Exploring Effective Math Education Strategies

Debunking Maths Myths | Sarah Powell, Ollie Lovell & Jen Buckingham

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Summary

In this insightful discussion, experts including Sarah Powell, Ollie Lovell, and Jen Buckingham gather to tackle long-standing myths about math education that impede student progress. They emphasize the importance of explicit instruction and dispel myths that inhibit effective learning. The conversation highlights how misconceptions regarding procedural vs. conceptual learning, standards of practice, and classroom methodologies contribute to declining math proficiency. Efforts to apply cognitive science and a structured approach in teaching are underscored as vital steps towards improving mathematics education efficacy. This event draws parallels with successes seen in reading instruction and calls for a similar science-backed revolution in teaching math.

Highlights

Experts debunk seven common myths that undermine math instruction, advocating for simultaneous procedural and conceptual learning. 🧐
The importance of structured and clear curriculum content is emphasized, with calls for less reliance on unstructured discovery learning. 📚
Explicit, step-by-step teaching methods are championed as the most effective for mastering mathematical concepts. 👩‍🎓
Discussion on cognitive science's role in enhancing educational practices, similar to advancements seen in reading. 🧩
Teacher improvement through professional learning and leadership is highlighted as crucial for progress. ✨

Key Takeaways

Explicit instruction isn't just a buzzword; it's the pathway to successful math learning! 🧠
Procedural learning and conceptual understanding should go hand in hand at all times. 🤝
Dispelling myths like discovery learning boosts effective teaching strategies. 💥
Teacher collaboration and leadership are essential to implementing evidence-based methods. 👩‍🏫👨‍🏫
Just like reading, math needs a science of learning revolution! 🚀

Overview

The session begins with a critical look at the myths that have long influenced math education, addressing notions such as discovery learning being the optimal strategy or that timed tests cause math anxiety. Experts dismantle these myths by presenting evidence-based research showing that structured, explicit teaching methods are far superior in achieving desired learning outcomes.

Sarah Powell leads the talk on dispelling misconceptions about procedural versus conceptual learning. She emphasizes that both should be integrated into math instruction to provide a balanced, comprehensive approach to teaching. The panelists agree on the need to teach mathematical algorithms directly to students for better understanding and retention.

Ollie Lovell and others draw parallels to the science of reading movement, advocating for a similar rigorous approach in math education. They stress that quality instruction depends on structured curriculum, cognitive engagement, and repetitive practice. The narrative closes on an optimistic note, with a call to action for evidence-based practices to become the standard in math teaching across the globe.

Chapters

00:30 - 05:00: Introduction to Mathematics Myths The chapter 'Introduction to Mathematics Myths' explores the enduring idea that children's natural curiosity will lead them to learn everything they need on their own, given sufficient opportunities and minimal guidance. This notion is appealing because it suggests a more passive role for teachers, who can rely on students' natural abilities and curiosity. Despite its romantic appeal, the idea has persisted over centuries, even though it may not fully account for the nuanced responsibilities of teaching.
05:00 - 10:30: Impact of Educational Approaches on Mathematics The chapter discusses the development of human skills, focusing on the distinction between biologically primary and secondary skills.
10:30 - 15:00: Challenges in Mathematics Education The chapter discusses the distinction between biologically primary and secondary skills in the context of mathematics education. Biologically primary skills, such as oral communication, are those that humans have evolved to acquire easily due to their significance in survival over the millennia. In contrast, biologically secondary skills, such as reading and mathematics, have not been naturally ingrained and require formal education to learn. This distinction highlights the need for structured learning practices in teaching mathematics, as it is not an innate skill like language.
15:00 - 27:00: Seven Myths of Mathematics Teaching This chapter discusses the creation of complex neuronal circuits in the brain necessary for translating written text into meaning. It emphasizes that for most young students, changes in the brain occur through deliberate teaching rather than mere exposure to text. Similarly, it argues that specific mathematical computation skills do not naturally emerge in children; instead, they must be deliberately taught. While the brain's neurological components and capacity exist, the necessary networks must be developed through targeted education.
27:00 - 41:00: Quality Mathematics Education This chapter discusses the formation of knowledge and skills necessary for mathematical procedures through intentional education. It draws on insights from neuroscience, particularly those of neuroscientist Stanislas Dehaene, to explain how the human brain, like the brains of other species, has an innate sense of number and quantity. The chapter suggests that by teaching in a certain way, we can harness the brain's natural abilities to enhance mathematical learning.
41:00 - 52:00: Overcoming Challenges in Mathematics Education The chapter discusses the intrinsic human senses of number, space, and time that exist independently of language, memory, and rational rationalization. It emphasizes the role of education in developing these senses into conscious understanding. With education, children can learn to apply formulas, manipulations, and more advanced mathematical concepts using mathematical symbols and language, similar to how written language and mathematical processes are cultural inventions necessitating specific cultural tools.
52:00 - 56:00: Conclusion and Call to Action The speaker highlights that proficiency in mathematics doesn't come naturally to all students, but asserts that all students can learn it effectively. They emphasize that substantial research over the years supports the effectiveness of explicit instruction in mathematics education. However, they also express a concern that, despite strong evidence backing this approach, many schools and educational systems are still reluctant to implement these methods. The chapter serves as a call to action for educators to adopt evidence-based teaching strategies to improve learning outcomes in mathematics.

Debunking Maths Myths | Sarah Powell, Ollie Lovell & Jen Buckingham Transcription

00:00 - 00:30 [Music] foreign [Music] [Applause] idea that children's Natural Curiosity will lead them to discover everything they need to know as long as they have plentiful opportunities to do so and a little guidance because of its intuitive and romantic appeal not to mention it lets some teachers off the hook for the responsibility of actually teaching this idea has endured for centuries
00:30 - 01:00 the problem is it's not true at least it hasn't been true since around the time human societies and economies moved out of the hunter-gatherer age the theory of biologically primary and secondary skills developed by cognitive scientists and evolutionary psychologist David Geary provides a powerful explanation in very broad terms the theory says that biologically primary skills are those that typically develop naturally through interaction with other humans and with the environment there are skills that humans have
01:00 - 01:30 evolved to acquire with relative ease because they've been necessary for survival for hundreds of thousands of years oral communication is in this category biologically secondary skills are those that the human brain has not yet evolved to acquire spontaneously they include for example reading and bats thus the invention of formal education and schools reading unlike oral language is not a skill that humans are born to do it's a biologically secondary skill in order to
01:30 - 02:00 be able to translate written text into meaning a set of complex neuronal circuits must be created in the brain for the vast majority of Youth students these changes in the brain occur as a result of teaching deliberate teaching of this skill not through exposure to books a spot of guesswork and a whole lot of optimism similarly performing specific mathematical computations is not a latent ability that will eventually emerge in all children the neurological components and the capacity are there but the networks
02:00 - 02:30 required for mathematical procedures are formed through learning that occurs as a result of deliberate teaching just like humans have areas in the brain that process meaning visual input and sound and by connecting these in the right way through education we can read print the untrained brain seems also have to have some innate sense of number and of quantity according to the neuroscientist stanisluster Hayne the human brain as well as that as other species is endowed
02:30 - 03:00 with senses of number space and time that are disconnected from language memory and rationalization so it's the job of Education to help children to bring these senses into their conscious mind and then to learn to apply formulas manipulations and more sophisticated mathematical abstractions through the use of mathematical symbols and language again like written language mathematical language and processes are cultural inventions that require cultural tools
03:00 - 03:30 to become proficient not just genetic ones so this is not breaking news it has been clear for many decades through classroom and clinical research that maths doesn't come easily to all students but they can learn my fellow speakers this evening will explain to you what this means for maths instruction but I don't think it will be a huge spoiler to say that Better Learning results from an emphasis on explicit instruction not that strong evidence is enough in the world of Education unfortunately many schools and school systems persist
03:30 - 04:00 with policies and practices that are based on the assumption that students learn best by working things out for themselves and that it's even better if they work it out for themselves in a group that approach ticks the box of the so-called 21st century or deep learning skills at the same time now this mistaken idea has even influenced the physical infrastructure of schools where new schools built over the last decade or so have open classrooms with furniture that is allegedly flexible but not flexible
04:00 - 04:30 enough to see children in rows again good research has shown that the Acoustics of open classrooms make it difficult to hear the teacher and interferes with student learning and this is particularly pronounced for students who have autism spectrum disorders or hearing difficulties seating students in group tables where children have to face each other and requires them to Crane their necks to see the ubiquitous electronic whiteboard at the front of the room encourages children to look at each other instead of at the teacher the obvious
04:30 - 05:00 consequence is distraction and the low-level sorts of disruption that characterizes so many Australian classrooms so why am I speaking at a maths event when I'm better known for my knowledge about how children learn to read it's because the same arguments that have been have infected and impeded progress in Reading are also preventing Improvement in performance and participation of Australian children in maths and are contributing to its decline therefore the same debate needs to be had with the same level of vigor and
05:00 - 05:30 urgency we need the maths Wars the debate over reading has been prominent as well as potent because there is so much at stake for a long time literacy has been a critical factor in quality of life including health and income facility with a written word is a prerequisite for social participation there's a deep sense of personal shame that's attached to illiteracy that is not present in the same way for students and adults who struggle with maths however the social and economic
05:30 - 06:00 consequences of low maths achievement have been underestimated for too long and will be a significant drag on this country's productivity and its competitiveness thanks to several decades of research on human cognition and learning and the example set by effective teachers in high performing schools we know a great deal about what effective instruction looks like in maths a key difference with reading is that maths is less dependent on the educational near of the home environment and therefore should be less susceptible to achievement gaps
06:00 - 06:30 associated with disadvantage if students have effective teaching and a well-designed curriculum but despite this knowledge our scores and international assessments have declined dramatically in the past two decades fewer students are taking Advanced maths courses in senior secondary schools and there's an ongoing shortage of maths teachers so why are these avoidable downward Trends happening maths is hierarchical early failures to
06:30 - 07:00 master content will jeopardize understanding and Mastery at subsequent levels it doesn't take very long for early difficulties in math to develop into a deep-seated sense of helplessness and ultimately withdrawal with respect to curriculum if insufficient Knowledge and Skills are built in Primary School the leap to secondary maths and upper secondary maths especially Advanced maths is just too great The Flow and effect is fewer people willing and able to teach math to teach maths necessitating more people
07:00 - 07:30 teaching maths without maths qualifications and the cycle continues and that cycle unfortunately is reinforced by initial teacher education programs that perpetuate the teaching approaches that created the problems in the first place when you consider all this you can see how we got to where we are today it's not a mystery educationists became fixated on the idea that children can be many mathematicians before they know the times tables or even how to tell the time even Australian states have finally
07:30 - 08:00 embraced explicit instruction for reading a slow to recognize that they need to do the same for maths continuing to endorse outdated and disproven Discovery learning approaches to maths it's taken a long time to get on the right track for reading instruction to say the least and we still have a way to go one thing I have learned it's not enough to present great research and a strong argument to people of influence in education it requires making the
08:00 - 08:30 evidence impossible to ignore there have been numerous people in Australia and around the world who are working towards this including Ollie Sarah and Erica and also some of the people in this room and and people present to their speakers at the present presented the previous event Eddie Wu and Greg Ashman so the cis's decision to make maths a focus of its education program is laudable and I know Glenn will be dogged in his work to shift the dial in maths the way we have for reading
08:30 - 09:00 thank you and I'd like to welcome associate professor Sarah Powell thank you awesome all right good evening it's so nice to meet all of you my name is Sarah pal and I am from the University of Texas at Austin and just really glad that Glenn and the center for independent studies asked us to come here this evening and also asked us to put together this brief about Math Miss and so I'm going to briefly share some of the myths that
09:00 - 09:30 undermine math teaching I'll say maths teaching to get it correct down here and under um so yeah so if I do sneak in a math here and there please you know please please excuse me for that so in this um brief that we put together we talked about seven common myths that we feel undermine the teaching of mathematics so I'll briefly just talk about those and hopefully that'll get our conversation going for this evening so one of the first myths that we talked about here you can read it there is that students
09:30 - 10:00 should not be exposed to procedural learning and until they understand the concepts behind the mathematics but when we look at the evidence and that would that's what Jen was really emphasizing right now those evidence-based practices when we look at the evidence behind conceptual and procedural learning we see that both of those should be taught in Tandem and so one should not be done before the other but in actuality we should be emphasizing both conceptual learning and procedural learning at the same time so that's something that we
10:00 - 10:30 need to think about as we design our maths instruction one of the second myths that we talked about is related to that but related to this idea of procedural algorithms so often we want to teach students algorithms that's a step-by-step process for working through a mathematics problem and some people will say well that's harmful we want students to create their own algorithms or come to these algorithms in a natural way and but what we actually know about
10:30 - 11:00 the research is that when we teach students how to solve solve a problem we teach them explicitly as Jen was just talking about that step-by-step process for working through a problem that helps students not only with the task at hand but also with the mathematics that follow so some of that higher level mathematics and so when we think about these algorithms we want to help students learn them and practice them so that they become proficient with these algorithms and we also see that research
11:00 - 11:30 tells us that when students have a good understanding of these standard algorithms that actually leads to improved mathematics outcomes over students who do not have a strong understanding of these algorithms our third myth that we talk about in this brief is thinking about inquiry-based learning and saying that that is the best approach to the teaching of mathematics and Jen just talked a little bit about this so with inquiry-based learning students are supposed to come to the learning of mathematics on their own some people
11:30 - 12:00 call this discovery based learning but what we know about research and this is probably one of the strongest research basis that we have is that when students participate in inquiry-based learning it doesn't always give every student the best foundation in mathematics and so instead of thinking about that approach as the best approach we would like to think about this approach using explicit instruction so helping model and helping practice the mathematics so that students have that strong foundation and
12:00 - 12:30 there are about 50 years of research probably more than that that support the use of explicit instruction so it's something that we cannot ignore I see that inquiry-based learning is often a little more fattish and we have to go back to that evidence and say this is how we know that students learn the best and then our fourth myth that we talked about was thinking about this idea of productive struggle productive struggle is an idea that students need to wrestle
12:30 - 13:00 a little bit with the mathematics in order to become really strong mathematics Learners and this is a very big key idea in the United States right now a lot of people talk about productive struggle but what we know is that when students are faced with productive struggle or a task that promotes productive struggle actually many students find the task frustrating and don't complete the task or are unable to complete it in a great way and the thing about productive struggle is that I think probably all of
13:00 - 13:30 us in this room would say you know it's helpful when students have to wrestle a little bit with the mathematics but many times the problem with productive struggle is how it's applied in the classroom so I'm looking at all of you and if I had one task that was going to promote productive struggle for all of you probably some of you would find it easy and some of you would find it incredibly difficult and maybe one or two of you would say yes Sarah this is in the right zone for me to learn and so if productive struggle is going to be
13:30 - 14:00 done well it really has to be done individualized and more often than not it's not and so thinking about productive struggle as is important it's actually more important to meet students where they are and move them forward from there instead of always trying to engage students in that productive struggle our fifth myth that we talk about in this brief was related to this idea of growth mindset and growth mindset is that if you understand that math is important and that you feel that it's an
14:00 - 14:30 important task to engage in then you are more likely to understand that that's going to help you increase your math learning and when we think about growth mindset there's actually very minimal evidence at this point right now that shows that growth mindset will lead to improved mathematics outcomes when people have implemented growth mindset interventions growth mindset interventions do lead to improved outcomes in growth mindset but right now
14:30 - 15:00 growth mindset interventions are not translating to improved outcomes in mathematics and I see this as one of those things where it would be really awesome if I did a growth mindset activity with students every five minutes every day and talked about growth mindset and then that would translate to improved mathematics outcomes but what we know is actually important is the teaching of mathematics all right and so growth mind set activities are not detrimental to students but are they going to be this magical thing that leads to Improvement
15:00 - 15:30 improved math outcomes no and the same thing with executive functioning training so this was our sixth myth that we explored in our brief um but executive functioning uh training would maybe help students with their working memory or their planning or their organization and we're seeing the same thing here as we see with growth mindset so when it comes to Executive functioning there are training programs that students can participate in many times in the US these are Tech based and
15:30 - 16:00 but what we're seeing right now is that when students participate in those executive training programs those improve executive training outcomes but guess what they're not improving mathematics outcomes so while that is really probably important especially with working memory we want to help students increase their working memory capacity but we can't just train on Executive functioning skills what do we also have to do we also have to teach the mathematics so that was our seven our sixth myth that we explored and then
16:00 - 16:30 our seventh myth that we explored was this one that is a myth about time tests causing math anxiety this is very very prevalent in the U.S and so people will say oh we cannot do timed assessments because that causes math anxiety well there's no evidence in no causal evidence that links timed assessments to mathematics anxiety there's a lot of anecdotal evidence so people and more often than not more often than not it's
16:30 - 17:00 adults they will say oh when I was in school I took these time tests and that caused me to be bad anxious well probably that timed assessment was about one percent of the activity time that students participated in math and so they may not always remember all of this other stuff that they did in the math classroom and maybe especially some of the ineffective instruction that they received and so more often than not they'll attribute that time test to their math anxiety but probably it was everything that they were doing in math
17:00 - 17:30 and probably they were not receiving that strong Foundation to mathematics that they need to receive and that is probably what exaggerated their math anxiety so right now we don't see that time tests are a detrimental thing to do with students but they do need to use be used appropriately so we need to introduce them in low stakes environments we do not want to publicly post students results from timed assessments um and so we just want to use them well and use them sparingly but classroom
17:30 - 18:00 teachers should not be afraid of using timed assessments because there is no causal link between time test and math anxiety so those were the seven myths that we explored in this brief and I think it gives us a good starting point to then talk about what Jen was talking about is those evidence-based practices so now that we are know that these are some of the myths that are out there well how do we come in and appropriately teach mathematics so I hope you'll read the brief and check it out and I'm happy to talk more about it tonight and I think
18:00 - 18:30 I'm going to turn it over to ollie I'd like to start today by acknowledging the gadigal people of the aorination as traditional custodians of the land pay respects to Elders past and present and acknowledge that unfortunately colonization and dispossession are both ongoing processes the theme of today's session is debunking maths myths as such I see our goal tonight is threefold firstly I hope that we can each leave with a clearer understanding of some of the myths that are currently undermining mathematics education
18:30 - 19:00 secondly in balancing the debunking of myths we need to develop clarity about what it takes for students to successfully learn mathematics and finally we should hopefully leave tonight with greater awareness of the gap between where we are now and where we could be as well as have some ideas about how we might close it Sarah pal has already thoroughly covered the myth so I won't attempt to recover this territory nor would I be able to do it with nearly the same thorough research as Sarah has instead I'll focus
19:00 - 19:30 on the final two points tonight sketching a picture of quality mathematics education and considering the Gap and what might be done to close it quality mathematics education when thinking about teaching and instruction one of the traps that it's easy to fall into is to focus on what the teacher is doing rather than what's occurring for the learner to quote John Wooden teaching is knowing the difference between I taught it and they learned it or to reference Graham nuttle we need to
19:30 - 20:00 focus Less on teaching methods and focus more on learning mechanisms this is why I rather than focus on quality mathematics teaching at the outset tonight I'm instead talking about what it takes for students to successfully learn mathematics so what does it take to learn maths as it turns out what it takes to learn maths is what it takes to learn anything really that is the construction of a coherent knowledge structure that accurately represents the external world
20:00 - 20:30 the quote John sweller who we have here tonight the major possibly sole difference between novices and experts consists of differential knowledge held in long-term memory argue and Sarah alluded to this as well that there's much more to learning mathematics than just knowledge and this is no doubt true for example students have to have the motivation to put in the intellectual effort to become successful mathematicians but luckily for us uh they these two
20:30 - 21:00 things are motivation and success go hand in hand as Greg Ashman pointed out in his CIS talk that preceded this one the greatest predictor of motivation turns out to be success as a result we can Target both success and motivation by focusing primarily on mathematical success and therefore on the building of knowledge this is something I see myself time and time again in the classroom once students do start succeeding questions like when am I ever going to use this seem to fade away Mastery schools
21:00 - 21:30 Australia captures this idea the idea really well with their informal tagline success is the fun we offer so if describing quality mathematics instruction requires describing Quality quality mathematics learning and if quality mathematics learning is the construction of a coherent knowledge structure then how do we help students to construct these knowledge structures in simple terms process of knowledge building is an iterative one whereby a student takes a new piece of knowledge
21:30 - 22:00 and integrates it in a meaningful way with that which they already know at its core this iterative learning or knowledge building process requires four things in simplified terms appropriately sequence information attention cognitive effort and practice by appropriately sequenced information I mean information that has the potential to be logically connected to something that the student already knows and information that itself is logically and systematically arranged in order that is we need well-structured and
22:00 - 22:30 sequence curricular lesson plans and learning intentions by attention I mean that students must actually attend to the new information that they're presented with in the words of peps McRae students remember what they attend to and this is because it is a tension that brings information from the environment into students working memories for processing by cognitive effort I mean that once students do pay attention and bring this new information into their working memory they need to do something with it
22:30 - 23:00 to meaningfully connect it to that which they already know this could be using it in a procedure self-explaining it and asking what did I take from that elaborating it or elaborating on it and asking how does this relate to that which I already know memory as Daniel Willingham tells us is the residue of thought and students need to think about this new information for it to stick and be become integrated into their long-term memories and by practice I mean that students need opportunities to reactivate this same knowledge over time ideally at
23:00 - 23:30 expanding intervals and with sufficient accuracy such that they're able to remember this new information for the long term further in many cases and for much of the content and skills contained within mathematics it's useful for students to practice to the point of automaticity as George Booker has pointed out strategymastery is key but practice to Mastery and automaticity must follow so summing up these four ingredients when it comes to learning mathematics we are building knowledge structures and to do that students need appropriately
23:30 - 24:00 sequenced information attention cognitive effort and practice the gaps in how to close them so if quality mathematics learning requires these four ingredients where do we currently stand in relation to each of these principles and what might we do to ensure that mathematics education better aligns with them to begin with there exists a significant challenge when it comes to the sequencing of information for our students this is for two main reasons firstly many Australian teachers are
24:00 - 24:30 teaching mathematics out of field as reported by Paul Weldon 30 of secondary school mathematics teacher fall into this out of field teaching category the second reason why students often don't experience a structured and coherent curriculum relates to resources at the primary level level there doesn't as yet exist structured programs for mathematics instruction that match their literacy counterparts such as Jen Buckingham's multi-lit and at the secondary level while there are a number of quality textbooks many schools and
24:30 - 25:00 many teachers seem for some reason to appear ideologically opposed to using them in my own experience the structured use of high quality textbooks by a well-run mathematics Department allows teachers to spend less time planning and working out which activity or Workshop worksheet to use next lesson and much more time refining exactly how to teach specific concepts with maximum Clarity how to use assessments and data to inform teaching and responding to students needs as they ride and even building learner
25:00 - 25:30 Independence therefore we can improve mathematics education by getting higher quality and better structured resources and programs into teachers hands and by supporting them to use them effectively on to our next principle of attention unfortunately this situation here isn't much more encouraging as Peter Goss and Julie Sunderman have shown the attention situation in Australia is quite dire with up to 40 of students students regularly either passively disengaged
25:30 - 26:00 low-level disruptive or aggressive and anti-social within our nation's classrooms turning the tide on this takes a shifting culture expectations and standards and it takes both Visionary and consistent leadership and day-to-day consistency in classrooms luckily for us the vast majority of students really do want to be engaged in their learning students are ready and willing to respond positively when the standards are set and when they're presented with high quality instruction I've spoken with a staggering number of Educators from around the country who've
26:00 - 26:30 communicated the same message to me they say things like as soon as we started improving our explicit instruction our behavior management challenges practically went away we can improve mathematics education by improving instruction and raising the attentional expectations that we have for our students within mathematics cognitive effort can take a number of forms from doing textbook exercises to discussing errors or explaining Concepts to a friend or parent however another trap that we often fall into in
26:30 - 27:00 Australian classrooms is getting students thinking but not thinking about mathematics this is due to what Wiggins and matai call an activity Focus perhaps the core message that Daniel Willingham communicates in his best-selling book why don't students like school is as follows review each lesson plan in terms of what the student is likely to think about this sem this sentence may represent the most General and useful idea that cognitive psychology has to offer teachers if we want students learning mathematics they need to be thinking about
27:00 - 27:30 mathematics which is unlikely to be the case when they are cutting up shapes or doing other Physically Active but not cognitively active tasks in the classroom we can improve mathematics education by ensuring that students maximize their time in class thinking about mathematics as for practice some students do engage with it but the issue here is that more of a structural one we know from cognitive science in the work of both Herman ebbinghaus and pioto Wozniak that students must think about a concept multiple times over time ideally over
27:30 - 28:00 expanding intervals for it to become securely stored in long-term memory the topic by topic nature of standard mathematics textbooks and teaching simply doesn't support this this is because students often see an idea in an isolated topic then don't see it again until that topic is returned to the following year in fact as Doug raw and Kelly Taylor have written quote the organization of practice problems in most most mathematics textbooks is one
28:00 - 28:30 that minimizes long-term retention the way around this is through structured retrieval synoptic testing daily reviews and other space practice approaches in short we can improve mathematics education by providing structured and systematic opportunities for students to practice Core Concepts over time in conclusion the learning of mathematics is the construction of coherent knowledge structures that accurately represent the external world to do this students need appropriate sequencing of information attention
28:30 - 29:00 cognitive effort and practice we're not currently where we could be in terms of each of these four principles as a result we can improve mathematics education by getting higher and better quality structured resource resources and programs into teachers hands and supporting them to use them effectively by improving instruction and raising the attentional expectations that we have for our students by ensuring that students maximize their time in class thinking about mathematics and we can improve mathematics education by providing structured and systematic
29:00 - 29:30 opportunities for students to practice Core Concepts over time the challenge is great but so is the opportunity as I hope I've Illustrated tonight quality mathematics instruction is far from Out Of Reach and focused effort targeted at each of these instructional principles will lead and has led to enormous gains in many Lighthouse schools and sectors across the country let's work together to share discuss and clarify what we can do to further improve Australia's mathematics education and let's work together to act to make it happen
29:30 - 30:00 thank you Sarah you you flashed at the end of the presentation uh something that I think a lot of people in this room would be excited about which is a science of math movement in the US uh can I invite you to tell us a little bit about that and why it formed and where it's going yeah so in the US just as there is in Australia there is a movement related to the science of reading so we're not we know so much about how students learn how to read and we need to get that information into the hands of teachers
30:00 - 30:30 and so there's a group of I would say around 50 to 75 of us who just were hanging out at conferences together over the last few years and we said well whatever they're doing in Reading is just as important to do in mathematics and so we started meeting I think about a school year ago just virtually and putting together some ideas and so one of the things we did is we created some briefs around myths of math which I know Glenn that's how you and I connected and then now we're starting to work on a
30:30 - 31:00 teacher Playbook so as Ali was talking about what are some of those important certain practices to do in the mathematics classroom so that when teachers are saying my students are struggling with math and what are the evidence-based practices in math that I should rely on then they could take this Playbook and start to do some of those things in their classroom so that effort is ongoing and anyone is welcome to join us it is not just a us-based effort and we have teachers and we have caregivers we have a lot of parents that have been attending some of our events we did a
31:00 - 31:30 book study in the spring semester and then we have just people who are really interested in math and getting the science of math into the hands of everyone so that students can benefit from that and only where you know that you're involved with several movements in Australia as well with a similar goal around it spreading knowledge around science of learning can you give us some optimistic words about the the movement in those communities optimistic words about the movement in the science of learning communities well
31:30 - 32:00 yeah I really think there's a there's a huge Groundswell in Australia at the moment around the science of learning I think it's very much started with the science of reading and it's I think that probably started I don't know Jen would know this much better than me but the sense like it is around 10 or so years ago really accelerated in the last five or so years to the point now that the the language that teachers are talking and in many school kind of the schools the waters they're swimming in are it's like starting to become taken for granted that this is the way that
32:00 - 32:30 literacy is taught and I'm starting to see I feel like we're at this the start of that Journey with the science of learning more broadly I mean I think it's important for us to be clear here when what we we mean when we use the phrase the science of learning when I use the phrases science of learning I mean things like retrieval practice spacing interleaving things like that elaborate elaboration and generative cognitive activities um we're starting to see that use more and more and we're starting to see it built into a lot of programs but I would say it's still the early days and a lot
32:30 - 33:00 a lot of teachers still aren't super familiar with these ideas but there are lots of events and increasing numbers of them happening and that's really really exciting and Sarah so leaning into this question about science we've had a science of reading Revolution really even if not by that name what are the is there an analogy in the way that we think about mathematics and the science of mathematics that we can that we can really leverage as far as getting everybody to understand that language well it for in the US the
33:00 - 33:30 science of reading really has developed not not from Educators but I think it was more from parenting caregivers who were saying my child's going to school and they've been in school for two three four five seven years and they're still struggling with reading and why do they not know how to read because we know a lot about the progression of reading and so it's really an exciting space and I know as Jen was talking about we did have these reading for Wars and some
33:30 - 34:00 sometimes those are still going on and how she's like yeah we need some math Wars and I completely agree with that so just as we know a lot of it the pro a lot about the progression of learning how to read we also know a lot about how students learn mathematics and Ali touched upon a lot of these in his talk and and thinking about some of the things about the science of learning and really the science of learning is the science of reading and the science of math right it's kind of more of the umbrella science there and if we know a
34:00 - 34:30 lot about the signs of Leaning and learning and I would also add to that the science of teaching how things should be effectively conveyed to audiences whether that's an audience of adults or whether that's an audience of young children then we need to take those things and translate them into practical things that can be done in the classroom well so on to the Practical things in early you know we've uh Sarah presented a series of of uh myths about math teaching how common do you think they they are in the practice of
34:30 - 35:00 Australian teachers or they're everywhere and I've I've seen them in so many schools and I mean that's kind of what I was alluding to in terms of the ideology around not using textbooks I was at a job interview once and I I kind of asked oh what what textbook mass textbook are you using to get a sense of they said oh we don't believe in textbooks so how does that make any sense to not believe in textbooks like the structured organization of information and practice for students um it's uh it's quite befuddling and
35:00 - 35:30 unfortunate really so where does that ideology come from is is this something now obviously educators are in the game because they're passionate about improving outcomes for students no one no one denies that so why is it that so often in practice we see that many of the practices it teaches ultimately become taught up in don't seem to be exactly those that I actually do translate to the best learning outcomes it's a good question I think I think a lot of that the answer that would probably be historical
35:30 - 36:00 um and I probably don't probably not the best person to answer that question but I think there's a bit of a crossover with the productive struggle idea that Sarah was kind of talking about for for students but I think there's a belief in some teacher circles that it's kind of productive for teachers to and develop some professionally if they're developing their own Learning lesson plans and things like that whereas actually the process of teaching the job of teaching is so immensely complex that expecting teachers to become experts in
36:00 - 36:30 curriculum design from their first year is just completely unreasonable especially when they're battling you know the kind of 40 disengagement that I alluded to in my talk as well so I think I think there's some kind of ideological things that underlie that um but there's I'm sure there's some other historical factors there too and Sarah we sort of up against it a little bit we're talking here about science and mostly invisible things so cognitive process but teachers typically are very experiential it's often about I tried this and I observe this and a lot of the feedback teachers get during
36:30 - 37:00 instruction is very much thinking feeling in the moment not necessarily that invisible bit behind the veil how do we overcome that as far as getting that understanding about attention to the cognitive process that might be might be invisible to the naked eye I guess well if we knew the answer to that Glenn we probably wouldn't be here so uh so I think we've got to think about this on on several fronts so the first and Jen alluded to this uh well at least we were talking to her earlier
37:00 - 37:30 about uh working with our teachers who are not teachers yet so really providing really strong pre-service teacher preparation as they are the university and they are doing their teaching certification so that teachers really understand you know here are these cognitive factors and these cognitive processes that students are using as they are learning math or reading or whatever it might be so pre-service teacher preparation is is one front but then now we have all of these teachers that are currently teaching in schools and so thinking about well how do we
37:30 - 38:00 help these teachers adapt some of the practices that they have that they may not be using and so that for us in the US that goes through a lot of professional learning that's provided at the school level the district level the state level and being doing webinars and just exposing teachers to these things because often teachers a lot of teachers that Eric and I work with Will especially related to inquiry-based instruction they'll say well that's what we've been told that we're supposed to do in our district and then we'll sit
38:00 - 38:30 down and say okay well here's the evidence that supports that and here's the evidence that supports explicit instruction and there may be a time and place for inquiry-based instruction but in order for students to do that adequately they have to have such a strong foundation in mathematics and how do we help students with a strong foundation in mathematics we have to model and give them as Ali was talking about all those practice opportunities and so really helping teachers see that but most of the time it's going through
38:30 - 39:00 conversations and through learning and a lot a lot of I think it also has to be in the media you know that there is this science of learning and we know so much about how people learn and let's translate that to the mathematics classroom are we a little bit up against it you know and that they've got to put out the fires effectively with professional development and that's that's sometimes self-selecting too it's teachers that have that have uh gone out of their way to select a program of training and additional learning that's maybe is already Affiliated and they're
39:00 - 39:30 perhaps are already doing some of that and they're getting more confident at it but how do we reach all the rest yeah that may not even be familiar at all well even when people attend professional learning you don't always have to pay attention right so your District said you have to be there but do you have to really pay attention to what's going on and take away things no you don't always have to do that uh I I think that's the question that we like we really need to think about so uh we're doing doing some things in the US where we're creating brief videos for
39:30 - 40:00 teachers to watch that are on YouTube about here's how you teach this and they're all grounded in you know thinking about explicit instruction and thinking about a focus on that mathematical language um but just in that they teachers can watch on their phone as they're picking their kid up from soccer practice right so you know professional learning doesn't have to be this extended long session but it can be these bits and pieces there the thing that we have found to be really helpful are people that work at the district level so
40:00 - 40:30 people that work over a series of schools and if they have really bought into the science of learning and the science of teaching they can say all right our district is moving this forward or it might be a school principal or a district superintendent when the leaders are saying hey this is something that's really important for us to do then it seems that then their putting in the appropriate programming programming and the structures that are going to bring people with them and I think that's hard because many times the
40:30 - 41:00 school principals or maybe the district superintendents they aren't the biggest math people right and they you know may have taught mathematics but maybe they didn't and many times they have a lot of questions for us of like what does really good mathematics instruction look like and so we really have to inform our school leaders about this and and fill their knowledge base related to The Learning of mathematics so that then they can say okay we're going to lead this effort and change things at the
41:00 - 41:30 district level or the school level and only seven as someone is working in schools and delivering instructional leadership within the school does an individual teacher come up against this you know so obviously it's great if there's permission from leadership to to to to try out something different or maybe demonstrate here's a great example of what to do if you're an individual teacher perhaps working in a school where there might be few confident experienced Math teachers how do you upskill yeah it's a good
41:30 - 42:00 question I think there's a there's a couple of things there first of all listen to my podcast but really reach out to a whole heap of um people people creating resources I personally find Twitter amazing uh there's so many Facebook groups that are you know passionate teachers but really just look for those connections outside of your school that will kind of nurt you in and that was kind of my experience that's been a number of years in a school that ideologically wasn't
42:00 - 42:30 wasn't really aligned with what I believe is quality mathematics education and I managed to stay in that school and hopefully have a positive impact because I was nurtured from outside of it um so that's the first thing but the second thing is there are plenty of schools and an increasing number of school leaders who are coming to realize what what it takes to do mathematics instruction well so seek them out and you probably do that through through broadening your networks and then try to get a job there because that you will find it so much more nourishing and rewarding and you actually to create
42:30 - 43:00 success stories that then spread the impact of the approach further teachers seek this information I mean how would how would a teacher out there one of the 300 000 teachers in the country how do they know where to where to where where that I guess that Hive of activity is that they can follow yeah I get I guess the kind of things I spoke about earlier podcasts Facebook Facebook groups are great Twitter personally it's fantastic there's professional organizations that have mailing lists and conferences and things like that
43:00 - 43:30 um the some of the best it can be quite hard to get started on something like Twitter there's like all these hashtags and all these different people and it's hard to know what to do but I had some great advice um from someone when I was getting started out because I tried about five times to get into Twitter and they said just find one person who you know tweets about the kind of stuff you're interested in and and follow them and just watch what they do and then you'll see that they will be retweeting other people and then you follow them and it will just naturally grow so um
43:30 - 44:00 yeah just find one person who who's kind of in this space or working on it and start there I'd say and Sarah some people would say that that having teachers try to become like cognitive experts is beyond the work at work of teachers how do you convince them that it is a great investment to make well well they not only have to be cognitive experts but mathematics teachers have to be experts in the content knowledge of mathematics they
44:00 - 44:30 also have to be experts in the teaching of mathematics and these are all different things right and then they all come together and they work together in tandem but in order to meet I think it gets to in order to meet the needs of all of your students so you have you know a large number of children in your classroom and you may have some students where you're going to need to work with them more on some of their cognitive factors perhaps they're going to have to help them more with understanding how to
44:30 - 45:00 work with their working memory if their working memory is over taxed sometimes and then you have some students that you're really going to have to go back and fill in not maybe the grade level below them but several grade levels below go back and pick up some of the earlier math knowledge and teach that so that they can come forward with you and then you're also going to really have to focus on your teaching at mathematics and so it's like all of these things I just listed three but think there are probably more that we could put into that but in order to be a really strong teacher you do have to do you have to be
45:00 - 45:30 like an absolute expert and all of them know but you have to have a really strong understanding of these different skill sets that are involved in the teaching of mathematics so that your students can learn mathematics oh yeah it teaches up for that I mean the teacher's already gone it's such a full plate with with all of the work they're doing have they got it in them to also upskill in in all this area as well yeah um so so building what Sarah was saying I think
45:30 - 46:00 it's one of the things is it's really important for teachers to know this stuff you know if it's it's kind of like a an engineer they have to understand the materials that they're working with they have to understand how the materials they're working with work under strains stress what their capabilities are and things like that that the materials that a teacher is working with is the human mind right we have to understand actually how it works if we want to design our instruction in ways that's going to understand how it behaves under stress and it's it's affordances and things like that so that's that's the first thing I guess
46:00 - 46:30 the second thing is that um some of the interesting research on kind of teach a belief change that I've come across is the work of Thomas gusky and he kind of contrasts two approaches one approach is kind of trying to convince people that something's really good and then show them how to do it this is kind of like the the growth mindset thing it's like going and being like Oh you know if you if you have a growth mindset you'll be able to learn mathematics and the other approach is helping them to do it successfully and then saying oh look at this stuff you just did it worked and this is why um and it's gusky has shown that approach is much more successful so I
46:30 - 47:00 think it's it's less about go standing in front of teachers and saying oh this is what's going to be most effective let me give you a you know 50 slide presentation on it and just getting in there beside them giving them resources that make their life easier helping them see the benefits of those resources and say isn't this great um would you like to learn more about why this worked and in my personal experience teachers are super Keen to learn more so we've mentioned explicit instruction several times now that might mean very
47:00 - 47:30 different things to different people Ollie what are some what are some of the ingredients or components that make up explicit instruction because of course it's an umbrella of a whole sequence of things yeah so I interviewed Anita artron explicit instruction I basically asked her what is the same question what is extensive instruction um if I recall correctly sure said it's two things one is it's explicit what students are going to know at the end of the lesson or the end of the teaching sequence that's really clear to both the
47:30 - 48:00 teachers and to the student and to its it's it's really clear to them what they need to do to show that they they know how to do that that's basically it and if we go into the classroom knowing what we want our students to know and what it's going to look like when they do it that puts us in a really powerful position to actually check for understanding kind of go behind that Veil we're talking about and see if we're making progress towards our Target and if we go into the classroom without those things we're kind of swimming in a world of uncertainty and Sir so the the world in urine which
48:00 - 48:30 is a special ed world is particularly enthusiastic about many of the elements around explicit instruction is that because the students need that additional frequency and dosage in instruction or is it that special Educators have got greater Stakes attached to the learning that is the students are unlikely to just progress without requiring that support it's really a combination of both so I feel that special education and a lot of the
48:30 - 49:00 teachers that we work with are general education teachers but have students who persistently struggle with mathematics but they see that okay well I need to break this down into these eight steps to help the student solve this type of math problem and that often comes through well first I'm going to model this so I'm going to like talk like okay these are the way the eight steps that we do this but then we're going to get into practice because that practices that's where students learn mathematics right so we can model all day long but
49:00 - 49:30 until students are really doing the mathematics with us they're not going to be learning the mathematics and so I feel that special education teachers have a lot of experience with students who struggle who don't know where to start or maybe did the first two steps of the problem and now don't know what's next and so they've just learned that wow through this modeling and through this repeated practice then students do learn the mathematics and so that gives them a good foundation so that they can move on and learn the next thing into
49:30 - 50:00 mathematics and the next thing and so on so yeah and you you also mentioned the issue about timed assessment yeah do you think that we underestimate the value of fluency when we talk about math learning and the ability to be able to quickly and accurately respond to uh to problems and stimulus is that part of where that comes from do we underestimate that you know I'm I'm not sure but when you bring up fluency first I think is always understanding the definition of fluency
50:00 - 50:30 right so some people when you say fluency they will go memorization right but fluency is actually doing something easily and accurately and so we need to make sure that students can first count easily and accurately and then add easily and accurately and then multiply and then find equivalent fractions and so on and so forth but with the timed assessments that just gives you a nice snapshot of how well does this student do this thing and so it and I think many times they're timed just because as Ali
50:30 - 51:00 knows because he's in the classroom and Eric and I know because we spend a lot of time with teachers teachers don't have a lot of time and so many times people will say well you want to do untimed assessments to just understand like you know how accurate the student is and yes that's true but with some of the students that we work with they might take 25 minutes out of your 30-minute intervention session to do that assessment and I feel that that's where timed assessments do come into play so let's do this for three minutes and then we're going to spend the next
51:00 - 51:30 27 minutes doing our modeling and practice so it just gives you a quick snapshot it could check in but it isn't all the data that you're ever collecting on that student so we need those brief timed assessments which are okay to do every once in a while you know maybe once a week or so on so we can check in but then you do want to spend the majority of your mathematics time really working with the students getting them to do all those practice opportunities so that they can learn the math and so Jen mentioned during in her comments that there's a need in this
51:30 - 52:00 space to ensure that the evidence base about science of math learning is too difficult to ignore or impossible to ignore Holly as a final question for both of you how how do we make the evidence based on this impossible to ignore um I think the I mean teachers care a lot about a lot of different types of evidence but in my own experience the evidence base that teachers most care about is what's happening in the in the classroom next door or what's happening in the school next door and what I've
52:00 - 52:30 seen really lauded in Australia when we talk about this transition to the science of reading has been a number of schools who following when a leaders really got convinced they go okay we're going to take this on and then their results just go off the chart and when that happens you can't deny it right you go okay what are they doing I want some of that so as soon as we get schools and this is already happening across the country in in a few schools when it starts to spread around mathematics in
52:30 - 53:00 the same way as it has around around literacy I don't think we're going to have to worry too much about what the journal articles say I think it's just going to catch on anyway Sarah how do we make the evidence impossible to ignore well I agree with Ali I think it comes to data we have an example in the United States related to reading but I believe is in 2019 the the 50 states the United States everyone released their reading data and there was only one state that saw increases and it was the state of Mississippi which uh more often than not doesn't
53:00 - 53:30 always show the best reading scores the United States but what had the state of Mississippi done they had investigate they had invested in the science of reading they had trained all teachers Statewide it was like this effort that they had done and so now everyone is saying well what is Mississippi doing we should be doing that and everyone in Mississippi says we're teaching according to the science of reading and so it's that data piece that Ali says I mean that really speaks so so much and we need to let the data do the talking and so if we get a few schools invested
53:30 - 54:00 in the science of math and we see oh my gosh look at this like 80 of their students are proficient 90 of their students are proficient what are you doing come tell us that's going to get this movement rolling some optimistic optimistic points for from both of you uh please join me in thanking Sarah Powell and Ollie Lovell [Applause] for decades CIS has been a fiercely independent voice working hard to
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