http://scopeblog.stanford.edu/2015/02/03/math-and-the-brain-memorization-is-overrated-says-education-expert/
http://www.youcubed.org/wp-content/uploads/2015/03/FluencyWithoutFear-Jan-28-2015.pdf
These are some questions to guide the discussion:
1. What are your thoughts about this research?
2. Do you require students to memorize anything in your class?
3. Do you see any advantages or disadvantages in your classroom of students memorizing facts?
4. What is your opinion of timed tests and do you use them?
5. Do you see students freeze up when taking timed tests or tests where they are required to memorize facts ?
I find it interesting that, according to the Ford article, both lower and higher performing math students’ brain activity is only different with regard to the hippocampus—the memory center. The fact that students show no difference in analytical ability is vexing. This seems to be a strong evidence of a well-worn idea, that rote memorization is not the best method by which to teach mathematics.
ReplyDeleteFor my part, I do think other subjects include memorization similar to the tactics used by math teachers. In an ELA class for instance, students may be asked to memorize and regurgitate the meaning of a word on a vocabulary quiz. I saw this a lot at DSHS in the Fall. Most of them would write the dictionary definition verbatim, illustrating in my eyes that they had no real concept of the meaning of the word, but had simply memorized the sentences corresponding to it in their class dictionary. I think this is similar to how math students are described in the Boaler paper, as not understanding the fundamental concepts or having “math sense” but only memorizing times tables. I always remember vocabulary terms being quite important in the sciences as well. However, I can see that, while the type of memorization is similar, the content holds different value depending on the subject. In math, students are asked to memorize number sets, times tables, and formulas that form the foundation of the entire discipline, whereas vocabulary terms in ELA are merely rudimentary and often are not attributed as much academic weight.
I don’t know that memorization is detrimental; or rather it wasn’t for me. I can remember many important facts and dates from my Social Studies classes and I think I understand the concepts and history behind them and I did little more in those classes than listen, take notes and then commit the information to memory. It seems that some of the issue depends on the individual.
As far as timed tests, I have not personally administered a timed test, save for the idea that a test must be completed within the given class time, e.g. 55 minutes. There was much anxiety about the PARCC tests prior to the students taking them. They were very vocal about their fear of not finishing on time. I didn’t have the opportunity to see their scores so I don’t know how they did or if they froze up but prior to the test, most seemed worried. I think what administering a timed test does, more than anything else, is create an incredible amount of undue pressure in the student that does little more than increase the difficulty of their performance on said test. Additionally, I don’t know if I can see a point to timing a test. It’s a test. They’re usually pretty comprehensive, long. Why not give the students the whole period with which to finish. There would be less pressure on the student, less anxiety and therefore better scores.
Jonathan, thank you for sharing your point of view and relating this to English. I am curious if whether any students incorporated their new vocabulary words in their writing? Or was it a "memorize, regurgitate, and forget" cycle? Also, if you have to teach vocabulary, what do you think you would do differently to help ensure the students are understanding rather than memorizing?
DeleteJonathan, I find with standardized tests its such a balance. At our school this year we downplayed testing a lot to keep students from stressing (which it sounds like was an issue for your students). But I think we downplayed it too much, to the point that we came across students who were bubbling in without reading questions just to get done quickly. We also had an issue with students falling asleep during the test. I struggle with that balance in my own classroom, yes I want you to study your spelling words, but I also don't want to trigger a meltdown if you don't get them all right.
DeleteI agree with Jonathan in the sense that I see memorization in the ELA classroom when it comes to vocabulary. In fact, I still remember many of my vocabulary words from high school and when I see that word I will remark that it was a vocabulary word. Did I only memorize those words or did learning actually happen since I still remember them years later. So I agree that memorization may not be detrimental to learning, but it may not be the best approach.
DeleteJonathan,
DeleteI am in complete agreement with your opinion about timing tests. The students are under so much anxiety to FINISH that they cannot take their time to show what they actually know. Anxiety, as we have learned is not good for the brain. I feel that testing corporations use the act of timing the tests to standardize them across the board so that no students have an advantage. Unfortunately, this does not help our students demonstrate knowledge.
-Jamie Hipp
Memorization in math is a topic I have given a ton of thought to. I can remember being taught very procedural based processes to solve math problems throughout middle and high school. My teachers would give us a process, work some problems using the process, and then I would work the practice problems exactly the same way. I didn’t even have to figure out the process for myself, it was just given to me. If I memorized the steps, I would make an A on the test. As for word problems, whatever word problems we worked together in class were the problems used on the test. This is not math! Math is about exploration, problem solving and looking for patterns, or discrepancies in a pattern. Asking students to memorize a formula and work 50 of the same problems, in my opinion, is not a good way to teach math. I feel that, currently, scores on math tests show which students successfully memorized formulas and plugged in numbers versus those who did not. Based on these scores, students label themselves “bad at math” before they have ever had an opportunity to succeed at real mathematics. I think it is really interesting that the only difference seen in the MRIs studied in Dr. Boaler’s research was in the hippocampus. We aren’t giving our students a tool that they can use to solve problems in real life; we are asking them to memorize math facts in order to succeed in school.
ReplyDeleteBut is there ever a place for memorization in mathematics? I think that before any memorization occurs, students should conceptually understand the material so that if memorization does occur it will have a connection to some bigger picture in the brain. For example, before students memorize multiplication facts, I think that they should understand what multiplication is. Let’s say we are multiplying 3 x 2. It is really easy to give our students a multiplication table and point out to them that 3 x 2 = 6 and then ask them to memorize the table. But do they understand why multiplication could be useful in the real world? Students need to understand that 3 x 2 could mean 3 groups of 2 objects each – it would be great to arrange some of the students into 3 groups each with 2 students per group. The students could then count the total and see that the answer is 6. What about 2 x 3? Rearrange the students into 2 groups with 3 students each and they see that the answer is also 6! Simple tasks like this help the students do more than memorize facts, we can help them create a math toolbox to use forever in the real world! I think that once the students have a solid conceptual understanding of material, it is then sometimes necessary to memorize certain facts. It becomes absolutely necessary for students to quickly call on multiplication facts in algebra. If they haven’t memorized these facts, they end up spending more time on the basic skills and less time on the algebraic content.
I think that sometimes timed tests/activities are necessary. If classes are 90 minutes long, but the students are taking a test that you designed to only take 45 minutes, then I think it is necessary to only spend 45 minutes. If the majority of the students don't seem to be completing the assignment in the time allotted, then it could be necessary to give additional time. Often when only one or two students are taking an exceptionally long time to complete an assignment, they tell me that "they can't remember" a certain piece of information. They aren't writing anything down or trying to work through the problem. This, to me, gives more insight into the memorization of math issue. If students memorize information in order to pass a test, they can easily forget that information and panic during a test.
I thought it was interesting when Dr. Boaler said memorization in mathematics can be detrimental to student learning, but I also agree with you that memorization has its place, BUT with understanding prior to memorizing. It is so interesting that you said students label themselves as being bad at math because they don't perform well on memorization tasks or skills tasks. Some students perform really well in math up until high school. I wonder if one reason students struggle in high school math classes more so than in middle school math classes is because for the first time, the content is putting all of your memorized facts together that you learned throughout elementary and middle school and applying them to a bigger, more conceptual picture. Food for thought. (I noticed many of the 8th graders taking Algebra 1 where I student taught said this was the first time in their lives they didn't "get" the material right away)
DeleteAmy, you are right! Without a conceptual understanding of mathematics what good is it to be able to recall a math fact quickly? If a student does not understand how to apply the information, it was never learned in the first place. It was only remembered. This will not help students in the long run because they will not be able to connect information they cannot apply inside, or outside of the classroom.
DeleteI do require some memorization in my 1st grade class. As a 1st grade teacher we provide so much of the foundation in math and reading that I find it is important to have students practice some skills as memorization. While 90% of my classroom is hands-on experiential, I do test their sight words weekly and have them study their words at home. Every student moves through the levels at their own pace, but I do flip flash cards and have them recite those words. Now they are seeing these words during reading, writing etc. but I think it’s important to know those words quickly because when they’re reading they can’t sound out every word. Plus, it helps me know which students are moving through their words at a reasonable pace, and who’s been working on the same words for a month. And that’s where I get stuck with this argument against memorization, of at least some things; students only have so much working memory. So when they are reading I do want them to know their sight words and know them quickly. They can’t sound out every single word or they’ll start to lose comprehension. And to be honest, they like their weekly sight word tests. I’m not insanely strict; I usually give them two tries to get a word right. Then when they pass a level they color in that level on their tracker. About 90% of my students pass each week. There are some students who do get upset when they don’t pass, but I let them be upset, then I help them make a plan to work on those words by letting them make their own flash cards or letting them practice their words in a reading center. I feel that it teaches them that they do have control over their learning.
ReplyDeleteWith math I don’t require memorization, but the school does require weekly fluency drills. Students are given a minute and a half to complete 20/25 math facts. They get more challenging as the levels progress. This to me is developmentally inappropriate (7 years olds need to finish things and like things to be done “correctly”) so to ease the stress I don’t grade it and it doesn’t count against them. I also let them practice fluency drills in a math center. We also do the drill 3 times a week and so they get used to it. I just call it practice and let them color in their data tracker at the end of the month to track their progress. I find that if I don’t make it a big deal, they do okay with it. Some students even like the challenge!
Overall, with timed tests I think it’s about how much pressure you make it out to be. If you need it to be timed for the sake of time (ie. We can’t spend 30 minutes a day practicing this, but 2 minutes a day is perfect) than ok. However, MOST of your teaching should NOT be memorizing facts. I think if we keep it light and fun students can be inspired by the competition with themselves.
I absolutely love how you have the students track their own progress and how you have students move at their own pace rather than forcing them to do something they aren't ready for. I think that really could make the timed drills beneficial to the students because they are essentially competing against themselves and their only goal is to improve upon their learning (and of course color in their data tracker for fun!). But it is only beneficial if they understand the meaning behind the math facts :) That is really sad that 7 year olds have to take timed fluency drills, that is a lot of pressure for them and for you! I think you handle the situation very well.
DeleteYou said that you give sight word tests, do you also give spelling tests? Or is that not until higher grades? (Sorry! I do not know my elementary school standards).
Katy, I do agree that small children need to memorize sight words. These words cannot always be decoded easily, so it is needed. Although I do not like to stress memorization of math facts, I love that you include math fact fluency in your math center. That is a great idea. That seems like a great way to take away some of the stress and pressure.
DeleteAfter reading Katy's post I had a thought. Sometimes I think memorization in the classroom could be more for the teacher than it is for the student. It is used to reassure the teacher that she is teaching or to check for understanding in students. In correlation with test scores, I think that some teachers may even encourage memorization because of pressure on herself. She wants her students scores to be good and therefore it may not matter if the information sticks beyond the test. This is just a thought. There could be pressure on both teachers and students for memorization and testing.
DeleteShelli, very good point. Unfortunately that could be the thought in some teachers minds, and possibly even students. They start picking up on "if I memorize and regurgitate I'll Ace my tests, I don't actually have to understand..." I think this is one reason why it is important to encourage higher order thinking and incorporate higher order thinking type questions and activities in class. It is amazing to watch and hear students develop their thoughts and watch them make connections, I think the key is allowing them the opportunity (meaning not succumbing to memorization tasks all the time)
DeleteThis is an interesting point about sight words. This year we started using a new word study program, Fundations, which distinguishes between high frequency words and trick words. Trick words are those words that are "sight words" that a student cannot decode based on spelling patterns. They learn decodable, high frequency words separately. I think it defines a good balance and limits the number of words they are memorizing. Also, when they learn a decodable, high frequency word students are able to apply this pattern to additional words.
DeleteWhat about the discussion we had earlier in the semester about the importance of some memory work to "stretch" the working memory? the need for firing often in order to wire? In other words, over exposure to sight words would allow for lots of fire, so that there is wiring, right?
DeleteYep... spelling tests too... but I LOVE our curriculum and they are super prepared and therefore do well on them. The first few were pretty rough though. Lots of tears. I used to give the option to take it during our time or take it at recess outside on the bench with me... a few chose recess. I think they felt more relaxed.... I hated it at first, but once again, it gives me a REALLY good idea of who's moving and who's not. In 1st grade they "collaborate" (give each other answers in the name of helping, which I dont want to discourage) so often, some of the clever students may sneak by. The only thing I fear more than inappropriate tests is suddenly finding out at midyear testing that they're super behind and I didnt know. So between reading small group,s fluency testing, sight word testing, fluency drills, and teacher led math centers I feel like I generally have a good pulse on where they are.
ReplyDeleteI had one student who had bad math test anxiety. He would see the whole test and flip out... I realized that if I cut up his test and gave it to him one question at a time it helped. I hate that we do this so young... but part of me wants to prepare them for this now rather than being steam rolled in 3rd grade by LEAP or PARCC.
ReplyDeleteI agree, but as unfortunate and scary as it might be for them, standardized tests aren't going anywhere anytime soon, so might as well get them prepared and help them stay calm and confident in their abilities :)
DeleteI enjoyed the readings this week. I thought it was interesting that Ford stated the working memory of high-achieving students and females are mostly effected by timed tests. She also mentioned “the core of mathematics is reasoning”. This was interesting because educators seem to always stress the importance of memorizing math facts. This hits close to home with me. I was never able to recall multiplication facts quickly as a child, but if I was allowed time to think about the problem, and draw it out, I was able to come up with the correct answer. I have kept that with me throughout my teaching. I do work on math fact fluency with my students, but I do not take timed tests as a grade. I do not want my students to have a negative view when approaching mathematical problems. I want them to embrace math and see that all of the pressure of memorization is not needed to be successful in math. I am more worried about my students being able to explain their thinking and get the correct answer. I feel that I have not been successful, as a teacher, when I ask a student to explain how they came up with an answer and they tell me they do not know. Engaging the students, mentally, allows the students an opportunity to think critically and discover their own ways of understanding concepts. If my students can show me their thought process and come up with the correct answer, I feel my students have actually learned something. It also allows the students to become active learners because they are in control of their learning. Although I do not like using memorization techniques, there is an advantage in the fact that it could take less time to solve math problems. Still, I would rather a full understanding of the concept than just the correct answer. Memorization and timed tests do not allow much room for connection of subject matter to real-life situations. It was also stated in the Ford article that the working memory shuts down under stress. I have seen where timed tests stress students out. How is that beneficial or stimulating to the adolescent brain? If the students cannot take the information learned in the classroom and apply it to other aspects of their life, it may not be the best way to teach.
ReplyDeleteI am so glad you found the readings relevant. I think this is a topic that hits home with everyone, no matter what subject or grade is being taught. You said "I feel that I have not been successful, as a teacher, when I ask a student to explain how they came up with an answer and they tell me they do not know." Do you think the students don't comprehend what or why they did something or do you think they have trouble putting it into words? Or a little bit of both? I have found that in middle and high school math there is a consistent problem that students don't know their math vocabulary so they have trouble explaining what they did. Or they mix up their vocabulary and I know what they are trying to say, however it is incorrect.
DeleteSometimes I think it could be both. I also feel students are lacking when it comes to math vocabulary. When I taught third grade, I would try and implement math vocabulary weekly. I would introduce a new term each week, during calendar math. We would take a few minutes each day working with the weekly word. Each student had to create their own math vocabulary dictionary. they could create pictures, word problems, etc. to help them to grasp the meanings of each word. I feel that this was extremely helpful. Creating the dictionaries gave my students a reference guide that they were able to understand, which made them more confident in their work.
DeleteAshley,
DeleteYou are clearly a wonderful teacher, as you encourage students to transfer the information (Zull) and make it their own. I know that if I was a student in your class, I would remember what I had learned long after leaving your classroom, as I had to truly understand the concepts to utilize them in creative ways.
-Jamie Hipp
I think it's awesome that you ask your students to show their thought process and their strategy for attempting math problems. So often, I feel that students get to high school math courses and they have never been asked to show their thought process or give a detailed explanation of how to solve a problem. It becomes increasingly harder for them to build these skills while learning even more complex math content. Like Meredith, I have found that there is definitely a math vocabulary issue. The students use the incorrect vocabulary, but they don't think it's a big deal when they use the vocabulary incorrectly. For some reason they think it is all interchangeable and it is a huge problem.
DeleteThe CCSS place a large emphasis on students providing evidence for their answers and to explain their thinking. This is very challenging! I think it's important for students to be able to make mistakes though, and often when students are asked to explain an incorrect response they realize right away why it was wrong. Zadina talks a bit about the importance of metacognition in teaching, and I think Ashley's teaching strategies align well to this!
DeleteI’m almost certain I have referred to this story in a prior blog post, but I will post again. My parents had a sticker chart on the wall of the kitchen when I was in the second grade. The goal was full 1x1 up to 12x12 rapid fire times table fluency. The sticker chart tracked my progress and the extrinsic reward was a trip to Disney World (that my parents were already planning) when all stickers were present. Once I memorized these facts, math became considerably easier, since my fluency was instantaneous. In reading these resources, it is clear that rote memorization may not be the best mathematical strategy for every child, but I do see the benefits of memorization across the curriculum.
ReplyDeleteSome students may fear memorization. I think it is important that students are explicitly taught this strategy but that it is not a requirement in any classroom. EngageNY Math encourages multiple strategies to solve any problem, increasing student ownership, choice, and teaching of useful strategies that might make sense to multiple students. If an educator teaches five strategies for solving a problem, they will be sure to teach at least one that appeals/makes sense to each student in class.
I can easily think of five things off the top of my head that I have memorized in my educational career:
1. The preamble of the US Constitution
2. The 50 states song
3. The planets
4. The Periodic Table
5. The Gettysburg Address
Additionally, like all people, I have memorized numerous addressed, phone numbers, social security/ID numbers, etc. Memorizing this information has aided in quick and complete recall. Mostly, however, I have memorized scripts for theatrical performances, and I require this of even my youngest students (1st grade). Every performance script that we rehearse to performance is tied to CCSS and/or state benchmarks/standards. One advantage is that, in a script, information is presented in the form of a story, which, as Zadina explained, is easier to remember. Another advantage of memorization is decreased cognitive load. When my students' fluency is instant after memorizing, it frees their working memory. I find that this leads to increased creativity. The only disadvantage that I see with student memorization is that this strategy is not very suitable for instructional time. Few teachers can truly devote the time necessary for students to fully memorize anything. Students must complete most of their memorization outside of the classroom.
In my classroom, I do utilize timed assessments, since most of my assessments are performance-based, participation, or oral presentation. I will use timed transitions with a stopwatch or timer, and ask students to self-assess at the end of the 30 seconds/1 minute to see if they were successful or unsuccessful. As my students are extremely competitive, they thrive on anything timed. After a few months, they also recognize memorization as one of the first steps to any rehearsal process, and will often share that information in a current class is information they already memorized in a script in Talented Drama class!
-Jamie Hipp
I thought that the findings in the research were very interesting but I don’t know if asking our students to memorize information is hindering them as much as we think. I do agree that in certain subjects memorizing dates and names may not be particularly necessary. In the subject of math I do think that memorization of addition and subtraction facts are necessary. They are the core tools needed to progress to harder mathematical operations. In my classroom now I am working with one of my students to memorize sums of ten. Many of the things that are taught to my students are to help them survive in the adult world, such as social skills, basic reading, writing and math skills. The content they are taught directly correlates to the goals set in their IEP’s. My intent is not to hinder them by making them memorize basic addition and subtraction skills, but knowing the possible breakdowns of a ten-dollar bill is a necessary skill for future interactions.
ReplyDeleteIn contrast, in previous years when I was teaching a full class of students I mainly focused on them understanding the content and finding different ways to get the answer. The curriculum that we were required to teach, specifically math, social studies and science, asked students to memorize specific information. I didn’t agree with the timed test and I still don’t. The short timed quizzes made my already anxious students’ anxiety go through the roof. The more times tests I gave did not help them learn or understand what they didn’t already know and I saw little progress as the year went on. However, their quiz scores did not correlate to the type of work they produced during class time. I saw much more progress in their daily classwork that those quizzes and that meant more to me. I tried to counteract their anxiety with a lot of verbal praising before and after the quizzes and during my lessons.
Morgan W.