'Memorization Often Comes Without Understanding'
(This is the final post in a two-part series. You can see Part One here.)
The new question-of-the-week is:
What is the appropriate role of student memorization in teaching and learning?
In Part One, Blake Harvard, Donna L Shrum, Keisha Rembert, and Sarah Cooper contribute their responses. You can listen to a 10-minute conversation I had with Donna, Blake, and Keisha on my BAM! Radio Show. You can also find a list of, and links to, previous shows here.
Today, Jason Batterson, Eric Jensen, and Carla Marschall finish up the series.
I published a post this past weekend sharing advice for how teachers might want to begin their distance/hybrid teaching year.
That post was just a "taste" of what is to come beginning on Aug. 1. You can expect to see at least 25 posts (and probably a lot more) in this column over the next two months answering many of the critical questions educators are asking themselves and others as we enter a potentially crazy year. And the responses will be coming from educators who have reflected on their own experiences of last spring, as well as what will have happened during the first few weeks of school this year.
But, first, here's Part Two on memorization...
Math and memorization
Jason Batterson is the creator and lead author of the Beast Academy elementary math curriculum at Art of Problem Solving (AoPS). Before joining AoPS, he taught and coached math in Raleigh,
N.C., coaching multiple team and individual state champions in algebra, geometry, and MATHCOUNTS. His first book, Competition Math for Middle School, has become a primary resource for introducing students across the nation to competition-level mathematics.
I can only speak to mathematics education, but I suspect many of the principles below apply to all areas of teaching and learning.
Students have a much easier time remembering things that they understand. Unfortunately, memorization often comes without understanding. For example, there are dozens of area formulas that students try to memorize by reading them from a list over and over again. They commit these formulas to memory for just long enough to pass the test, then move on to whatever they need to memorize next. These students are doomed to repeat the process a year later when the topic comes up again. On the other hand, students who can relate all of these formulas to just a few well-understood facts and principles have very little to memorize and can apply what they know moving forward.
Most students know how to find the area of a rectangle. If they can relate it to areas of other shapes like parallelograms, triangles, and trapezoids, they can often discover these area formulas on their own. Even better, if they can't remember a formula for a particular shape, they can usually find its area by dividing it into pieces they understand. Building upon a solid foundation, students can move on to more complex shapes, even ones that are three-dimensional.
Formulas are not the only things students memorize at their peril. For many, math is learned as a series of steps to be memorized and repeated, over and over. You may remember learning a process like the one below for converting a mixed number into a fraction.
Students can perform these steps repeatedly without ever knowing why they work, and they can only apply them to a very specific type of problem. It's much better for students to think through the conversion using what they know about fractions.
Notice that these steps require the same computations as before, but they give meaning to the steps. We multiply 4×5 because we want to convert 4 into 20 fifths. We add the 2 fifths we already had to get 20+2=22 fifths. Students who understand fractions this way are likely to discover the traditional algorithm on their own, and it's much easier to remember something you've discovered.
Memorization, particularly when it comes to formulas and algorithms, is almost always unnecessary for the student who thoroughly understands a few basic concepts. These students can then apply what they know to a broad range of problems and situations.
Understanding One Key Exception:
There is one area where memorization is absolutely critical. As an 8th grade classroom teacher, there was one very accurate predictor of success that I used in my classroom every year: a timed multiplication-facts quiz. Students who struggle with multiplication facts are at an incredible disadvantage when it comes to virtually every skill taught in an 8th grade classroom.
Consider fractions. Why are fractions so difficult for so many students? For one thing, it's virtually impossible to do anything with fractions if you don't know your multiplication facts. Multiplying fractions is difficult for obvious reasons. Converting a mixed number to a fraction also requires multiplication. Adding two fractions with unlike denominators requires finding a common denominator, which is really frustrating if you don't know your multiplication facts. Simplifying a fraction like 45/63? If you don't know your multiplication facts, you don't even notice that 45 and 63 are both divisible by 9.
If you're a math nerd reading this who is still unconvinced, try a simple computation with fractions in any base other than 10. (For example, try simplifying 13/22 in base-5 without converting to base-10.) It's really, really hard to wrap your mind around and gives a glimpse into the mind of a frustrated student who doesn't know their times tables.
So, there is at least one area of mathematics where memorization is really important. But for the most part, math students should be doing very little memorization.
"The role of memory is critical!"
Eric Jensen is a former teacher who grew up in San Diego. With a Ph.D. in human development, he synthesizes brain research and is listed among the top 30 educators in the world at Global Gurus.org. He's written over 30 books and co-founded an academic-enrichment program, held in 14 countries with over 70,000 graduates:
I have asked large groups of teachers, nationwide, over the last 10 years: "What are the biggest things that annoy you?" In the top three (their order changes) are consistently discipline issues, re-teaching, and getting kids to grade level. Many experienced teachers and trainers would tell you that all three are actually related.
How? They all three are common issues for teachers who come from the framework of: "I taught them, they just are not getting it." Or, "Our content is what kids need to get." I am sorry to say, they are wrong.
The short answer to the question at the top (in bold) is, "The role of memory is critical!"
I have written about, taught, and continue to teach teachers memory tools. They belong in our schools because of three things:
1) Memory is the residue (and evidence of) learning. Learning is the residue (and evidence of) teaching. What you teach is irrelevant; what students can show evidence of (memory) is everything. My question is, "How soon can you take ownership over the problem and start helping students perform better?"
2) Memory skills are part of a cluster of "Learn to Learn Skills." Those skills include (among others), summarizing, retrieving, and critical reading. If you do not teach students memory skills, and reinforce what has been learned, why are you teaching anything? Effect sizes of memory are over the top! My question is, "How will students learn these skills unless you teach them?"
3) Memory can help students get to grade level. Kids who grow up in poverty (51 percent of those in public schools) underperform in five critical areas. Language is first, and the next two are both memory skills (long-term and working memory). Clear evidence shows chronic stress impairs declarative-memory formation. The question is, "How badly do you want your students to reach grade level or above?"
Yes, I am an absolute believer (and I say this in my books) that memory skills (short term, working memory, and long term) are ALL critical to teach. Anyone who thinks memory is unimportant should spend some time with a patient who has Alzheimer's disease.
Memory must be integrated
Carla Marschall is experienced in P-12 curriculum development and implementation, having worked in a variety of curriculum leadership roles in international schools in Switzerland, Germany, and Hong Kong over the past 10 years. She currently works as the head of curriculum development and research at United World College of South East Asia in Singapore. She is co-author of the book Concept-Based Inquiry in Action (Corwin, 2018):
Recall, repetition, and drill. Flash cards, cramming, and regurgitating facts. These are words and images that come to mind when we think about memorization in the classroom. However, when memorization occurs meaningfully, when memorization goes hand in hand with the development of student understanding, it is a powerful tool for empowering students. It all comes down to how the memorization of content connects to the larger aims of our teaching and learning. Do we want to create critical thinkers who can articulate their own ideas and transfer these to new contexts? Do we want our students to "connect the dots" and see patterns within and across subjects? If so, memorization must be integrated purposefully into student learning experiences.
When we think about memorization, we often view it as an isolated activity. Learning vocabulary in a foreign language by heart, recalling formulae in mathematics. These discrete activities seem disconnected from the "big ideas" we want students to understand. But we know from cognitive science that the rote learning of facts is actually a less effective way to encode and store information in our memory. It's like trying to catch a fish with our bare hands. When we try to memorize facts with no context, the working memory goes into overdrive, and information consequently slips through its metaphorical fingers.
Information in the brain is organized conceptually: Our mental schemas categorize and structure ideas and relationships between them so we can access them easily. This means that we store individual facts under larger conceptual headers in the brain. We may, for instance, place the idea of a giraffe under "Animals" and the notion of a bridge under "Structures." By organizing our teaching around conceptual understandings, statements of conceptual relationship that transfer, we make content "stick" and become meaningful in the process. This strengthens our students' mental schemas, allowing them to see ways to apply their learning. What strategies can we implement to make students' memorization meaningful in this way?
Be Strategic About Content
We need to ask ourselves: "Why do students need to memorize this particular content?" By starting from what we want students to understand, we can identify essential content. This enables us to scaffold students' thinking from the factual to conceptual level, making it transferable to new contexts. Then, students can use memorized content in more complex ways throughout a unit of learning, for instance through projects or performance tasks.
Make Use of Retrieval Practice to Strengthen Student Ideas
Through retrieval practice, learning strategies that ask students to recall information, the memory is strengthened, and forgetting information is less likely to occur. By strategically using testing, spacing, and interleaving, we support the development of student understanding. The research on retrieval practice is clear: These learning strategies aren't just about memorization for memorization's sake. When students develop mastery of classroom content, they can use information flexibly, see connections, and articulate "big ideas." Likewise, using retrieval practice as a learning strategy allows us to locate knowledge gaps that may hinder the development of conceptual understanding.
Ask Students to Use Factual Content as Evidence for Ideas
When we ask students to use factual content as evidence for their ideas, we give the task of memorizing an authentic purpose. Through class discussions, collaborative learning opportunities, and assessment tasks, we can require students to "back up" their thinking using information they have memorized. By asking students to provide factual content as proof for their ideas, we reduce the likelihood of students overgeneralizing or forming misconceptions.
Memorization that is contextualized and meaningful is therefore crucial to developing student understanding. By analyzing the purpose of the recall activities we give our students, we can make choices about what learning may be superfluous, disjointed. or irrelevant. By organizing our teaching and learning experiences around transferable understandings, we can help our students make connections and engage in deep learning.
Thanks to Eric, Jason, and Carla for their contributions!
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Education Week has published a collection of posts from this blog, along with new material, in an e-book form. It's titled Classroom Management Q&As: Expert Strategies for Teaching.
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