

It seems intuitive that the engagement and critical thinking that results from discovery learning would benefit students. However, there is also research to support the value of discovery learning. Kevin Hall, one of the commenters on Dan Meyer’s blog, directed readers’ attention to “Practice Enables Successful Learning Under Minimal Guidance,” Journal of Education Psychology (2009).

Hall also referenced the article “What Needs to Develop in the Development of Inquiry Skills,” Cognition and Instruction (2000), to support the effectiveness of project-based learning.

Edutopia highlights several more studies that have shown the advantages of project-based learning.

The following is a continuation from a previous blog post of observations and reflections based on the first of four classroom visits I made last week.

After the students completed the warm-up and the teacher reviewed the answers, the students completed six problems using individual student response systems. Although I use a different model, I also utilize student response systems in my own classroom. I did not get a close look at the type of student response systems the students in this class were using, but the student response systems that I have offer six possible answer choices (A-F). My students associate themselves with their individual response system by typing in a unique three-letter code at the beginning of class.

One major benefit from using student response systems is they instantaneously provide feedback for the answers students choose for a given problem. As soon as the students are finished inputting their answers, a teacher can view a bar graph that shows how many students selected each answer. If everyone gets a problem right, move on to the next problem. If a large number of students give the same wrong answer, address the misconception on the spot while the problem is still fresh in the students’ heads.

Unfortunately, student response systems have the major drawback of requiring all students to answer the same question at the same time. Students think at different speeds and consequently require different amounts of time to answer the same question. With the student response systems, however, all students must spend the same amount of time on each question. The silver lining is that the teacher can find out the exact amount of time that elapses between the question being displayed and an individual student inputting his/her answer. The teacher may want to provide students with an additional assignment for them to work on during the time between when they answer each problem and when the next question is displayed. It may be difficult, however, for the students to constantly jump back and forth between the student response system questions and the assignment. Another negative consequence of students working on the same question at the same time is the tendency to cheat. I noticed this in the classroom I observed and have witnessed it in my own classroom as well. A student pressing a button is more easily visible than an answer written on a paper. Also, students tend to look around to their peers who have already answered the question for input on their own answer.

I have found the best use of the student response systems to be brief, informal assessments. On a scale of 1-5, how well do you understand this concept (1 being not at all, 5 being completely understand)? I also use them for three to four problem exit tickets at the end of a lesson. I do not record the results in the gradebook or use the results as a measure of mastery of the skill. Instead, I just use the data to get a picture of how well my students understood the day’s lesson. I have also used the student response systems for review exercises. My students love the instant feedback of knowing whether or not they got a question right.

Spring break for my school system is just wrapping up. I decided to use the time off as an opportunity to visit the classrooms of some of my professional counterparts in Nashville and Atlanta. When I sent out an e-mail to a contact in the Metro Nashville Public Schools system, the subject of the response was “Shouldn’t you be at a beach somewhere?” Did that last year. It was time to make an unusually mature decision and spend my break productively this time around.

I had the privilege of visiting math classes in four completely different schools. In Nashville I visited two public high schools: one small learning community high school and one magnet school. Both of these teachers graciously invited a complete stranger into their rooms on short notice. In Atlanta I visited the classrooms of two fellow members of the Dobbs 21st Century Learning Cohort. Both of these classes were in private high schools with one of them being a single-gender school. The latter two visits also included post-class conversations with the teacher about teaching math. Thank you to both of you for not only welcoming me into your classroom on short notice but also sacrificing a significant portion of your planning time in a busy day to talk with me. When I first applied for this fellowship, I did not anticipate developing such strong relationships with fellow members of the cohort. I really do admire all of the cohort’s participants and facilitators and enjoy all of the time we spend together. Those 2.5 hour meetings would not move nearly as quickly as they do were that not the case.

All four of these classes and my own ranged widely in terms of the race, socioeconomic status, and investment level of the students. It would be naive to think that the same strategies could be used in all of these classrooms in order to achieve similar results. At the same time, all of the classes share a universal goal of student achievement and are composed of students with a mixture of learning styles. There are strategies that can successfully make the jump between all of these different classes. There are other strategies that can make the same jump with some tweaking. And of course the teachers of these classes face similar challenges, especially as they attempt to integrate 21st century skills into their curriculum.

All of the classes featured both teachers and students using technology proficiently. One class had an LCD projector attached to the ceiling that was linked to an InterWrite SchoolPad. The teacher used the SchoolPad to demonstrate the steps needed to answer the warm-up questions as she moved around the classroom. This mobility obviously enhanced her ability to monitor students. It is also easy to envision her allowing students to demonstrate how to answer problems from the comfort of their own desks. This would eliminate the time wasted when a student moves from his/her seat to an interactive board and then moves from the board back to the seat. It would also prevent any showmanship at the front of the class that would distract from the purpose of the exercise. While I have not used the SchoolPad myself, it did seem like it would take some practice in order to use it effectively in conjunction with the projection. In this area, interactive whiteboards have the advantage. Writing on an interactive whiteboard is as straightforward as writing on a dry-erase whiteboard.

Additional observations from all four classroom visits and the two conversations still to come in (very near) future blog posts…

Online-Based Courses

March 23, 2010 | Uncategorized  |  1 Comment

In a previous post, I reflected upon the first chapter of the book Disrupting Class. While scrolling through the headlines in my hometown news folder on Google Reader, I recently ran across an article related to the book’s projection of a fast-approaching drastic increase in the number of students receiving computer-based instruction. The article, “New Programs Aimed at Boosting Metro Graduation Rates” from the Nashville’s The City Paper, informs us that Metro Nashville Public Schools is investing in a program to provide students with access to online-based courses. The investment itself, $263,100, is relatively small. Just like many public school districts in the Atlanta area and around the country, Metro Nashville Public Schools is having to make significant budget cuts. I am going to wonder “aloud” how great an impact the current financial state of many school districts is having upon the utilization of online-based courses. I wish that I had the knowledge to express an opinion on that matter. In Disrupting Class, the authors discuss how online-based courses are the only option for schools that otherwise are unable to offer certain courses due to limited resources. The City Paper article seems to suggest that Metro Nashville Public Schools will be utilizing online-based instruction in a similar manner. The article also mentions that “students who lack credit in a certain subject” will take the online courses as well. Seems like that description could fit a large number of students. I need a bit more clarification to understand who that second target group would consist of. I definitely need to finish Disrupting Class during spring break, which is only a couple of weeks away.

I now have direction in the development of my culminating artifact. The artifact will be housed in a class wiki. In pairs, my students will create mini-lessons for the concepts that we have covered in eighth grade math. These mini-lessons will aid my current students in reviewing for the CRCT and will also hopefully benefit future students, who will be able to view the lessons on the wiki. Ideally, the times that my students are working on these mini-lessons will be staggered to help manage available resources and improve my ability to assist the students. One possibility for creating the lessons is for students to use the combination of the Promethean ActivBoard in my classroom and Jing. Unfortunately, my ActivBoard has been out of commission since late December. I have been actively working to have the ActivBoard repaired and am optimistic that these efforts will be rewarded in the near future.

One of the first steps that I need to take is to create a rubric and develop (or find) a couple of examples to give my students a clear vision of what I expect their final products to look like. I have been directed toward some examples at the Mathtrain.TV site. The slope rap that I discussed in a previous post should be able to fit into the format of this project. The students can create  either a series of images or a video to accompany the lyrics.

I have confiscated a few “raps” over my 2.5+ years of teaching eighth grade math. They have all featured a 4:1 ratio of non-profane to profane words and themes of sex and violence. Earlier this week before school, I noticed a few of my male students quietly creating a rap. They immediately stopped what they were doing when I approached and began to reassure me there would be no more of it. I caught them off guard though. Instead of scolding them, I encouraged their work but with a new focus: slope. I was pleasantly surprised that they accepted the challenge and even did so with enthusiasm. Every few minutes they would proudly summon me back over to the table to show me their lyrics and ask for feedback. The most encouraging thing about the entire incident was the particular students that were creating the slope rap. These were not my high-achieving students. Instead, they were the students that are the least invested in school and are frequently suspended for misbehavior. There was excitement visible on their faces when I mentioned the potential of recording their rap and putting it on the internet.

Last year while on a youtube binge, I watched several “raps” about math topics. They all featured a teacher. The ones performed in front of a class also included laughter and shock from students. I couldn’t see myself doing it. I wasn’t even so moved as to share the videos with my students. I do not know why the thought did not cross my mind to instead have my students create the raps, keeping my unqualified mouth and mind out of the process. I of course know that I am not the first one to come up with this idea, but I have not come across any examples yet.

Laura suggested that I have students create mini-lessons that could be posted on a wiki as my culminating artifact. I am thinking that the slope rap could be a part of this. Now, not all of my students are going to want to create raps, but it might be a good way to invest my students that would have been least invested to begin with. First they can create a rap about the math topic of their choice. Then they can produce images and video to accompany it to form a lesson.

When recovering from jaw surgery this summer, I used some of my large amount of free time to set up a twitter account. I was active on it for a few weeks before abandoning twitter completely when school started. I signed back in this weekend and decided to set up a separate account for education and technology. I used the spreadsheet that Laura has posted on the wiki to start following about a dozen people. Right away my efforts were rewarded with a simple applet on linear equations in slope-intercept form, which is exactly what we are covering in my class at the moment. I will probably be doing more lurking than tweeting here in the beginning. Just so you know who is watching you though, I’m @midschoolmath on twitter.

Culminating Artifact

January 25, 2010 | Uncategorized  |  5 Comments

In order to develop a plan for my culminating artifact, Laura suggested that I create a blog post about my class and the resources available to me. I teach eighth grade math in Atlanta Public Schools, so my students are assessed on their mastery of the 8th grade math Georgia Performance Standards (GPS) using the 8th grade math Criterion Referenced Competency Test (CRCT) in April.

There are four domains within the 8th grade math GPS: Algebra, Numbers & Operations, Data Analysis & Probability, and Geometry.

The largest domain, both in terms of number of standards and number of CRCT questions, is Algebra, which includes the following concepts: simplifying and evaluating algebraic expressions, solving algebraic equations, solving and graphing inequalities in one variable, relations and functions, interpreting slope as a rate of change, determining the meaning of slope and the y-intercept in a given situation, graphing linear equations and linear inequalities, and systems of linear equations and linear inequalities.

Numbers and Operations includes the following skills: finding square roots, distinguishing between rational and irrational numbers, simplifying expressions with integer exponents, and expressing and using numbers in scientific notation.

The key concepts in Data Analysis & Probability are set theory, Venn diagrams, tree diagrams, addition and multiplication principles of counting, probability of simple independent events and compound independent events, gathering data that can be modeled with a linear function, and estimating and determining the line of best fit from a scatter plot.

The Geometry domain requires students to master investigating the characteristics of parallel and perpendicular lines, applying properties of angle pairs formed by parallel lines cut by a transversal, understanding the properties of the ratio of segments of parallel lines cut by one or more transversals, understanding the meaning of congruence, and the Pythagorean theorem.

Thanks to a T3 grant, I also have several technology tools to aid in teaching this content. There is a mounted LCD projector in my classroom to accompany a Promethean ActivBoard. I also have access to a classroom set of MacBooks (laptops) and a classroom set of ActiVotes (student response systems).

Learning Contract

January 19, 2010 | Uncategorized  |  1 Comment

I have been thinking quite a bit the last few days about adjustments that I want to make to my learning contract. Originally I placed an emphasis on inquiry-based learning. In doing so, however, I strayed from my passion – technology. This is not to say that inquiry-based learning and educational technology cannot go hand in hand. I simply want to ensure that I focus on using educational technology effectively in the classroom. While we may not be able to pinpoint with confidence the skills that our students will need to be successful, digital literacy will be of great value. Math and reading are important subjects. While controversial, No Child Left Behind has certainly succeeded at placing a great emphasis on these subjects in public schools. Great effort is being put into increasing math and reading scores in schools with the highest percentage of students receiving free and reduced lunch. However, it is the students in these same schools that are the most digitally illiterate. While grants are available to facilitate bringing technology into these schools, there is little to no pressure to ensure that all students are gaining the experience and technology skills they need to have future success in life after school.

I want to use technology in my classroom in a way that improves my students’ ability to master content standards, enhances their digital literacy, and fosters effective collaboration. In order to meet these goals, I need to improve my research habits. I must research daily by reading articles, blog posts, and books. As I read, I must reflect constantly and always be thinking how I can use what I am reading in my classroom this year.

The post that follows is an ongoing reflection upon Chapter 1 of Disrupting Class: How Disruptive Innovation Will Change the Way the World Learns by Clayton M. Christensen, Michael B. Horn, and Curtis W. Johnson.

Teachers need to differentiate instruction based on learning style. It is a sentiment that has been expressed in nearly every professional development session that I have attended as an educator and one that I agree with. Yet, I struggle to envision and have yet to witness an example of a traditional classroom with differentiated instruction that meets the learning style of each individual student. I have seen surveys that ask students a series of questions and spit out a learning style for that student. What if the students do not understand the survey questions? What if the students write down numbers without thinking to be done with the survey as quickly as possible? The teacher will spend the rest of the year gearing instruction toward the student’s misdiagnosed learning style. This can’t be the best way of determining a student’s learning style. A classroom that truly meets the needs of every learner must first have an effective method of discovering a student’s learning style.

Chapter 1 of Disrupting Class discusses Howard Gardner’s eight intelligences: Linguistic, Logical-mathematical, Spatial, Bodily-kinesthetic, Musical, Interpersonal, Intrapersonal, and Naturalist. Without any formal assessment, I would identify logical-mathematical and interpersonal as my strongest intelligences. Maybe my weak intrapersonal intelligence has led to a misdiagnosis. There are definitely some intelligences in there that are glaring weaknesses (such as linguistic, as demonstrated by my blogging). I have long held the opinion that developing curriculum and designing the manner in which the curriculum should be implemented (down to individual lesson plans and learning activities) should be done by a group of people. The task can be overwhelming for a single individual. Thinking about the multiple intelligences lends further support to my idea of a group of people completing this task. One would think that a teacher with strength in a certain intelligence can better design a learning task for a student with the same strength while struggling to design tasks for students with strengths in other intelligences. Also, strength in a certain intelligence might enable one to better design tasks geared toward several of the individual intelligences.

A strong statement from page 37 of Disrupting Class:

But in most U.S. schools, especially at the middle and high school level, even a heroic effort by a teacher to pay attention to multiple intelligence patterns is, because of the way the system is arranged around the monolithic architecture, almost guaranteed to fail. When that teacher caters to one type of intelligence, some students will tune in, but others will tune out.

I am copying my blogging comment partner Ted and writing a reflection post about the article “21st Century Skills: The Challenges Ahead” from the September 2009 issue of ASCD Educational Leadership. Hopefully I will only be copying Ted’s idea and not his actual post. I read Ted’s reflection this morning, but a day of school leaves me with only wisps of the memories from that morning. I now realize that I should have read this article from the start instead of watching the video that I commented briefly on earlier today. By the time I finished reading the article, I was ready to follow Rotherham and Willingham into battle. As they pointed out, the task will be momentous, but I’m on board. In highlighting the passages that struck a chord with me, I was highlighting nearly the entire article.

The authors identified the three most important components necessary for the the “21st century skills” movement to be successful:

First, educators and policymakers must ensure that the instructional program is complete and that content is not shortchanged for an ephemeral pursuit of skills. Second, states, school districts, and schools need to revamp how they think about human capital in education – in particular how teachers are trained. Finally, we need new assessments that can accurately measure richer learning and more complex tasks.

The article also dismisses the argument that the “21st century skills” movement should focus purely on the skills and that the actual content is insignificant. Instead, the article stresses that the skills and content must be stressed equally and be intertwined:

But all content is not equally important to mathematics, or to science, or to literature. To think critically, students need the knowledge that is central to the domain.

Also, speaking to the importance of our cohort, collaboration among teachers is critical. This collaboration, however, does not just involve teachers within one building. Instead, forums that foster collaboration among teachers everywhere must be established and maintained.

As the title suggests, this article identifies the challenges that the “21st century skills” movement faces. The authors, however, do not ignore, dismiss, or downplay any of these challenges. At the same time, the purpose is not for them to be naysayers. Rather, the challenges and their magnitude are recognized in full so that they can be addressed. Otherwise, the “21st century skills” movement will be a failure.

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