Do you have a boring worksheet that you want to make more interesting?

Yesterday, I shared a worksheet I was using in my math course for preservice elementary teachers on Twitter. It got enough of a positive response that I thought I would share it here with a bit more context. Here is the Tweet:

Got a boring worksheet? Make it more interesting by adding 2 sentences. #mathchat pic.twitter.com/UebsbuCjJP
— David Coffey (@delta_dc) April 17, 2014

I made the point that this combined two worksheets. The original worksheet came from fractions4kids.com. This one reminded a lot of the future teachers of worksheets they did in elementary school. Some of the teachers had bad memories about those times. I told them they were not alone. A lot of students become disenchanted with mathematics once they encounter the way we teach fractions - rules without reasons. 

We also talked about how pointless it seemed to do all the problems. How much practice did they really need? How much proof did the teacher need in order to know whether the kids could follow the procedure? I shared (confessions of a bad math teacher) that sometimes I might only assign the odds or evens. Still, the only choice I was offering students was the choice to do it or not do it. And many chose the latter.

Fortunately, I learned from Brian Cambourne the importance of providing learners with choice.

Learners need to make their own decisions about when, how, and what "bits" to learn in any learning task. Learners who lose the ability to make decisions are disempowered. p. 187

This lead me to begin altering my approach to assigning work, which is evident in the second worksheet. I began adding a line or two asking the learners to pick the problems they did or did not want to do and why.

There was nothing special about the first worksheet. It could be on just about any topic. But the extra instructions, the two sentences asking learners to make choices and explain those choice, seemed to make the task much more engaging. And not just for the learners. I found reading their rationale behind their selections much more interesting than simply checking their answers.

Finally, teachers could have fun with the extra instructions. A group of student teachers came up with the idea of asking their high school students, "What items would you assign your best friend? Your worst enemy? Why?" So what questions might you add and why?

What are the Conditions of Learning?

Note: The original version of this post was written for my other blog, The Learning Museum.

I never teach my pupils; I only attempt to provide the conditions in which they can learn.

Albert Einstein

In this post, we explore the learning theory developed by Brian Cambourne from his research on language acquisition in natural settings. His book, The Whole Story: Natural Learning and the Acquisition of Literacy, introduced the idea that certain conditions were necessary in order for us to learn language. These conditions were further explored in this article, Toward an educationally relevant theory of literacy learning: Twenty years of inquiry. In both the book and the article, Cambourne describes the eight Conditions of Learning in detail. Below is a figure from the article representing the relationships that exist between the Conditions.

From Toward an educationally relevant theory of literacy learning

Cambourne's work focused on applying these Conditions to literacy instructions. Others, have sought to consider their application in other learning environments. Edmunds and Stoessiger wrote a book and article about their efforts to apply the Conditions to mathematics. Jan Turbill's doctoral research examined the use of the Conditions in teacher inservice. ReLeah Cosset Lent wrote Engaging Adolescent Learners: A Guide for Content-Area Learners using the Conditions as a framework.

From Engaging Adolescent Learners

And I wrote a guess blog post on how I used the Condition to learn to Tweet.

How do the Conditions of Learning fit into your practice?

How will I stay engaged?

Based on prior posts, it might seem that I do not want teachers to consider engagement when planning lessons (here). In this post, I intend to describe how teachers and learners share in fostering the conditions that contribute to engagement. This is reflected in Cambourne's Learning Plan shown below.

Again, engagement is at the bottom of this plan because it is a foundational condition to learning. Immersing learners in the discipline is placed on top as a reminder that it influences everything else that is done in the classroom. The remain conditions are split between those that focus on learners' behavior (purple) and those that start being the teachers' responsibility (green). The ultimate goal, however, is that over time the learners will also take on these behaviors as well - setting expectations for themselves, offering one another feedback, and providing their peers with models of success. 

Helping learners to take responsibility for their own engagement is also a gradual process that requires teachers helping learners move through awareness, acceptance, and adjustment. This starts with helping learners to be aware of what being engaged looks like (as I described in this post). Having this anchor experience allows us to continually monitor our engagement during learning activities.

I try to design learning plans with Cambourne's Conditions in mind, but I leave learners to evaluate their own engagement throughout the activities. Early in the semester, I provide a table like this:

The learners are asked to reflect on their level of engagement after each phase of the workshop (schema activation, focus, activity, and reflection). At the end of class, they answer three questions that hopefully support their awareness (What did you notice?), acceptance (So what does this mean?), and adjustment (Now what will you do to improve your engagement in the future?).

Their answers reflect the shared responsibility learners and teachers have for fostering engagement in classrooms. The learners accept that they need to be better about things like making connections, asking questions, and monitoring their own engagement. They also describe how it is hard to be engaged if expectations are unclear or if they are not sure how to complete the task. This is on me, as the teacher, and it has reinforced my need to keep in mind my initial responsibilities regarding Cambourne's Learning Plan. Consequently, all involve adjust their behavior in order to improve engagement.

There is one more piece to encouraging learners to take responsibility for their engagement that I have just added this year. I have replaced Participation in my course grading with Engagement. This change will be the focus of the next post. Please stay tuned.

Is direct instruction a better approach to teaching math?

I received the following in my email today:

An intriguing question that I often wonder about myself. Cambourne's research found that learning requires engagement, which means it depends on how engaging the lecture is to the learner. I clicked on the link hoping for some clarity. I was disappointed.

Here is a sampling from Paul E. Peterson’s article, Eighth-Grade Students Learn More Through Direct Instruction, reviewing the research:

As an instructor myself, I’ve had trouble making up my mind. I can cover a lot of ground in classes where lectures consume about two-thirds of the time. But those classes get less enthusiastic student evaluations than some smaller classes where students are encouraged to solve problems through discussion. I, too, like those problem-solving classes. They require less preparation and are easier to teach.

Before we more on, here are my reactions to this portion of the article. The first is nit-picky, but when Peterson says, “I can cover a lot of ground” it is a red flag for me. I, too, cover more material through lecture, but research shows that many students fail to cover the same ground or retain any memory of the landscape. Second, there is the statement, “I, too, like those problem-solving classes. They require less preparation and are easier to teach.” All I can say is that if planning a problem-solving lesson requires less preparation, then it is not really a problem-solving lesson.

Peterson continues:

So when Guido Schwerdt and Amelie Wuppermann of the University of Munich figured out a way to test empirically the relative value of the two teaching styles (see “Sage on the Stage,” research), it is worth trumpeting the findings. These analysts took advantage of the fact that the 2003 Trends in International Mathematics and Science Survey (TIMMS) not only tested a nationally representative sample of U.S. 8th graders in math and science, but also asked their teachers what percentage of class time was taken up by students “listening to lecture-style presentations” rather than either “working on problems with the teacher’s guidance” or “working on problems without guidance.” Teachers reported that they spent twice as much time on problem-solving activities as on direct instruction. In other words, U.S. middle-school teachers have drunk deep from the progressive pedagogical well.

It is important to note that the results are based on teachers' reporting instructional approaches and not direct observation. This is important because Stigler and Hiebert (1999) found that: “Although most U.S. teachers report trying to improve their teaching with current reform recommendations in mind, the videos show little evidence that change is occurring. Furthermore, when teachers do change their practice, it is often in only superficial ways.” (The Teaching Gap p. 12) This also comes from TIMSS data. However, there is no corroborating evidence in Schwerdt and Wuppermann’s study that supports teachers’ claims that they are using problem-solving approaches.

Furthermore, as the Learning Pyramid shows, not all direct-instruction methods are equal in their effectiveness. A demonstration (think aloud) would be a superior method to simply “covering content” through a traditional lecture. Again, Cambourne has shown that demonstrations are a necessary condition for learning but not sufficient. Learners must be given the opportunity to take responsibility for their learning and “give it a go.”

None of this seems to matter to Peterson who ends his review with, “Sadly, U.S. middle-school pedagogy is weighted heavily toward problem-solving.” In my opinion, what’s sad is that he would try to pass this research off as settling what is clearly a complex issue.

My reading of the Schwerdt and Wuppermann study suggests that it tries to answer the question, “Is traditional teaching really all that bad?” without considering how their methodology might misinterpret the data. I already discussed the problem with associating teacher reporting with using observable data. I am also concerned that they combined, “working on problems with the teacher’s guidance and working on problems without guidance” into the single problem-solving category.

Watch this lesson of a U.S. classroom where students are "working on problems with the teacher’s guidance" (from the original 1995 TIMSS research) and decide for yourself whether this teacher “drunk deep from the progressive pedagogical well.” (You will need to sign up for a password but it is free.) My answer is, “No,” but this would be categorized as problem-solving time in the Schwerdt and Wuppermann study.

“Is traditional teaching really all that bad?” – based on this research, the jury is still out.

Is there a Learning Museum?

Once again, Twitter has inspired me. This morning, I saw the following tweet from the National Math + Science Initiative:

Here's the money quote from the article: 

It also reinforces the emerging concept of “free choice” learning, which holds that people get most of their knowledge about science from someplace other than school or formal education.

What caught my attention was the phrase "free choice" learning. The idea that people take responsibility for their own learning is also found in Cambourne's work. This got me thinking about ways to change schools so that they more closely resemble museums where people learn, which led to this tweet:

The perspective that schools currently serve as "fact factories" comes from Sir Ken Robinson and Seth Godin.

I began to wonder what would be in a Learning Museum (not to be confused with Joe Bower's Museum of Education) and decided that it would have rooms dedicated to these topics:

• What does learning look like?
• How is a learner different than a student?
• When and where has learning occurred?
• Why is learning important?
• What if I want to be a learner?

A google search found a Museum of Learning but no Learning Museum. Therefore, I decided to open a virtual Learning Museum. As curator, I will gather learning artifacts, but I cannot do it without your help. If you have any exhibits related to learning that you might like to share, please include links to them in the comments. I will try to gather them into the different rooms so people can stop by and improve their ability to learn. Again, from the article:

“The holy grail of science museums is not to provide someone all the knowledge they need, but to inspire them, to become a launching point,” said John Falk, an OSU professor of science education and national leader in the free-choice learning movement. 

The Learning Museum is now open. I hope it inspires you. Please visit often.

"What if they come at you with a pointed stick?"

Brain Camborne has spent his career researching learning in natural settings in an effort to "find an educationally relevant theory of learning." This research led to Camborne identifying eight conditions present to support learning. The figure below comes from his book, The Whole Story, and shows how he envisions the conditions working together in a language arts classroom.

Engagement is central to these conditions; "the necessity for engagement underlies the whole plan, guiding and influencing all of the teacher's actions and interactions with the learners." Camborne found that three factors impacted learners' level of engagement (see figure to the right). 

In watching this Monty Python sketch, I was reminded of these factors and how they are too often ignored during instruction. [Sometimes it takes the extreme to become aware of the obvious.]

Why did only four cadets show up for the self-defense class? What might they expect from past lessons? Did they not show up because they felt they did not have the resources (guns, 16-ton weights, or tigers) needed to be successful? Were they uninterested in learning how to defend against assailants wielding fruit (instead of pointed sticks)? Or did they feel unsafe (and rightly so)?

More importantly, how do we unsure that our lessons address potential, purpose, and protection?