Bryan Meyer

Knowing Alongside doingmathematics.weebly.com/blog/knowing-a…

Does mathematical modeling improve society? This week’s episode of Computational Conversations with @JonMcLoone youtube.com/watch?v=xwn2TZ… #computation #modeling #podcast

New High School content on the website today! flynneducation.com

@averypickford @mathillustrated Nor axioms on the goal(s) of math ed 😉

Yes, students do best when discovery is an integral part of their classroom experience. When teachers know how to set up these situations, it is effective for all students. #iTeachMath

(High) school math is so out of touch… “There is a difference: How much math is there in the CURRICULUM and college? Or how much math is there in your REAL WORK as an engineer?” cc: @conradwolfram @nctm youtu.be/MhanyR5Rfk0

@Dean_of_math I propose anyone engaging in this tired debate cite an ACTUAL lesson plan and ground their critique in actual details of the lesson.

Dear world, “Discovery learning” is not a thing. Using inquiry or PBL does not mean that students are just left to their own devices. It’s a highly intentional approach that involves a great deal of planning, assessing and growing.

@C_Hendrick What are recommendations based on #5 (performance =\= learning)? As in, what should teachers do about this in regards to assessment and grading practices?

How learning happens in seven general principles ⬇️ 1. Working Memory Capacity is Limited: Our working memory, responsible for holding and processing information in real-time, has a limited capacity. This limitation means that when learners are exposed to large amounts of new information simultaneously, they may struggle to process it effectively. Focusing attention is essential because distractions or overload can lead to cognitive strain, reducing the ability to learn. Teachers can support this by breaking information into manageable chunks, allowing students to engage deeply with smaller parts before moving on to the next concept. 2. We Learn Through Meaning and What We Already Know: Learning is enhanced when new information connects to existing knowledge. When learners relate new content to things they already understand, they create a stronger foundation for retention and comprehension. This process, known as schema-building, helps students make sense of complex ideas by fitting them into an established framework. Teachers can facilitate this by introducing new concepts through familiar examples or linking them to relevant prior knowledge, making learning more meaningful and long-lasting. 3. Novices Think Differently Than Experts: Novices often approach tasks with means-end analysis or trial-and-error methods or simple strategies because they lack the knowledge to recognize patterns or apply sophisticated approaches. In contrast, experts draw on rich mental models, using prior experiences and refined techniques to solve problems more efficiently. This difference means that novices need structured guidance to develop these mental models over time. Teachers can help by gradually introducing students to expert strategies, enabling them to progress from basic skills to more advanced understanding. 4. To Remember, We Need to Forget: Storage strength is the measure of how well information is embedded in long-term memory, indicating its durability over time. Retrieval strength is the ease with which information can be accessed from memory at a given moment, which fluctuates based on recent use and context. Unlike storage strength, retrieval strength is influenced by context and interference from other information. To remember something long-term, it’s essential to boost its retrieval strength, which can be achieved by actively retrieving the information. Unlike passive studying, retrieval requires you to recall the item on your own, strengthening memory more effectively, especially when the retrieval is challenging. This principle explains why strategies like interleaving (alternating topics) and spacing (spreading out sessions) are so effective. By allowing time for slight forgetting, these methods make retrieval harder, ultimately enhancing memory retention. This “adaptive forgetting” is crucial for retaining core concepts. 5. Learning ≠ Performance: A high test score or good performance in the classroom doesn’t necessarily mean that true learning has occurred. Learners might perform well temporarily by memorizing facts or rehearsing specific methods without understanding the underlying concepts. This principle highlights the difference between short-term performance and deep, long-term learning. Effective assessment should look beyond scores to evaluate true comprehension. The rate of assessment matters which is why regular checking for understanding is so important. Teachers can use open-ended questions, application tasks, and reflective discussions to gauge whether students genuinely understand the material. 6. Achievement Leads to Motivation: Success in learning (however small) can foster a positive cycle of confidence, self-efficacy, and motivation. When students achieve their goals, even in small steps, they are more likely to believe in their ability to succeed in future learning tasks. This sense of accomplishment encourages them to take on new challenges and persist through difficulties. Teachers can support this cycle by setting attainable goals, providing regular feedback, and celebrating incremental progress to reinforce students’ confidence and motivation. 7. Learners Are Bad at Knowing How to Learn: Many students are unaware of effective learning strategies, often relying on passive techniques like re-reading, highlighting, or cramming. These methods feel productive in the short term but are less effective for long-term retention. Evidence-based strategies like retrieval practice, spaced learning, and interleaving have been shown to improve memory and understanding, but students may need guidance to adopt these methods. Teachers can enhance learning outcomes by teaching students about these techniques and encouraging their use, helping students develop more efficient and powerful study habits. (Thanks to @MrAlexKoks for the design)

@rastokke As a HS teacher, I used to hear colleagues say this same kinda thing…blaming the middle schools. Instead, I’ve started to ask middle schools: “what are the pressures you feel about preparing kids for high school? What can we do at the HS level to lessen that for you?” Try?

On Friday, my episode is specifically focussed on the transition from high school to university math. Many students think they're prepared, but find they're not. We'll discuss what we're observing at the university level, the background knowledge that's needed to succeed, etc.

@jedediyah I can’t seem to find these (your?) machine learning resources on the page?

Instead of marking that math task, consider looking at it, finding examples of interesting student work, sharing those examples with the class, and continuing the learning. No marking. No writing. Just learning.

@BisforBerkshire Education levels probably correlate strongly with income level, as does life expectancy (I would imagine). So this seems like a map of avg income level more than anything?

Pretty startling to see how closely these maps of life expectancy and education levels track.

Years ago, @Mathowitz introduced me to Circle Tic Tac Toe. Yesterday, I decided to put a seasonal twist on it and create Spider Web Tic Tac Toe for Halloween. mathequalslove.net/spider-web-tic… #mtbos #iteachmath #puzzlingclassroom

I decided to put a seasonal twist on a classic chess puzzle to make a new Halloween Puzzle for my students to tackle as one of this week's puzzles. Can you solve the 8 Bats Puzzle? mathequalslove.net/8-bats-hallowe… #mtbos #iteachmath #puzzlingclassroom

@NolanFossum @Dean_of_math @NCTM @LatrendaK @kdykema They said the recording would be up tomorrow.

@Dean_of_math @NCTM @LatrendaK @kdykema Typically all their webinars show up under the members portal.

Today's the day! Be sure to join us for a webinar on reimagining high school #mathematics, presented by NCTM President @LatrendaK and Past President @kdykema. Spots are limited! Sign up here: nctm.link/aHqZ1

@minilek @CAgovernor Further, the 3-year curriculum should illustrate how the standard HS math content can be taught conceptually and how it is connected to meaningful issues in the world (it can integrate data science and other modern maths into the core content rather than as distinct courses)

@minilek @CAgovernor I suggest the development of a 3-year HS math curriculum that prepares students to be ready for a calculus class in their 4th year (leaving Calc open to ALL students who are in grade level in 9th grade; this is very rare now).

Today I spoke at a joint oversight hearing by the Assembly Committee on Ed and Higher Ed about math education requirements for university admission. It looks like the @CAgovernor office has some explaining to do.

@DavisTeaching I know there will be problems with all such tests, but I still think it would be a huge improvement for someone to create a prototype of a new exam that reflected the modern needs of high school mathematics education (and allowed much fuller access to all types of tech tools)

@DavisTeaching It’s wild to me how many people accept the test as the driver of policy and practice. There was a large opt out movement a while back (which I think got squashed because they started monetarily penalizing districts?); we need something like that again.

Standardized testing is one of the biggest shams in education. Every conversation derived from it is as meaningless as the arbitrarily-, ill-, & poorly- defined and constantly moving target that testing is - a din of nothingness, nonetheless endlessly destructive

@minilek @tomloveless99 All Boaler stuff aside, it is a weird claim to say something needs improving so that we can bomb people and extract resources from the earth.

Math-Ish also continues to claim 2.8 years of learning from a 4-week youcubed summer camp, which has been repeatedly debunked by @tomloveless99 (see e.g. ams.org/journals/notic… and educationnext.org/californias-ne… -- someone from youcubed responded at educationnext.org/stanford-summe…)

@TracyZager Crazy how much this aligns with my own personal and professional experiences. Thanks for sharing! For whatever it’s worth, I’m wrestling with the same questions. Wish I was at the conference to connect with you. Hope a path emerges for you…and happy to connect any time. ❤️