Category Archives: Research

Interleaving and spacing practice

How might we help students with learning and remembering without giving them 30 of the same math exercises each night? 

This is a question that I had pondered for a while.  I really enjoy reading about cognition, so in addition to my cognition book for grad school, I was also reading “Why Don’t Students Like School?” by Daniel Willingham (@DTWillingham) and “Make It Stick” by Peter C. Brown, Henry L. Roediger III, and Mark A. McDaniel.  The topics of interleaving and spacing practice kept coming up.  While it is more difficult for learners, it helps increase the “stickiness” of what they are learning.  Willingham states, “But something else does protect against forgetting: continued practice” (p. 117).

Interleaving is the opposite of how most math teachers assign practice work.  Typically, math teachers assign massed practice – students work out examples that are all on the same topic.  Interleaving is mixing up the topics. This is much harder and slower for learners initially.  From Make It Stick, “…research shows unequivocally that mastery and long-term retention are much better if you interleave practice than if you mass it” (p. 50).

Spacing is what it sounds like, spreading out practice instead of cramming.  If you will study for 3 hours, it’s better to space out that 3 hours instead of doing it all at once the night before a test.  You will forget less and remember longer by spacing.  More from Willingham, “If, on the other hand, you study in several sessions with delays between them, you may not do quite as well on the immediate test but, unlike the crammer, you’ll remember the material longer of the test” (p. 119).  Spacing is for the long term.  As a teacher, I want my students to remember for the long term.  The math they are doing in my class will continue to be built upon in future coursework.

Catalyst for change

Even with reading about this in 3 different books, I still hadn’t made any changes to the practice work I assigned to my students.  Then in November 2014 I attended the NCSM Regional Conference in Richmond, VA and heard Steve Leinwand (@steve_leinwand) speak for the first time.  (If you’ve never heard him live, I highly recommend rectifying that situation!)  Steve also spoke about spacing, interleaving, and giving students no more than 8 practice problems per night.  That was it, I was sold.  I couldn’t escape that I was being directed to change my assignments.  I try to have one major takeaway from any conference that I implement immediately – changing how I did practice was done my first day back at school after the conference.  I told students what I was doing and why.

Here is how it looks (typically) in my classroom.

New Unit:

Day 1 – 8 problems – 4 are low-level on the new material, 2 are medium-level on review material, 2 are high-level on review material

Day 2 – 8 problems – 4 are low-level on the new material, 2 are medium-level on Day 1 material, 2 are high-level on review material

Day 3 – 8 problems – 4 are low-level on the new material, 2 are medium-level on Day 2 material, 2 are high-level on Day 1 material

This pattern repeats throughout the unit.  It cuts down on end of unit review time because we’ve been reviewing all unit long.  Additionally, we use ALEKS & I would assign some exercises on ALEKS that were review.  I could see details of each student with each topic and use the weak topics as our warm up the next day in class.  New this year: our math team has agreed to have all unit tests include some amount of material from previous units.  We are hoping this shows students the importance of remembering what they’ve learned.

If you want to read more on this, I recommend the 3 books listed at the top of this blog post.  In addition, read anything and everything by the incomparable Henri Picciotto (@hpicciotto). He has an excellent post on how he lags practice.  I haven’t done lagging that way, yet!  Finally, you may want to check out the #eduread thread on Twitter.  A conversation I had there last week inspired this blog post!

#EdCampATL session on Hattie

Here are the links to Hattie resources I’m using today:

The Keynote I was planning to use! ha!

1. “Quiz” on what has the highest effect size:

2. Answers to the “quiz” (don’t peek! take the quiz in #1 before you check your answers!):

3. Full list of Hattie Effect Sizes:

Links to books I mentioned:

Hattie’s “Visible Learning”

Hattie’s “Visible Learning for Teachers”

Hattie’s “Visible Learning & the Science of How we Learn”  <—-haven’t read this one yet

Daniel Willingham’s “Why Don’t Students Like School”



Teaching Methods & How Students Learn – my educational views

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!