Edit 8/29/13: This post was originally titled about my reflections from the NCTM Interactive Institute in DC earlier this month. However, the post ended up not reflecting on the actual sessions at all, but became my treatise on how I view education. Therefore, I changed the name of the post. The content below is the same.
This was my second NCTM event, my first being the national convention back in April. I must say, the one thing that made this better is not arriving in a snow storm! However, I missed Desmos, Mathalicious, & math trivia. This blog post will start with my reflections on the theme of the conference and then I will give highlights of the sessions I attended.
As I left the conference yesterday, I had lots of thoughts swirling about. Cathy Seeley closed with a recap of the 2.5 days plus some added commentary. As I sat there, I wondered if others felt as inadequate, and maybe even confused, as I did.
The focus of the Institute was the CCSS Standards for Mathematical Practices. We spent a lot of time on rich tasks. Excellent tasks, some that would be too far over the head of my students, but excellent tasks nonetheless. Here is my struggle. Are they saying that every single thing we teach should be done through a rich task? I know that we “cover” too much in one year in American mathematics. I know that deeper is better than broader. I also know if I teach everything through tasks, we won’t even get close to what needs to be accomplished in a year. Things I’m held accountable for. I should also add that I tend to be a cognitivist in my educational thinking more than a behaviorist or constructivist. I believe all 3 are needed in education, but those are my leanings.
The other struggle I’m having relates to various analyses of research that I’ve read (or am in the process of reading):
Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching by Kirschner, Sweller, and Clark (I’ll call it KSC below)
Visible Learning, a Synthesis of over 800 Meta-Analyses Relating to Research by John Hattie
Visible Learning for Teachers by John Hattie
For example, my reading of the analysis by KSC leads me to believe that below-level and on-level students benefit most from direct instruction before discovery activities. In addition, that really only the honors/AP type students would benefit from discovery before direct instruction, and it appears only minimally. I don’t think anyone would argue we about providing rich tasks for our students. It seems to me that the discussion is WHERE in the sequencing they should occur and should they be the ONLY types of things we ask our students to do. From KSC, these rich tasks should come after some direct instruction, not before, and definitely not the only type of instruction.
In addition, both works by Hattie promote the use of direct instruction. If you don’t have these books and you are a teacher or administrator, you need them. period. Hattie measured effect size on learning of various education related items – contributions from student, home, school, teacher, curricula, and teaching approaches. He says that most anything you do to increase learning will work to some degree, it’s obviously better than nothing. However, some things have a better than average rate of increasing student learning. He found the average effect size to be 0.40. Therefore, if you want greater than average learning for your students, seek to implement the items greater than 0.40. He also doesn’t say not to do anything lower than 0.40, but those shouldn’t be the only things you do.
Direct instruction has an effect size of 0.59. Yeah, you read that correctly. This thing that gets railed against all the time has a proven effect size – kids learn from it. In Appendix B of the first of his books I mentioned above, it is listed as #26 out of 138 items. It’s effect size of 0.59 is tied with Cooperative vs. Individualistic Learning and Study Skills. Group work is constantly encouraged, but direct instruction tends to get represented as bad. Inquiry-based teaching has an effect size of 0.33, lower than average. Now it’s not bad, it’s just not as high as direct instruction.
Problem-based learning has an effect size of 0.15. From Visible Learning, pg. 211:
“As will be seen, this is a topic where it is important to separate the effects on surface and deep knowledge and understanding. For surface knowledge, problem-based learning can have limited and even negative effects, whereas for deeper learning, when students already have the surface level knowledge, problem-based learning can have positive effects. This should not be surprising, as problem-based learning places more emphasis on meaning and understanding than on reproduction, acquisition, or surface level knowledge.”
Again, it appears to me, that some type of direct instruction for surface learning should come before rich tasks and problem-based learning.
So, when I attend something like NCTM’s Interactive Institutes or read awesome math blogs & tweets, I’m left wondering if I’m doing it all wrong. I keep hearing and being told that effective math instruction needs to be inquiry and problem based, that direct instruction is bad, and heaven forbid if you give your students a worksheet (though appropriately titled as a graphic organizer). Then I come back to what I’ve read in these meta-analyses of research and wonder why no one seems to talk about what is being shown. Am I reading bad research? I don’t think so, but maybe I’m wrong. Why can’t we talk in the math world about the benefits of a variety of teaching methods? And let’s be honest, the reality is kids need to just know and memorize some basic math facts and formulas. The high school student who barely has to think about 8 times 7 being 56 is ahead of the student who needs to reason it out or use a calculator. This low-level knowledge & recall will help them apply their higher-order thinking skills to deep problems. When I think of Vygotsky’s ZPD, I don’t think many of my students would be able to do the higher-order stuff without the lower-order stuff at least having been referenced.
I’ve decided that when I attend these types of things or read awesome things on the web, I need to remember “all things in moderation.” Direct Instruction – yes. Rich Tasks – yes. PBL – yes. Basic Memorization – yes. Graphic Organizers/worksheets – yes. Manipulatives/hands-on – yes. Flipped Classroom – yes. SBG -yes. Transdisciplinary Ed. – yes. All of these together (plus more not listed) can create a rich learning experience for a student.
This is long enough, I’ll put my recaps of the sessions in another blog! ha! Any feedback or pushback to my thoughts above is much appreciated!