In this time of distance teaching and learning, the tropes about traditional teaching:bad and progressive teaching: good are flourishing. This article (in the preciously named “The Conversation” no less) is no exception.
Some snippets:
Traditional modes of instruction have emphasized that math is best learned through studying and memorizing alone, with the teacher demonstrating procedures and then checking students’ answers.
This is news to me. I teach in the traditional manner as do many people I work with, and I don’t recall that the emphasis is studying and memorizing alone. Yes there is memorization and yes there is homework. There is also discussion in the classroom and analysis of mistakes which this article assumes does not happen with traditional teachers. The quoted passage even links to an article by Deb Ball, former dean of the ed school at U of Michigan who speaks to the ed-school party line.
Gone are the days of students sitting quietly while the math teacher does all the talking at the chalkboard. Discussion is important in the mathematics classroom.
This one even links to an article published by NCTM called “Sociomathematical Norms, Argumentation and Autonomy in Mathematics” I don’t recall teachers doing all the talking; they did ask questions–quite a bit, as do I. But “teacher talk” as it’s also called is viewed as bad; facilitation is viewed as good. Interesting that the so-called “flipped classrooms” rely on videos which entail someone doing a lot of the hated “teacher talk”. But it’s OK in a video. As long as it doesn’t happen in class, where facilitation and student-centered inquiry-based learning is key.
Traditional math teaching, where the teacher assumes an authoritative role, is a major cause of math anxiety.
Right. Best that teachers take a subservient facilitative role. (See “teacher talk” and other no-no’s.)
This type of thinking is pervasive in ed schools and persists in the edu-establishment. And for those who have fought to instill other ideas, they are met with the jiu-jitsu-like response of “We’re all saying the same things!”
News flash: We’re not.
traditional math 
Reblogged this on Nonpartisan Education Group.
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Breaking: Fake news in academia!
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They all want the music education model where they hope/assume that students are getting private lessons at home or with private instructors. They get to do the engaging musical part at school, which is more like after-school enrichment. However, rarely does any student without years of private lessons ever get into All State choirs, bands, and orchestras. They are the ones with full musical understanding. The music teachers would really have problems if they didn’t have enough students getting private lessons.
Schools with full inclusion are now assuming/expecting that parents and tutors will pick up the slack and do the dirty direct teaching work in all subjects. They don’t mind that it’s done. They just don’t want to do it themselves. They don’t want to have to deal directly with the consequences of increasing the range of student ability and willingness and the issues of social promotion at a very low Common Core proficiency level. In math, this means NO assurance of mastery that comes close to a STEM level in K-6. By the typical math split in 7th grade, it’s all over for many. But many educators still claim to offer more mathematical understanding. Are they really that ignorant to the help we parents now have to give at home?
For our state’s Solo and Ensemble Honors adjudication and honors concert, the 15 best student musicians who do get selected to perform have their private lessons teacher listed in the program, not their school’s music teacher. Music teachers know how this world works and don’t fool themselves. It seems that the other educators who want this model drink the rote Kool Aid.
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You know someone hasn’t the courage of their convictions when they can’t honestly represent the view they hope to discredit.
I wonder what they do with all the old images of traditional classrooms with a student at the board presenting a proof or derivation with the teacher standing over, yardstick in hand? Those images were derogatory too, but at least they admitted that traditional math class involved students presenting work. It’s as old as the hills. One can go right back to Plato demonstrating the method with the simpleton, which was in Q&A format — and NOT memorization; the student was required to think and respond with what he thought. Of course I always thought Plato’s discussion of this was silly because the student obviously did not understand initially, and was let, by questioning to correct reasoning, and then he asserts that the child is “Remembering”. Ah … but not memorizing. Nevertheless, the point is made, that traditional instruction involves, among other things, active reasoning by the student and two-way conversations.
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Hi Barry,
I’m the second author on one of the articles you’ve quoted here. Thank you for taking the time to engage with our work and share your ideas.
In the paper about math anxiety, the author says that all study participants indicated that they learned in traditional classrooms. I’ll leave it to you to read and decide if the indications of “traditional classroom” align with how you are thinking about “traditional math”.
What I take away from reading the paper on math anxiety (that is cited in our writing) is that the role I play, as a teacher, can lead to:
1. Students being scared to ask questions.
2. Students trying to avoid math, leading to lower performance due to lack of practice.
3. Students being afraid to share their solution strategies with peers, or teachers.
4. Students feeling like they’re being ignored when they ask a question.
5. Students being confused if they feel that they’re not given a direct answer.
I try my best to keep this in mind while I’m teaching. I agree that there are issues within math education that we are looking to address and welcome any discourse that sheds light on these important issues. I hope that we can come together to continue to enhance the teaching of math in ways that benefit students, teachers, and parents.
Wishing you all the best,
Cristina
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Thank you for replying. You state: “In the paper about math anxiety, the author says that all study participants indicated that they learned in traditional classrooms.” Why does the author feel that this is important to state? Does the author define what is meant by “traditional classrooms?” The implication I’m taking away is that traditional classrooms cause math anxiety for the reasons you have enumerated.
I teach in what is viewed as “traditional”. I am at the front of the room, students sit in rows, I teach using explicit and direct instruction. This does not mean that I talk for 45 minutes straight. I ask questions, I have them work problems to demonstrate what I’m doing, I give challenge problems. In classes where students are afraid to speak out, I have them work the problem on a white board, or on paper as I come around. If they are correct, I call on that person to give the answer aloud so they are not afraid of making a mistake.
I leave enough time for them to work on homework (yes, I assign homework), and provide assistance during that time. This is so that when they go home they have a leg up on how to do the work rather than going home and saying “I can’t remember how we’re supposed to do these.”
The implication of the article you cite is that in traditional classrooms students tend to suffer math anxiety. Have there been studies of non-traditional classrooms, and the effect on math anxiety? There is also the implication that in bygone days, there was no discussion–the teacher did all the talking. This was not my experience having gone to school in the 50’s and 60’s. My objection is to this very frequent mischaracterization.
I hope this clarifies where I stand.
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Hello everyone,
Thanks for creating this opportunity to discuss mathematics education. I am really excited for these discussions.
I’d like to be clear about some misinterpretations. I think it’s important that we try to understand what we mean when we talk about and extend one another’s ideas.
I am in no way promoting that we should view the teacher as a ‘facilitator’. If you knew me or my work, you would know that ‘facilitator’ is not a word that I use when I talk about the teaching of mathematics. Indeed, the teacher’s role is much more important and complex than how I think about a facilitator. Since you point specifically to research about sociomathematical norms, that body of research describe the teacher’s role as a representative of the mathematical community
I’m not sure what you mean by “teacher talk”…but think that we might be able to agree on some ideas about “telling”. Here’s a nice article that has influenced my work and my own teaching.
Click to access A_time_for_telling.pdf
I do agree that teacher’s can feel that they shouldn’t tell.
It’s a bit unclear to me what you mean by “traditional math”. Either way, maybe you can see some of your ideas in a piece that I wrote where I promote the use of ‘mad-minute’ worksheets.
https://search.proquest.com/openview/c66110c5366a90e71403c45613fc1d8c/1.pdf?pq-origsite=gscholar&cbl=43656
In the end, I think we do better by being open to one another and not taking too many liberties, as we interpret one another (especially, since we don’t really know each other 😉 ).
I think we are all passionate about doing what’s best for students and figuring out what ‘works’. So let’s do it!
Wishing everyone health and safety,
Looking forward to responses.
Tina Rapke
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Tina I’m not sure if this is you but if it is I have to say, I fundamentally disagree with most of what is stated in this article https://www.yorkregion.com/news-story/9912452-7-tips-on-how-to-inspire-kids-to-learn-positively-without-taunting-them-this-long-march-break/ As a parent, I would object to having you teach my child this way, as I’ve seen no evidence about how this approach is effective in comparison to one that involves daily classroom practice, mastery of math facts, and the regular use of the 4 standard algorithms…as a start.
As for your own personal favourite study, that’s great. However I’d like to view education as a profession and, if that is the case, I would also prefer to then rely on empirical data which has been the universal gold standard for over 50 years https://www.tandfonline.com/doi/pdf/10.1207/s15326985ep4102_1?needAccess=true&.
Ever heard of Project Follow Through? As an education professor, I’m sure you are familiar with its conclusions https://www.nifdi.org/what-is-di/project-follow-through. Again then, as a parent, I’m curious as to why you would prefer to cite a study that’s much more obscure, rather than point to the conclusions of single largest educational study EVER CONDUCTED.
I’m fine for these discussions as long as they’re productive. However when it wanders into specific viewpoints, as someone who is responsible for teaching young children and shaping minds, I would prefer to stick with what works, rather than venture out into Never Never Land.
Thanks.
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Hi Tara,
Let’s see if there are a few things we can be productive with. Before I start, I want to say that I am very aware how these discussions can become adversarial in nature. I am trying my best not to take things too personally and focus on how we can be productive together.
In that spirit, I will try to be direct in the choices I’ve made, thoughtful in my response and open to your ideas. It’s hard to be productive when people feel like they are being attacked.
Thank you for directing attention to “Project Follow Through”. I think that there is much to gain through the results of that study. I am looking at how with direct instruction: “Teachers follow carefully constructed scripts that have been designed to maximize learning and minimize confusion through faultless instruction” (I’ve cited this from the Project Follow Through website: https://psych.athabascau.ca/open/engelmann/direct.php).
I feel that this is a place that we might find some in commonality in our ideas. My opinion is that “Good” direct instruction is hard and takes a lot of effort and thoughtfulness!! Based on the study’s findings, it seems like they were able to reasonably produce it and support it. So this is a good thing. I would guess probably learned a lot had to “buy in”). This same kind “structure”/”scaffolding” that attends to kids’ ideas and how to respond to them is seen in this response to the other article you included: https://www.tandfonline.com/doi/abs/10.1080/00461520701263368
This takes us away COVID-19 circumstances and math in the home. I think this is where we should be talking about teacher education and the kinds of questions organizations like WISE can be asking, in addition to the ones already being asked.
Yes, I was interviewed for the news piece: https://www.yorkregion.com/news-story/9912452-7-tips-on-how-to-inspire-kids-to-learn-positively-without-taunting-them-this-long-march-break/
The reporter included 3 tips from me. I would like to hear more about why you fundamentally disagree with those 3 tips and what other tips you might have liked to see. I provided tips based who I think will be implementing them (parents) and the research that I know. These tips aren’t about me teaching people’s kids math….This is about math in a typical home (one that probably doesn’t have a parent with a background like mine 😉 ).
I don’t think it’s reasonable that parents should be expected to enact “good” direct instruction while under the restrictions COVID-19 has evoked. Parents are busy with jobs and may be feeling overwhelmed for several reasons. This just seems to me like a very tall order.
That’s why I suggest mental math. It’s likely something parents are familiar with. Plus there are many recommendations that it should be more emphasized in all grade levels because of the possible gains.
The research on attitude in math ed (that is based on 1, 600 students) can be paired with research on mental math to identify pathways forward.
On a slightly different note and to be positive, I think what we should celebrate is that we have seen some movement/traction on telling and direct instruction in the math ed literature. I see more opportunities if matched with the push towards “fundamental math” (as it’s being called in Ontario).
I’m saddened that you are feeling that I’m wanting to push the discussion into “Never, Never Land”. I always saw myself as someone who was practical and who sees the time I do spend with kids in the classroom very precious and comes with great responsibility. To this end, I think I might be able to learn from our exchanges, so that I don’t come off as something different.
Wishing you health and safety and looking forward to your response.
Tina
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I find it interesting that Tina finds my use of the term “traditional math” to be unclear, given the authors are the ones using the term in the article. To wit: “we often discuss the traditional classroom that those studying to become teachers are familiar with” , “Traditional modes of instruction have emphasized that math is best learned through studying and memorizing alone, with the teacher demonstrating procedures and then checking students’ answers”, “Traditional math teaching, where the teacher assumes an authoritative role, is a major cause of math anxiety”, “If you grew up with traditional math instruction…” and “Gone are the days of students sitting quietly while the math teacher does all the talking at the chalkboard”.
Since you are the ones using the term, maybe you’d like to define it for me, rather than asking me to do so. My point is that your examples of what you consider to be traditional math mischaracterizes it as something that has done harm to students and as such it is inflexible and rigid in its approach. The last quote I provided above is an example of such mischaracterization. I don’t recall teachers doing ALL the talking as I’ve indicated in another comment.
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“It’s a bit unclear to me what you mean by “traditional math” is the standard fallback line that educrats/consultants et al. like to use when they’re being called out for promoting nonsense in the classroom. Another one of my faves is, “but we’re all saying the same thing!”
No we’re not.
If we were, math education wouldn’t be so poor in North America, nor would tutoring rates be spiralling upwards over the past 30 odd years. The bottom line is that kids are kids are kids, and the more we learn about Cognitive Science, the more we understand that what is most lacking in their foundational math skills, is the building blocks which promote meaningful and higher order thinking of mathematics. And the most crucial of these building blocks, is memorizing math facts. And one of the biggest factors concerning rising math anxiety in kids, is a deficit of their math facts. Nowadays, classroom practice and memorization of times tables, and fractional arithmetic are the exception, not the rule. So is long division, even though we already know that these operations are absolutely crucial to a child’s cognitive development for problem solving and basic arithmetic.
We know what works, but continue to blatantly disregard the, ahem, handwriting on the wall, which suggests that the ed wheel does continuously go around and around, but avoiding the basic tenets of explicit math instruction will only continue to do a disservice to our students, and to our teachers.
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Interesting. I have two takeaways.
First, I think the term “traditional teaching” is being used very one-dimensionally. Memorize and study and talk all period? Who has ever done that? I was in school once and I never had that experience in a high school math class. And I was taught by nuns in the 70’s!
Second, and this is my AP Statistics teacher side talking, I am not entirely comfortable with how this data had to have been collected. (Sorry, I will go back and read the article more thoroughly!) I assume the students had been diagnosed with math anxiety. Did they then answer the question about being in a “traditional” math class?
What I wonder about is what they weren’t asked. Were they also asked if they were motivated by grades in general? I teach in a private school where “making grades” is paramount in the student culture.
Sadly, we have many, many students who are able to have good grades be strict transactions in which they don’t have to try too hard. Turn in a half-baked paper in English. Fill in guided notes in history. Learning math is a very different animal. You actually have to learn some math to get the grade you want. It’s tough to do that in a math class.
Seems to me with this whole traditional-versus-constructivist discussion we might be missing the forest for the trees.
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Sigh.
First, I would again add that there is nothing rote about memorizing basic facts, like adds and subtracts to 20 or the times table. You practice and practice and then other ways of understanding and using sink in, like making 10s and how 7*9 is 7*10 – 7. When we did long division by hand, like 5629/27 we had to estimate how many 27s go into 56 and we learned to do 2*27 = 2*20 + 2*7 in our heads. Like duh! Nothing new. Traditional. People forget the learning they went through because it now seems so rote to them. It wasn’t back then.
Second, why aren’t any educators explaining why K-6 is all about fuzzy collaborative learning and high school AP/IB is all about direct teaching. There are no models of successful high school group learning classes. Why is that? Don’t bring up Phillips-Exeter with its Harkness Table, because there is a LOT more going on there. Besides, there is the more traditional Phillips-Andover model. OK, so who gets to decide? In K-6, students and parents have no choice whatsoever. Talk about better understanding is only cover for lower CC expectations for all with no choice to accelerate properly. The skills enforcement and acceleration has to come from home or tutors. Ask us parents what we had to do at home when Everyday Math was taught at school. Ask the parents of all STEM-prepared students. Ask us. Please! K-6 teachers make it VERY clear that we are not to question anything, so we keep quiet.
Third, success in math REQUIRES individual students get good at doing homework sets (P-sets). There is enough struggle there even with good teaching, but still we hear about teachers who think that adding in more struggle is good. However, with in-class group learning in K-6 that allows fuzzy group talk to replace individual effort and mastery (understanding), then those P-set skills never happen and it’s all over by the 7th grade split to the Algebra in 8th grade track – the only path to a STEM career. Getting good at doing P-sets is a mandatory skill, but K-6 blows it off.
Fourth, students LOVE to be good at skills. It excites them and forms the stepping stones for becoming good students in all subjects. They do well and work harder to stay that way. Math is difficult because there are so many opportunities to have gaps on a very integrated scaffold of skills and knowledge. Full understanding is built on a carefully-mastered skills, not the other way around. The base skills provide base understandings and the problem variations and higher-level problem skills build higher levels of understanding. You could do a proof in math, but not have the understanding to apply it to all variations. Another duh!
If students can get good grades with limited understanding, then it’s not because the skills are rote, it’s because the tests were very bad. In all of the college math and computer science classes I taught, NOBODY could pass with rote skills. All you have to do is change the homework problems slightly to test their understanding. Problem variations form the basis of all homework and the variations lead to better understanding.
No, we’re seeing the forest for the trees. This is not a subtle distinction and the split is based on two separate worlds of low individual expectations and high individual expectations. K-6 is driven by no choice fuzzy ideas and full inclusion group learning, and high school is driven by college and reality. I went through this with my son. This is not about CC because it’s been going on for decades now. CC just institutionalizes low expectations and learning in K-6. However, by high school, most students don’t care about CC and care about PSAT, SAT, ACT, and AP/IB – traditional classes with high individual expectations. More students will not make the nonlinear transition to high school without parental or tutor help. Ask us parents. We’ll tell you. The academic gap is being increased, but we parents won’t let our kids fail, so this change is not so obvious.
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I would like to add more details to the above. I saw a change when my son was in the early grades of a very full-inclusion school, where one child cut up the group work of a team my son was on and the teacher thought it was good learning moment for them. The change was that the schools tried harder to help the kids at the lowest end – who were probably at least one year behind grade level. However, the most able kids were left alone or offered silly differentiated learning methods. I felt that some teachers really didn’t like kids who could remember things easily – they thought it was rote memorization. When we naively told our son’s first grade teacher that he loved geography and could find any country in the world, she said; “Yes, he has a lot of superficial knowledge.” We saw this attitude over and over and their comments were done in a way to position parents as either stupid or helicopter parents – to stay out of their business.
Many parents found that they had to keep quiet and support their kids at home. We would talk about this on the soccer sidelines and at the grocery store. This was encouraged when they urged parents to go to the math open houses to learn how to help (with MathLand, remember that?) when they advocated flipping the classroom. Some parents even felt it was their duty to enforce mastery at home. Nobody discussed whether this was fair to the students whose parents didn’t have the time, money, or ability to help out. I distinctly remember thinking that what schools wanted us parents to do was FAR more than turning off the TV and showing a love of learning. It’s not that they don’t think mastery is a good thing. They just don’t want to do it. Then they turn around and claim somehow that skills are really more about speed rather than understanding. However, students can’t do the problems on the tests even if they have a lot of time. I would be their biggest supporter, but they show no proof whatsoever.
If kids at the lowest (below grade) level are helped by full inclusion, and the kids at the upper (perhaps affluent) end are helped at home or with tutors, then you won’t see a big change in the low CC statistics. You might even see a slight improvement. However, the kids in the middle are hurt the most, and I remember being told by an older and experienced teacher just that. It’s also not fair to the kids and parents at the upper end. I’ve tutored some of those bright kids in the middle in math in high school. It’s sad. They could be STEM-ready students, but they have so many gaps in skills and understandings.
Full inclusion spreads the range of abilities in each classroom and there’s no magic fairly dust differentiated instruction that will fix that other than the differentiated instruction parents add at home. All discussions in K-6 math about better understanding are just cover for lower expectations. One could claim that with a slower pace of coverage, you can achieve better understanding, but there is no proof of that to show how kids in the low slope learning of K-6 math are better able to accelerate to the upper slope of traditional IB/AP math tracks in high school.
High schools need to do a simple survey of all of the parents of kids who get to pre-calc or calculus in high school about what they had to do at home to enforce mastery. You’ll find that it was far more than turning off the TV. You won’t find any student who made that non-linear change in slope because of the magic understanding they developed in class in K-6.
You can’t widen the range of students with full inclusion in K-6, lower the learning slope and expectations, and then somehow claim better understanding. I got to calculus in high school with absolutely no help from my parents. That’s not possible these days – by definition. Our state’s CC test provider even says so. CC is NOT STEM LEVEL. The K-12 linear CC slope offers only a high probability of passing a college algebra course. The College Board understands this STEM lack and hopes that their Pre-AP algebra class in 9th grade (with a focus on remediation and mastery skills) will get the nonlinear transition done with 4 courses in 3 years. They’re dreaming or just covering up for the CC.
Many educators want to float all boats on the Common Core sea of social justice, but if you want to fly, you’re on your own. Many kids can fly, but they will end up floating. High schools offer traditional flying lessons, but K-6 doesn’t get you there without help at home or with tutors.
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