Make Math Moments Academy › Forums › Full Workshop Reflections › Module 1: Introduction To Making Math Moments That Matter › Lesson 12: The 3Part Framework & Two Groups of Students › Lesson 12: Discussion Prompt

After watching the video in Lesson 12 answer:
What are the characteristics of students in
 The “good at math” group
 The “poor at math” group; and,
 common amongst any in both of these groups?

“good” seek understanding, fast thinkers, multiple strategy approach to a problem
“poor” slow thinkers, struggled to understand, single strategy approach to a problem
common among many in both groups: want to understand, are capable of doing the mathematics, want positive feedback, trouble thinking on their own

Good at math: Willing to try, not afraid to make a mistake, willing to talk ideas out with group members
Poor at math: afraid to be wrong, so therefore will not attempt, thinks asking for help is a sign of weakness
Common in both groups: The both know more than the think

Love the commonality you shared! So true… students are constantly doubting when they are full of ideas, tools, and strategies that they can use to help them problem solve.


Both:
Want high grades to impress parents/peers
Good at answering teacher questions (as questions are targeted and differentiated)
Could have neat workbook
Could be competent at other subjects (knowledge is domain specific)
Unresilient (even some top pupil struggle when first reach a challenge)
Good student:
Motivated
Attentive
Good prerequisite knowledge
Can follow instructions
Retains most of new knowledge practiced in class
Clear workings shown with an understanding that method is equally important as the solution
Poor student:
Unmotivated
Poor attention
Poor prerequisite knowledge
Struggles to follow simple instructions
Can do many of tasks in class but struggles to retain most of new knowledge practiced in class
Thinks the only important thing is the answer

Thanks for sharing! The commonality that jumped out at me was the lack of resilience that both groups tend to demonstrate. We often get tricked into thinking that some of our successful students are resilient, however when we challenge them, they quickly shut down – sometimes throwing more of a stink than students who have struggles.


“Good At Math Students”:
are confident
have good problem solving strategies
have a growth mindset
know how to advocate for themselves
have been successful in the past
“Not Good at Math” students:
lack confidence
struggle with solving
do not feel successful
have a fixed mindset
struggle to ask questions when stuck
easily shut down
can be behavior problems in class
are difficult to engage
Students in both categories:
need support
deserve good and thoughtful feedback
are students who deserve the best from the class
are capable of learning

Great list here!
Something I often ask during this lesson is about whether some of the items listen in the “not good at math” group might also apply in the “good at math” group? In particular, do we have enough information to know for certain?
Often I find that I make assumptions about the “good at math” group simply because I haven’t witnessed characteristics that I see in the “not good” group. Then I wonder whether I’ve ever put the “good” group through a similar level of struggle as compared to the “not good” group. What are your thoughts?


Good at math group: often like routine, are good with math facts, like to please others/adults
Poor at math group: often need more wait time; may not respond to the routine, may not see the point, maybe asks a lot more “what if” questions that seem off topic to most people
Common: want to feel good about class, a mix of introverts (like to follow step or just be left alone) and extroverts (in a group setting wanting to share their thinking/wanting to just talk)

I don’t like the stereotype… I feel similarly to to Amalia.
I used to think that to be good in Math meant to answer questions quickly and correctly all the time. I was not good at Math: I learn slowly and ask questions about my learning. Now, I think that deeper learning is more important. I also think many of our students are not so quick in mastering western learning styles. I work with Indigenous students and their families, many of whom are very adept in Math and in traditional ways of knowing, often times not computing with their nonIndigenous teachers.
All children are good at Math, at problemsolving and helping each other to be “successful”… the problem is not that children are grouped in either “good” or “not” categories… all belong in the middle (in my mind). The issue is that someone or the system slowed their learning down…maybe to a crawl. Providing interesting, openended, nonlinear, nonproceduredriven experiences is the key here. Unfortunately, too many of us have spent our lives working within a safe box, and so are unprepared to take the risk that students can solve problems to great depth and breadth if we just let them do it. Parents and teachers sometimes are the worst offenders for inculcating procedural, onesolution, doitmyway thinking… not what we need as a model for 21 Century learning.

The “good ” math students have good memorization and recall skills . They come to me with good math skills. They are good rule followers. They may see math the same as the teachers. “Poor ” math students do not share their ideas so they are not validated.
They both want to succeed and they both may not remember things long term.

good at math: established habits of perseverance/growth mindset, accustomed to praise/success, outspoken/confident
poor at math: gives up easily, not articulate, gaps in automaticity/understanding
common: curiosity, positive feelings after successful moments

Interesting Venn Diagram because I have seen students transfer from one end to the other through out the year. For example, Students will show qualities of a Bad math student during linear functions, but will then show qualities of a good math student during quadratics.
Good Math Student Group:
 Can Solve, justify, and model problems
 Faster at calculations
 Family support is strong
 Will lead discussions and have higher engagement in small groups
 Will Question
 Learn from Failures
Common Math Student Group:
 Can grow to be better math problem solvers
 Have ideas to share
 Desires Success
 Love Positive feedback and needs encouragement to thrive
Bad Math Student Group:
 Get stuck when multiple steps/calculations are involved
 Fear of Mistakes
 Dwell on failure
 Not likely to ask questions
 Fear of perception of their intelligence

I think it’s worth mentioning again that which students are in which group often comes down to teacher perception, along with the characteristics that we use to classify them. Many times how we would classify students isn’t how they would classify themselves.
“Good” math students: complete the homework, good math facts recall, compliant
“Bad” math students: don’t do the homework, struggle with mental math
Common to both: a desire to be successful. Nobody wants to fail at something, but the traditionally “bad at math” students have had so little success that they’ve often resigned themselves to that fact and so can appear apathetic.

So true @nathanvaillancourt We’re the ones putting the labels on them based on our own definitions! It’s good we recognize this!


Good at math:
– they get it, understand some important relationships of concepts
– they have built confidence in their math abilities, see themselves as a math person
Poor at math:
– have not engaged in the mathematical processes
– do not understand the math instruction and examples
– missed some needed background
– think they are simply not smart in math (not a math person)
Common to both:
– intellectually capable of understanding
– both groups benefit from concrete models and visual representations of math concepts
– both benefit from taking steps from what they already know to extend to a new problem

Good at Math
 able to follow algorithms
 know their math facts
 can manipulate numbers
 confident
Bad at Math
 can’t use or follow steps in an algorithm
 don’t know their math facts
 struggle working with numbers
 easily frustrated
Common to Both
 use strategies to make sense of numbers
 want to do better in math
 can see math in a visual way
 become embarrassed if they don’t understand a math concept
 love praise and feedback
 This reply was modified 11 months, 2 weeks ago by John Gaspari.
 This reply was modified 11 months, 2 weeks ago by John Gaspari.

Good at math:
• High logical thinking.
• Confident solving problems
• Confident to be able to understand things after if they don’t understand at the first time.
• Don’t afraid to solve problems
• Understanding deeply the rules of math.
Poor at math
• Difficulties or very slow understanding logical things.
• Not confident with new math situations.
• Not confident to be able to resolve problems
• Not interested in math.
• Difficulties to maintain the concentration.
• MÀGIC THINKING: they don’t understand the rules or they don’t feel able to understand them, So, they just memorise the rules and they use them if they remember, if not, everything are possible to do.
Common characteristics
• They can be hard workers or not.
• I’m sure that their brain is really similar so they should be able to learn math.
• Both are in the trouble of teenager.

Hey @laura.las heras ruiz Good list here. I feel that this one:
MÀGIC THINKING: they don’t understand the rules or they don’t feel able to understand them, So, they just memorise the rules and they use them if they remember, if not, everything are possible to do.
might belong in the both column. I was a memorizer and had a hard time understanding what I was doing, but I was considered good at math.


Good at Math confident problem solvers, motivated and devoted, has grit, hopeful
Poor at Math not confident problem solvers, vocabulary and previous concepts are weak or nonexistent, gives up quickly, no grit, no hope, does not see a purpose in learning math
Common both make mistakes, both need to solve problems to learn, both need to ask questions and be curious, both need to actively listen, both need to struggle to learn

Both
 Practice
 Take notes
Good
 Practice & correct mistakes (check answers)
 Make note of what they don’t understand to review or ask for help later
 Attempt a solution
 Ask questions when unsure
Bad
 Practice, but don’t check answers – or don’t correct if checked and wrong
 Give up without trying
 Sit quietly when struggling
I tried very hard to keep external factors out of this list (family support, health.. etc). Also, if I could think of a counterexample student, I’d leave it out (Bad – don’t know math facts; I know some very smart math kiddos that are poor at their multiplication facts). Much of what I listed fits more into Good/Bad students rather than Good/Bad @ math.

There’s a lot of good ideas on here. I’m more interested in the common attributes of both types of students, as I’m hypothesizing that we will learn to use that to our advantage. So from what I can think of, both groups have the following in common:
– Enjoy talking about personal interests
– Enjoy making decisions that have consequences (ex. gamification)
– Show most growth when working within their zone of proximal development

Good at Math: Number sense, see a purpose for Math, confidence, parental positivity and support, organization and structure, mindset of overcoming failure in order to try again.
Poor at math: avoidance tactics, lack of confidence, lack of prior knowledge, very little grit and perseverance, lack of organization
Both: curiosity at the beginning, influenced by prior experiences with Math, established mindsets–whether good or poor and ageappropriate learner characteristics

Thanks for the great share!
I wonder re: good at math and number sense… is it known facts or is it a true ability to reason with numbers (or maybe both?)


“Good” like rules, can and will memorize and apply them.
“Bad” think that they’re missing the “magic math gene”, it’s not likely they feel, that they can learn, so they copy each other,the teacher, the internet.
Both groups want to succeed, find the right answers.

As a coach, I hear teachers talk about their high school students not knowing their multiplication tables, and listing that as a reason students can’t factor quadratics. Or, “they can’t add and subtract, so we can’t work on solving equations.” It’s a perception I’m starting to call the “math as a stack of bricks” mentality: if an earlier brick is missing or weak, you can’t stack anything on top of it.

I’m taking this course as a coach. I taught the way you encourage teachers to teach, because I was trained in the way of Magdalene Lampert, Deborah Ball, and “that kind of teaching”. Now I manage a team of 13 teachers in grades 712, and I’m trying to figure out how to change their minds about math and math class. How do you get teachers to see themselves as the droning teacher in the meerkat video….and then do something different?

Good at Math: Work quickly, generally don’t want to be wrong, work better alone, are better at completing rote practice problems
Bad at Math: Work slowly, dread going to math, anxiety about testing, have many missing assignments,

Good at math: Seek understanding, not afraid to fail, motivated, multiple strategy approach to a problem
Poor at math: Afraid to fail, struggles to understand, unmotivated, single strategy approach to a problem
Both: Want to understand, are capable of doing the math, want positive feedback

Good at Math: work hard/persevere; answer questions in class; ask questions; feel confident in their abilities; have good number sense; want to understand why things work the way they do
Poor at Math: give up easily and get frustrated; don’t like to speak up in class; afraid to ask for help; have trouble making connections; just want to be told how to do problems
Common to Both: Want to do well; don’t like to make mistakes; think there’s one right answer or way to do things in math
 This reply was modified 2 weeks ago by Kerri Brodie.

Thanks for sharing your ideas here with the group!

“Good” – Know their math facts, fast at math, can follow procedures, rules
“Poor” Don’t have math facts memorized, slower at math, get confused or can’t remember rules
“Both’ Math applicable to both, curiosity, like to have fun

Good points! I resonate with the characteristics you shared.