Math Ed consultant & K-8 Instruction Coach. Singapore Math Specialist. Former Zearn consultant & EngageNY/Eureka Math Curriculum Writer. Bill Walton enthusiast.
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One of the greatest math understandings an emerging middle schooler can possess is that a fraction is also a division problem. Far too many fifth graders struggle with this connection.
A girl rolls a dice and it triggers her to solve the equation 3 + __ = 9. She writes down 4 & no one is present to provide corrective feedback. All the while, the classroom possesses all the optics & trappings of joyous learning & progressive education through stations
Teacher: "Our mornings are very chill."
I nodded my head and said nothing but was left thinking. 'Why? It's the most optimal time for students to be doing the most challenging work of the day.'
My son's kindergarten teacher assigns sight words for practice. I know that some educators don't believe in sight words. What is the argument for & against this practice?
I wish that K & 1st graders were encouraged to practice addition & subtraction w/in 10 facts w/ the same urgency that 3rd graders are encouraged to practice their times tables.
Tutoring since Covid hit has helped my math teaching philosophies evolve. I've always advocated for practicing basic skills, but looking back I think I started giving in to pushback I received from teachers, administrators, & "researchers."
their times tables in 3rd grade have sailed through fraction & decimal concepts & are more than ready to take on the challenges of algebra.
Those who didn't have gradually become more frustrated with the subject & don't seem to be prepared for the rigors of middle school math.
Observed classes at a school yesterday.
EVERY class had frontal seating.
EVERY lesson was explicitly taught.
EVERY teacher taught with controlled urgency.
LUCKY, LUCKY students & parents!
@MrZachG
you would've loved it!
Actively tutoring K-5 students over the past 4 years has helped crystalize this understanding:
There is WAY too much passivity towards mastering arithmetic in the early grades. The cumulative nature of math demands ease & comfort with the following skills & ...
Enter any Elem school staff room & you’ll likely hear Ts mention Ss who don’t pay attention & follow directions well. Ask them if their S behavior is related to their seating arrangement & you’ll likely get a dismissive answer or an admission that it never crossed their minds.
For too long, I said "Automaticity of times tables is not necessary, so long as students can arrive at answers without expending too much mental energy."
This was a mistake.
There are a number of 5th & 6th graders who I've been working with for 4 years. Those who automatized
I recently worked with an advanced 4th grader who attends a private school that prides itself on 21st century learning.
When faced with the problem 27 x 17, the fourth grader had no efficient method to solve.
27 x 10 + (20 x 7) + 7 x 7...it took them over 3 minutes to solve.
A high-stakes, well-planned, directly-instructed math lesson requires deep concentration, and missing any part of it harms student outcomes
Interested in knowing - how many teachers allow their students to use the bathroom during lessons?
Calendar math is wildly popular in lower elementary grades and uses up 10-15 minutes of a 45-minute math block. I'm not against calendar math, but I don't think it warrants the percentage of math instructional time that it often occupies.
Aiming to strengthen memory might be the most over-looked aspect of elem education. Building memory doesn't need to be painful for children. Sadly, memorization is frequently stigmatized as "mass recitation" &/or "Drill & kill." The thoughtful practitioner knows differently.
If it was true that facts are unimportant & you can 'just google' anything, then people would have googled the science & know that knowledge encoded in long term memory is the basis of critical thinking. In other words they would have just googled the fact that they were wrong.
@robyn_pinilla
Not questioning anyone’s right to use their sock &/or personal days nor am I judging the teacher. They may have very good reasons to be out. I just want my child in a stable environment and to be educated and I know that both are often compromised when his teacher is absent.
Years ago, I visited a private school.
In one classroom, there were 3 adults for 20 students. The class was loud, inattentive, & collectively confused by the lesson.
I was dumbfounded that parents were willing to pay $30k+ to send their kids there.
Math instructional idiosyncrasies within a school's same grade might seem trivial, but the cumulative effects of receiving instruction in different ways exponentially increases the challenges for teaching with each passing year.
In most elementary classes I visit, there is an abundance of time spent having students collaborate in small groups, often in stations. Seems crazy to think that 2-3 minutes of this time couldn't be spent having students practice retrieving math facts with partners.
I work w/ 8 4th - 6th graders from the same school.
Each has > average intelligence, attends over 95% of school days, is raised in a home w/ 2 educated parents & puts forth > average effort.
Each also struggles with single-digit computational facts...
...Tuition is ≈ $50k
Eureka Math 2.0 is incredible!
It's taken all the greatness from the first edition & corrected the challenges to implementing it.
- Lessons are shorter
- Problem Sets are better & easier to use
- The new activities are engaging & meaningful!
@eureka_math
@amber_reid1
@marielib08
”An inquiry-based approach doesn’t work…You can’t wonder and inquire about things you don’t know.”
- Kimberly Lockhart discusses the overlap of teaching reading & mathematics.
@MmeLockhartLDSB
Her reply: "I don't like doing it that way because it's too easy. I like breaking it up."
This reinforced my belief that it's ridiculous for students to not be taught the standard algorithm. Should a child want to calculate efficiently & accurately, it's ludicrous to not arm
Walk into any American elementary school classroom – public or private, urban, suburban, or rural – and you’re likely to see an archipelago of student groups with no designated ‘front of the room.’
Yesterday, I was tutoring a third grader on the long division algorithm (2-digit dividends with 1-digit divisors). I can't imagine trying to do this virtually with 25-30 kids during the pandemic.
I'm conflicted. I have great respect for
@rastokke
&
@greg_ashman
but one of the greatest educators I've ever worked with advocates for Thinking Building Classrooms. I need to read
@pgliljedahl
's book & draw my own conclusions.
Recently, I was passing by a classroom & I heard a kindergarten teacher say, "Remember! When you see the word 'More' always add!"
I doubt that the teacher gave the statement much thought.
More important than an elementary math curriculum is an instructional shift that increases student participation.
High percentages of students routinely passing through class never engaging with content, answering questions, etc.
Recently tutored a student who was posed a problem in which she needed to multiply 2-digits by 2-digits to solve. After struggling through partial product permutations, I posed the question: "Why don't you just stack the numbers (standard algorith )?"
Thank you,
@C_Hendrick
!
"It is hard to dispute that having a self-belief in their own capacity for change is a positive attribute for students. Paradoxically, however, that aspiration is not well served by direct interventions that try to instill it.
After thinking about this for 16 years, I've concluded:
As soon as children learn the meaning of 1 more or 1 less on a number line, they should begin practicing +1 & -1 facts.
Armed w/ a strategy to solve, there is no reason to wait on committing facts to memory.
I recommend that any new or aspiring T read the following:
Teach Like a Champion
@Doug_Lemov
Practice Perfect
@Doug_Lemov
Teacher Man by Frank McCourt
How the Other Half Learns
@rpondiscio
The Truth About Teaching
@greg_ashman
The mathematics community lost a legend Tuesday morning. You might never have heard of Madge Goldman but if you've been positively impacted by Singapore &/or Eureka Math, she is a big reason why. Several decades ago, the Gabriela & Paul Rosenbaum foundation began supporting math
“I think the big news here is that it’s not totally different. Our brain’s all learn in relatively the same way.”
- Holly Korbey on why the Science of Math is similar to the Science of Reading
@HKorbey
Practicing equivalent fraction calculations without times tables comfort is exhausting & frustrating. Practicing equivalent fractions with times table automaticity is simple & can even be fun.
Highly educated parents can’t necessarily teach Math better than their child's teacher. Their advanced mental models often make it hard to deconstruct concepts. Like the hall-of-fame athlete who struggles as a coach, the great mathematician is often a poor instructor.
#iteachmath
How many instructional days did the child's T burn on conceptual understanding of multi-digit multiplication & flexible thinking, only to exacerbate this S's confusion?
In the end, the child needed to be retaught the concept a year after they were supposed to have learned it.
@MrZachG
Perfectly said, Zach! My 5 year-old plays soccer but he practices different than a professional. Your tweet reminds me of 1 of my pet peeve's - school's requiring Ts to refer to Ss as "mathematicians" during class. Not necessarily against it. I just find it a little patronizing.
I recently presented a 4th grade S with a simple multiplication problem. They proudly said, "No problem" before incorrectly distributing 2-digit numbers using what they remembered from learning the area model. As I retaught the concept, a thought kept running through my mind:
Arranging students with challenging behavior problems into independently-run learning stations defies logic.
I'm trying to decide whether or not replacing "defies logic" with "is the height of madness" is an exaggeration.
A teacher spends 2 minutes explaining the contents inside a bag (plastic frogs). Few students look at them &/or listen, no learning is advanced, & immediately after distribution the teacher buzzes around the room re-explaining the directions.
A child is given an independent practice assignment and sits for over 5 minutes doing nothing.
She is confused, disinterested, or both.
Co-teachers & a learning support specialist are in the room the entire time & nobody is aware.
This was a great listen!
Daisy Christodoulou brilliantly articulates the importance of traditional Math & Literacy instruction in preparing Students for the 21st century.
Ep 18. Education myth-busting with Daisy Christodoulou
@rastokke
@daisychristo
@kav1948mary
I observed the mistake that I described.
I don’t think it makes much sense for teachers to have students practice calculations without a system for corrective feedback. Answer keys can help with this but a station model makes it challenging to uphold. I
Far too many teachers underestimate their students' latent capacity to focus, and their own ability to build their students' powers of concentration; and, prematurely surrender to only attempting meaningful explicit instruction via small groups - most commonly through stations.
Educators are doing themselves a disservice if they don't listen to this.
S3E4: Patrice Bain on "The Room Where it Happened" via
@MrZachG
@PatriceBain1
“The big story about elementary math education is we have the majority of American students are not succeeding in math…we know in general what helps students learn more and we aren’t using it.”
- Holly Korbey
@HKorbey
Already besieged by work, very few first-year teachers would consider tacking daily journal writing onto their already strenuous workload. Too consumed with the immediacy of the next day & all the preparation it entailed, I would’ve never considered taking on extra work.
This is the best paragraph I've read in a very long time!
“It’s more important to be good ancestors than dutiful descendants. To many people spend their lives being custodians of the past instead of stewards of the future. We worry about making our parents proud when we should
I walk by a classroom during reading and hear the students getting a lot of repetition practicing letter sounds through choral responses.
I walk by the same classroom during Math & only hear the teacher's words, none of which are prompting the students to respond or practice.
One of the most consistent missed opportunities in elementary math is Kindergarten teachers not immersing their students with numbers & building fluency with single-digit computation.
Tutoring 5th graders has led me to conclude: I don't think expressing a fraction as a division equation & vice versa can be overemphasized in the middle elementary grades.
#ElemMathChat
This was a great, great episode! I don't think I've ever heard a teacher talk this articulately & meaningfully about math instruction & the balance between conceptual & procedural understanding. David Morkunas is sensational!
@DaveMorkunas
1 thing that I would like defined:
1/3 Math teacher David Morkunas
@DaveMorkunas
is such an inspiration! Check out my latest episode for more great conversation about teaching math effectively!
Ch 9 of
@greg_ashman
's The Truth About Teaching offers outstanding advice to all teachers. He also mentions educational technology "hype."
I always find it discouraging when impoverished schools have interactive whiteboards in every room, but a shortage of books.
I really enjoyed this episode!
The segment on teaching mental math strategies after the standard algorithm has caused me to rethink everything I've been trained in as a teacher and teacher trainer.
@rastokke
Last week, after tutoring a 3rd grader, I posted my sympathy towards Ts who were required to teach the long division algorithm virtually during the pandemic.
I received some sarcastic replies, some of which satired the idea of teaching the LD algorithm at all.
I considered all
Devastating decision! This ripple will be felt for a long time.
Anti-school choice advocates don't have a leg to stand on when decisions like this are made. It makes me want to enroll my son in a charter school that values basic skills.
"Students w/o multiplication tables memorized will be stopped cold when attempting multi-step problems...b/c their working memory is occupied calculating simple math facts" Important to memorize times tables!
Great article
@mikemalione
@savemathnow
Another great episode!
Stephanie simply & beautifully states - in so many words - that there are no shortcuts to getting Ss on grade level in reading.
S3E14: Stephanie Stollar on Structured Literacy that is Truly Responsive via
@MrZachG
@sstollar6
I am tutoring a girl who told me that she needed practice with her times tables. I asked if she ever practiced them in class.
"No. He tells us that he expects us to know them by now."
I think her T should provide in-class practice or at the very least recommend this website:
I was recently talking to a teacher whose class was 9% on grade level & felt obligated to do a 3-day PBL project that their administration was pusing for. The teacher felt that less than half of the students on grade level would be able to get something out of the PBL.
I recently heard a conversation between an educator & a HS student. The HS student said that he wanted to go to college, but he wasn't good at Math. The educator replied: "Not to worry. Everyone's bad at math."
The educator wasn't joking.
Sarah Cottingham & I take a deep-dive into when students should move from concrete to pictorial & pictorial to abstract representations of equivalent fractions.
@SCottinghatt
Just finished listening.
Season 3 is off to a great start!
S3E1: Tom Sherrington and Oliver Caviglioli on Instructional Coaching via
@MrZachG
@olicav
@teacherhead
On Tuesday, August 31 I will be releasing episode 21 of Centering the Pendulum. My guest will be
@Doug_Lemov
, who will discuss his books Teach Like a Champion & The Coach's Guide to Teaching.
This is a book all educators would likely find interesting. In ch 3, grant mentions the power experts have in judging whether or not an innovation is great.
@eureka_math
is wildly successful becuz it was written by many master teachers.
"There is considerable evidence that seating Students in rows facing the teacher is preferable to seating them in groups...(Wheldall and Bradd, 2013)"
-
@greg_ashman
, The Truth About Teaching
Happy to finally learn that there is research to back this up.
#iteachmath
@rpondiscio
@rpondiscio
raises an excellent point which far too many educators ignore - The pursuit of conceptual understanding MUST constantly be weighed against class time. The choice to stay on a concept longer is also the choice NOT to teach something else.
Just finished The Truth About Teaching by
@greg_ashman
. Although designed for new Ts, any educator can gain a lot from this book. This is one of the best ed books I've ever read & if I ran a T training program it would be mandatory reading.
...study it closely and then use the lesson as an opportunity to review place value, estimation, addition, subtraction, multiplication, & division, and you'll realize the LD algorithm is a beautiful system to practice all of the aforementioned.
I don't prefer or recommend learning stations as a math class structure, but if a teacher insists on using it, I always suggest that activity explanations NEVER last longer than 2 minutes.
A few weeks ago, I listened to season 2, episode 12 of
@MrZachG
Progressively Incorrect podcast. His guest was
@Miss_Snuffy
, founder of Michaela Community School in the UK. During their talk, Ms. Birbalsingh shared her rationale for requiring row seating arrangements.
"What do you notice?" is a common 'dead' question to begin early elementary math explorations. Although meant to stimulate engagement it often distracts.
"What do you notice about x?" is a more pointed question that focuses the student on the topic to be explored.
@Real_Edu_Leader
I don't think it's curriculum.
I feel like addressing basic skill fluency is something that schools, teachers, & parents need to value regardless of the curriculum being used.
A major theme of my most recent podcast touches on unprepared first year teachers. If you - or someone you know - would like to discuss ways methods for better preparing first-year teachers, please DM me!
Just finished reading The Math Gene by
@profkeithdevlin
. Great book! I found his climbing a mountain metaphor on pages 264-265 to be especially helpful in understanding why some people do and do not succeed in the subject.
#iteachmath
This excerpt from
@Doug_Lemov
's "The Coach's Guide to Teaching" addresses the forgetting curve. It's valuable reading for coaches & Ts, but also any person in any walk of life who are interested in building skills & knowledge.