Make Math Moments Academy › Forums › Full Workshop Reflections › Module 1: Introduction To Making Math Moments That Matter › Lesson 1-2: The 3-Part Framework & Two Groups of Students › Lesson 1-2: Discussion Prompt
AdministratorMay 1, 2019 at 11:39 am
After watching the video in Lesson 1-2 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?
MemberJanuary 28, 2021 at 3:18 am
“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
MemberJune 3, 2021 at 11:39 am
I suppose what I am hearing you say is that if the “Poor” can speed up their thinking, take advantage of the struggle to understand, and seek multiple strategies or approaches to problem solving, they can become “Good”. I am liking that. Thanks for your contribution.
MemberJanuary 28, 2021 at 4:30 pm
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
AdministratorJanuary 29, 2021 at 6:47 am
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.
MemberJune 7, 2021 at 2:57 pm
Exactly!! I wish that students and parents would understand that being “good” at math is a choice that they make by having the right attitude about it. They have to be willing to try and they have to be willing from their mistakes.
MemberJanuary 29, 2021 at 11:29 pm
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 pre-requisite 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 pre-requisite 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
AdministratorJanuary 30, 2021 at 6:30 am
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.
MemberJanuary 31, 2021 at 10:17 pm
“Good At Math Students”:
-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:
-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:
-deserve good and thoughtful feedback
-are students who deserve the best from the class
-are capable of learning
AdministratorFebruary 1, 2021 at 7:16 am
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?
MemberFebruary 1, 2021 at 4:54 pm
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)
MemberFebruary 1, 2021 at 5:54 pm
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 non-Indigenous teachers.
All children are good at Math, at problem-solving 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, open-ended, non-linear, non-procedure-driven 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, one-solution, do-it-my-way thinking… not what we need as a model for 21 Century learning.
MemberFebruary 1, 2021 at 7:37 pm
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.
MemberFebruary 1, 2021 at 9:12 pm
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
MemberFebruary 3, 2021 at 12:36 am
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
MemberJune 2, 2021 at 6:28 pm
My takeaway from your post is the family support. I have seen a student that became a new person every time she spent her weekend with the father.
MemberJuly 1, 2021 at 2:59 pm
Mental math – this one I’ve had the experience myself – I’m really good at math, but mental math (if you mean add, subtract, multiply, divide, etc. on the spot), I can’t do that.
*I’ve tried, but am not good at all (I think it’s that part of my brain – memory, or quick thinking) maybe affected by my epilepsy?
but I’m great at problem solving (am even a graduate of computer science)
*I don’t think quickly, but I get the concept, and can think through a problem.
Give me a calculator and I then can work at the speed of the others in a group.
I suppose it depends on your definition of what “mental math” is. Maybe I’m misinterpreting.
- This reply was modified 3 months, 2 weeks ago by Velia Kearns.
MemberFebruary 3, 2021 at 8:21 am
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.
AdministratorFebruary 5, 2021 at 6:30 am
So true @nathan-vaillancourt We’re the ones putting the labels on them based on our own definitions! It’s good we recognize this!
MemberJune 2, 2021 at 6:33 pm
True. I once went to the principal to express my gratitude for finally having student with both high IQ and EQ. To my surprise, the principle said the numbers I was referencing were the students’ locker numbers. Perception is powerful.
MemberFebruary 3, 2021 at 10:48 am
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
MemberFebruary 3, 2021 at 8:15 pm
Good at Math
- able to follow algorithms
- know their math facts
- can manipulate numbers
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
MemberFebruary 7, 2021 at 4:49 pm
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.
• 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.
AdministratorFebruary 8, 2021 at 5:59 am
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.
MemberFebruary 8, 2021 at 11:07 pm
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
MemberJune 4, 2021 at 3:56 pm
I was having trouble trying to figure out what both categories have in common. Your post helped me see it: they are both problems solvers, they both make mistakes, they both struggle with the new learning. Thank you.
MemberFebruary 9, 2021 at 3:36 pm
- Take notes
- 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
- 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.
MemberFebruary 9, 2021 at 8:14 pm
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
MemberFebruary 12, 2021 at 9:32 am
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 age-appropriate learner characteristics
AdministratorFebruary 13, 2021 at 7:15 am
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?)
MemberFebruary 14, 2021 at 2:14 pm
“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.
MemberFebruary 16, 2021 at 2:49 pm
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.
MemberFebruary 16, 2021 at 8:15 pm
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 7-12, 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?
MemberFebruary 24, 2021 at 1:31 pm
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,
MemberMarch 1, 2021 at 4:03 am
Good at Math
- Volunteers answers
- Good memory/knows math facts
<i class=”” style=”background-color: transparent; font-family: inherit; font-size: inherit;”>Bad at Math
- Reluctant to speak out
- May not have automatic recall of math facts
Common to Both
- Wants to understand
- Struggles when faced with an unfamiliar challenge
- Enjoys feeling successful
- Fear of making mistakes
- This reply was modified 7 months, 2 weeks ago by Selena Gallagher.
MemberMarch 1, 2021 at 12:24 pm
I believe that students who are ‘good’ at math are the ones who are interested. They pay attention, take notes and ask questions. They complete the assignmnets. Students who believe they are not good at math have just not put in the effort to learn, have low conceptual understanding and have lost interest. These kids no longer have a growth mindset and just beieve that they are not a ‘math person’. Both groups are capable of being successful with support!
- This reply was modified 7 months, 2 weeks ago by Tracey Long.
AdministratorMarch 2, 2021 at 6:37 am
While I understand / agree with this at a high level, when we zoom in we should be cautious to default to believing that students who aren’t successful just aren’t interested or won’t put in the effort. Often times there are outside factors that cause that disengagement. So not putting in an effort is often a symptom not a cause.
MemberJune 2, 2021 at 6:45 pm
I suppose you are right. Students that are interested in the story. We as educators will have to tell fascinating stories, if we hope to keep our students from falling asleep, like the meerkat in the video.
AdministratorJune 3, 2021 at 7:16 am
For sure. I think about when we are in conversation at a party (what are those? Its been so long due to covid)… you try to find engaging topics to discuss with a group of friends rather than just making boring statements sharing facts from your life. We need to try and draw students in this way as well.
MemberMarch 2, 2021 at 6:30 pm
“Good at Math” students are engaged, they persevere even when learning is hard, they have achieved some level of success, they can connect what they are learning to prior experiences, collaborate and build on others’ ideas.
“Poor at Math” students are often confused and disengaged, and have experienced shame or embarrassment due to their failure to understand.
Characteristics that are common to both groups: you can have any type of behaviours in both groups, including hard-working, quiet, loud, neat, messy, etc.
MemberMarch 8, 2021 at 12:21 am
Characteristics of a good maths student: Persevere even when things are hard., Engaged, Curious, Think deeply about Maths
Poor at maths: Give up easily, Don’t engage, Find things easy and so they think that they are too good really complete the task, Slow to try, Simple single strategies, I am done – tick
Common: They want to be able to do math. To feel successful
AdministratorMarch 8, 2021 at 6:42 am
We always ask our math moment maker friends why they think some students land in that “not good at math” group? Are these characteristics something students bring to math or did math bring them out in the student?
MemberMarch 15, 2021 at 10:02 am
Good at math:
- willing to explore mistakes & why they don’t work
- see math as relevant and enticing
- willing to consider alternative viewpoints and strategies – develop their flexibility
Poor at math:
- afraid to make mistakes, mistakes reinforce their ideas about their lack of ability
- tend to stick to memorized procedures and lack flexibility, number sense
- have strong negative emotions tied to mathematics (fear, anxiety, hatred)
- when released from the mindset they’re stuck in (when they start believing in themselves) can make spectacular gains
- have the potential to achieve math at a high level
- benefit from reinforcing the idea that math is evident in all aspects of life, that math is relevant to them, and that everyone can achieve in mathematics
MemberMarch 21, 2021 at 12:14 am
Good at math: love math or at least don’t mind it; things come easily; growth mindset; feel like a valuable part of the class; willingness to share ideas with class/group
Poor at math: give up quickly; hate math; more “failures” than “successes”; fixed mindset; don’t feel valued by teacher or classmates; unwillingness to share ideas with class/group; don’t recognize what they don’t know
Common in both: want positive parent contacts; don’t like making mistakes; share common interests outside of school; hesitant to show complete work (“I can do it in my head so why do I need to write it out?” “Why waste my time? It will be wrong anyhow.”); don’t want to be/appear different than peers; want to know when they do something well
MemberMarch 31, 2021 at 2:51 pm
I have attached the 1.2 Task Placemat also.
Good: like math and are confident with math and problem solving
Poor: many gaps in learning, not confident, don’t like math because they think they are bad at it
Common: have trouble advocating for themselves, ability to learn, different ways of learning
MemberApril 17, 2021 at 7:23 am
Characteristics of students who are good at maths
Language rich – strong readers and writers
Visual / Audial learners: can effectively listen, watch and understand
Compliant learners: get stuck in, get the work done, do the HW
Some like Maths and see themselves as good at it
“Get it” quickly – it just clicks for them
Characteristics of students who are not good at Maths
Struggle to read and interpret worded problems
Struggle to communicate mathematical ideas in writing
Get distracted, side tracked, don’t use time efficiently
Don’t do HW
It doesn’t make sense, doesn’t click easily, try to remember by rote rather than true understanding
See themselves as bad at Maths
MemberMay 7, 2021 at 11:51 am
I have struggled with this activity for the past several days because I don’t put my students into such categories, so I wouldn’t know how to define each. I have students that make teaching a challenge (which I welcome most times) and ones that are a breeze (but at times it’s hard to know exactly what they are thinking). So most don’t fit into a “stereotype”. I prefer to see each of my students as individuals with limitless potential.
AdministratorMay 7, 2021 at 10:37 pm
That is fantastic to hear! The goal of this reflection is to bring out some of our learned biases about students who seemingly excel and those who tend to struggle with mathematics…
One of my biggest realizations was that I had assumed those students who were achieving at high levels in my classroom had resilience when in reality, I was simply not pushing them to productively struggle.
MemberMay 12, 2021 at 9:11 am
Students who are good at math:
*Are typically also good at other subjects.
*Are good at memorizing steps and algorithms.
*Are typically unafraid to ask for help.
Students who are poor at math:
*Take more time to process.
*Struggle with retention of steps and algorithms.
*Typically struggles to ask for help.
*Tends to shut down when the math gets too difficult.
Students from both categories:
*Want to get the answer right.
*Want the take the “easiest route” to get there. I’ve noticed both groups don’t enjoy a challenge.
*Need and want encouragement and positive feedback.
*Want to know how the math is going to apply to their life. That age old question of, “when are we ever going to use this?”
AdministratorMay 12, 2021 at 9:15 pm
The part that resonated with me the most from your reflection is that both groups don’t enjoy being challenged. I noticed this quite a bit in my classroom and realized it had a lot to do with how we had essentially done all of the thinking for them in mathematics. Once they are nudged to think, that willingness for a productive struggle comes and they almost thirst for it!
MemberMay 17, 2021 at 5:36 pm
I think my good math students are quick with computation, follow directions and rules
I think my poor at math group are slow with computation, easily confused by rules, poor reading and comprehension skills.
Both groups want to learn and succeed, like to have fun, enjoy praise
MemberMay 19, 2021 at 9:01 pm
Good math group: Tend to enjoy the subject, and are engaged. They also have strategies to help them be successful, and generally have strong attendance and attitudes towards school.
Poor math group: Often lack engagment, and confidence in math. Can be unwilling to participate, and often have poor attendance.
Common: Both groups really want to do well, and both groups have the potential to do well!
I find that both groups often have family members who will tell them that math is challenging, or that they were not successful with math when they were in school.
MemberMay 28, 2021 at 5:01 pm
“Good at math” students have usually had positive experiences in doing math. Many of them are quick at calculating.
“Bad at Math” students have often had negative experiences in math classes and may be slower in calculating.
All of the students have friends and families. They like their phones. Many of them have jobs. They like music, sports, cars, or other things.
MemberMay 28, 2021 at 9:50 pm
Good: confidence, take risks, ask questions, learn from mistakes, can use multiple concepts simultaneously or apply what they know to new areas.
Bad: silent, don’t read word problems, cannot apply to other topics, low confidence
Both: have interests/challenges/successes outside of math class, may have math anxiety, want to be successful, want to be engaged
MemberMay 30, 2021 at 3:17 am
Good at Math: Approach problems with different aspects, seek challenges,
Poor at Math: hesitant to try somethig different, need visual or hands on support(manipulative), give up easily
Commonalities: make mistakes,
AdministratorMay 30, 2021 at 6:51 am
Thanks for sharing!
Based on these characteristics… how many in our classrooms have typically had those “good at math” characteristics? I know for me, even my “good at math” students typically didn’t enjoy a challenge or push themselves… they just really enjoyed mimicking and knowing the answers quickly.
We will learn how to make changes in the workshop so that all students feel successful in math class and are seeking out a challenge!
MemberMay 30, 2021 at 11:31 am
My perspective is that of a secondary math teacher teaching often quite senior-level math courses at the academic level.
Note: The two lists are best viewed alongside each other, e.g., items 2, below, growth mindset vs. fixed mindset.
Good at Math
- view math as a set of tools
- growth mindset
- struggle is often necessary and accepted
- many ways to solve the problem
- can identify erroneous solutions easily
- has ways to check answers
- math is a process
- confidently and consistently uses math principles
- does the homework
- high level of understanding; easily explains reasoning
- views math as a building process of interconnected skills, regularly uses prior learning in new tasks
- understands units, scientific notation and rounding
- uses calculator correctly (order of operations)
- has strong reading/writing skills; can do word problems
Poor at Math
- math as algorithm
- fixed mindset
- struggle is bad
- one way to solve the problem (the teacher’s way so alternatives proposed by others, e.g., peers, tutors, parents, must be invalid)
- accepts their answer regardless of whether it is sensible or not
- doesn’t know how to check the answer (other than to re-do then often repeating the same mistakes)
- math is about the answer
- confidently applies malrules, e.g., adding two negative numbers gives a positive outcome; inconsistently applied math principles
- does little/no homework
- little/no understanding; has difficulty explaining reasoning
- views math as a set of independent tasks, little use of prior learning in new tasks
- inconsistently uses correct units, scientific notation or rounding
- makes frequent calculator errors (incorrect order of operations)
- has difficulting with reading/writing skills; gives up quickly on word problems
- lacks persistence; gives up easily
AdministratorMay 31, 2021 at 8:07 am
Great share here. When I picture the lists side by side as you mentioned, I can envision a continuum and I could see different people falling on different places along that continuum.
MemberMay 31, 2021 at 11:12 am
MemberJune 1, 2021 at 12:11 am
Good students: Have a lot of background, feel confident, want to get right answer
Struggling students: Want to get right answer, lack confidence, lack background of success. Have skills, but may not know how to deploy them.
Both: want to do well, at risk for tuning out if bored or frustrated, may not see connection to prior math or real world
MemberJune 2, 2021 at 6:54 pm
Your post brings to mind, the concept of self fulfilling prophecy. Confidence beget confidence and lack of it beget distructive struggle.
MemberJune 1, 2021 at 11:39 am
I would say that the difference between “good” and “bad” at math is mostly due to the mindset of students and those around them.
Those that are “good” have had positive experiences in the past, were told they were good at math, and/or had parents that recognized and encouraged the importance of math. This led them to engage more fully in math tasks, be willing to practice and reason, and created a greater confidence in their ability to use math.
Those that are “bad” at math have gotten used to being told that they aren’t good at math, or have a support system that falls into the “some people just aren’t good at math” mindset. This has given them the chance to not engage as fully (why engage if you just can’t do math?) which has created gaps in understanding.
Between both groups, I have found that they thrive when lessons are based around understanding and accessibility, may look for the easy way out, need to see success to be willing to continue with struggle, and worry about failing at completing a task.
MemberJune 1, 2021 at 2:51 pm
I enjoyed ready your response. I do agree with what your stated.
MemberJune 1, 2021 at 2:47 pm
Wow. This is challenging for me.
For the “good” at math: successful with math tests/homework; grades are important to the student
For the “bad” at math: unsuccessful with math tests/homework; can appear to be lazy; read poorly
For both: slow workers; draw the problem before working on it
AdministratorJune 2, 2021 at 7:13 am
Definitely a challenging task here especially since the purpose is to show that actually many students come with similar characteristics … some hide those characteristics and others don’t reveal a characteristic (like disliking struggle) because we haven’t challenged them enough to see it. Overall, our students are just students and many come with the same assets (and challenges).
MemberJune 2, 2021 at 9:58 am
“good” show a willingness to try, a willingness to fail, display confidence, are faster computers (e.g. know their math facts and can arrive at an answer quickly) as compared to the “poor” who show less effort, have a predetermined outlook “I’m not good at math” that becomes a self-fulfilling prophecy, slower computers (may not know or understand their math facts), slower to grasp concepts (may need more processing time) and ALL students are capable, curious, intelligent and HUMAN
MemberJune 2, 2021 at 6:20 pm
Good @ Math students:
They tend to have prior knowledge or a good foundation:
The have Fluency and Parental support that are obvious.
They are eager to impress the teacher.
Poor @ math students;
They have been socially advanced and have not experienced productive struggle.
They tend to be shy and hadly want the attention
They experince low family support.
They are both from socioeconomical background.
They buy into the idea that there is math gene.
They are product of their environment.
MemberJune 5, 2021 at 1:49 pm
Azuka – I feel you on the parental support/mindset. That was one of the first things that came to my mind, and it is what I can see among my friends as well. Growing up education and in particular math/science was considered to be our “inheritance” while other friends had parents saying that they “didn’t get it” when it came to their math homework. I don’t really remember getting help very often for math homework, but I remember the support and the parental attitude towards it.
MemberJune 2, 2021 at 8:24 pm
Good math group students are students who have good mental math/numeracy skills. They are good communicators and have good recall memory. They are literate.
Poor math group students are students who have trouble visualizing math, and don’t understand why they need math or see its validity or relevance to their own lives. They have poor literacy skills.
Common amongst both groups are that they both tend to have trouble thinking on their own (need help to get started). They are usually unwilling or shy to get started and “play” with a problem unless given specific instructions/directions. They want to succeed/pass and are afraid to make mistakes.
AdministratorJune 4, 2021 at 6:59 am
That is a key point we notice and hear all the time about struggling to think on their own. One thing we’ve realized along the way is that our lessons that were fairly traditional for many years didn’t give students the opportunity to think… we spoon-fed everything and thus students didn’t know HOW to think. We will explore how we can change this in our math classes as we move forward.
MemberJune 3, 2021 at 12:34 pm
“Good” math group- usually compute quickly; able to apply skills to problems that look slightly different; Enjoy challenging themselves and productive struggle; have confidence that they will be able to succeed.
“Poor” math group- Easily frustrated; unwilling to take risks that they may be wrong; often successful when new problem is identical to given models; want steps or formula to solve.
Both- want success; Respond to praise
AdministratorJune 4, 2021 at 7:01 am
I find that most students in both groups get frustrated easily when they are challenged… the difference is that our “good at math” group tends to have enough understanding that the math isn’t challenging enough to cause that struggle…
MemberJune 3, 2021 at 6:38 pm
I filled in my diagram and then read through the earlier posts to find that my diagram didn’t much differ from those of the majority. The thing that stood out to me though, was that as I was reading through the lists, students kept coming to mind who did not fit the ‘mold’ or whose ‘label’ would change day to day.
There were several comments in previous posts about preconceived notions and judging students without truly knowing what they are thinking or what they are capable of doing. While I would love to say that I never do this, I can’t, not honestly. I can say that I work every day to be conscious and aware so that I am not putting kids into boxes – because they can read how the teacher thinks and feels about them. Then they act accordingly.
Keep an open mind and believe the best of each kid every day when they walk into the room. Everyone wants to be a “good” student – it’s our job to give them every opportunity and the support to get there.
AdministratorJune 4, 2021 at 7:03 am
This is a great reflection and I think the style of lesson we are teaching can dictate whether we will be judging preemptively or not. Get those students problem solving and use that time to understand where they are all entering from and now to nudge them forward. Thanks for sharing!
MemberJune 3, 2021 at 7:51 pm
Good – comes naturally, likes to memorize (although CAN lead to problems), risk taker
Poor – afraid to ask questions, missed a previous concept – feels people will laugh at them – not a risk taker – wants the answer to be right the first time
Middle – wants to understand, wants to apply, continues to persevere
MemberJune 4, 2021 at 3:54 pm
Good at math:
Open to making connections between new things and things they already know to internalize the learning
Perseverance to continue with a task even if it involves hard work
Not afraid to make mistakes
Poor at math:
Afraid of making mistakes
Afraid of being judged by peers or teacher
No perseverance to continue when the work gets tough or it takes longer than one step to get the answer
Foundational gaps that make new learning even harder
What they have in common:
I am having trouble in this area, as I see these categories as opposing each other.
MemberJune 4, 2021 at 3:57 pm
(sixth grade) Good math students: smart, fast, get answers quickly, like the class, pay attention, either understand the “why” or don’t really care why as long as it works
Poor math students: slow, hate math already, want to see examples with “easy” numbers before moving onto how thing work with harder numbers, they want to understand the why it works and the why they need to know this, they give up before they even get started
Both: Want to be good math students and to understand math, they want math to be fun and not the same old repeat – homework-review- new stuff- examples-homework and every 4-5 days throw in the quiz….
AdministratorJune 5, 2021 at 7:36 am
Thanks for sharing!
Something that might be worth considering is keeping that floor low (using manageable numbers) for all learners to develop a concept prior to the numbers being more challenging / harder to manage. This can really allow you to get to the concept vs. Getting distracted with procedures early on.
MemberJune 5, 2021 at 1:59 pm
I teach middle school (6-8).
“Good” at math students tend to…
- have parents that have a positive attitude towards math. They may be educated themselves or more involved in their child’s academic life than others, or just with the positive attitude.
- have a higher attendance rate, and therefore less gaps in learning.
- be “rule followers” that are comfortable using an algorithm more than they are creating their own, at least at first.
The “poor at math” group tend to …<div>
- have parents with a negative or ambivalent attitude towards math or maybe even academics in general. They start the parent-teacher conference by saying that they never got “this far” (6th grade – 8th grade) in math or that they farm out any math questions to the older sister/brother and can’t help their child with questions they might have.
- have a lower frustration tolerance.
- have gaps in learning, sometimes relating to issues with attendance either in the current year, past years, or both.
- struggle with multiple steps – they enjoy doing simple arithmetic, but struggle with order of operations problems or any type of word problem that has them do more than one thing.
Both groups have …</div><div>
- human dignity.
- parents/guardians/others that care about them and want them to succeed.
- the capability to learn and do math.
- a need for feedback.
- to be pushed in order to have that productive struggle.
MemberJune 5, 2021 at 8:43 pm
“Good at math” just means the student got the right answer. It does not necessarily mean they grasped the concept. For many, it just means they know when to apply the rules. For example, the class was learning how to multiply by 10, 100, or 1000 and therefore the next test will be about that. Student learns to add zeros on test (or move the decimal point) but does not truly understand the why behind it, place value.
“Bad at math” means they didn’t get the right answer. Unlike the other group, they don’t “blindly” follow a rule.
Common amongst any in both these groups: the concept is not understood . (Speaking for myself) the content was taught without context. There is little purpose/point to the lesson. It’s like teaching students vocabulary without explaining meaning.
AdministratorJune 6, 2021 at 8:55 am
Great reflections here Rachelle. In the next lesson we’ll look more about how we can at the overlap and work towards teaching with context!
MemberJune 6, 2021 at 5:55 pm
“Good” at math: have a stronger foundation, perseverance, critical thinking skills, understand the “why” of math
“Poor” at math: lack of confidence, limited experience and foundational knowledge, ‘self-fulfilling prophecy” (mom was bad at math so I am bad at math – poor mindset)
Common ground: need practice, relevant problems to them, influenced by the teacher
MemberJune 7, 2021 at 12:03 pm
From a mathematical standpoint only –
“Good at math” – organized, linear thinkers who appreciate/can follow step-by-step procedures, ask questions when confused, able to analyze errors and find mistakes in order to correct work, solid foundation in number sense and place value, can tell when an answer or result is logical
“Poor at math” – difficulty following multiple steps, give up easily when confused, not interested in figuring out why or where a mistake was made, often a weak foundation in number sense or place value, does not recognize that an answer or result is illogical
Common to both – dislike word problems and open-ended questions, dislike homework
AdministratorJune 8, 2021 at 7:05 am
Definitely truth here from a math standpoint only. In my experience some students who feel they are bad at math have really strong number sense and want to know “why things work” …. but struggle to follow procedures. It’s a shame that in my past self I contributed to those students feeling like they were bad at math.
MemberJune 7, 2021 at 2:28 pm
Good at math: confident, comes easy to them, book smart
Bad at math: not confident in their ability, previous poor marks in math, not fast at facts
Both: math anxiety at times
MemberJune 8, 2021 at 9:38 am
Good at math: mathematical self-confidence, they have patience and perseverance when faced with novel math situations
Bad at math: have developed a self-perception that they are not math people, often struggle with perseverance when problem-solving
Both: need a facilitator to help them make connections and build their math schema so that they can apply what they know in all sorts of situations
MemberJune 8, 2021 at 11:18 am
The “Good” at math group:1. – They have had more positive experiences with math…have been successful at the “Math Student” Game
Learned their Math Facts early in their school career
View themselves as “Good” at Math
Participate in Class
Do well on Assessments
The “poor” at math group
They act up in class
They won’t try a task or problem by themselves
They won’t ask Questions
Need help getting started
Common Amongst Many in Both of These Groups
Ask “When am I ever going to use this
”Are aware of who is good and who is bad at Math
Don’t like being graded or assessed
MemberJune 8, 2021 at 2:44 pm
Good at math have multiple ways of thinking about a question and care about the solution – not the answer, poor at math just want an answer
Good at math fluency of number facts, poor at math rely on basic facts/calculator
Good at math make connections to other parts of the course and other courses, poor at math see each idea in a “silo”
Common know that they need math for further learning,
MemberJune 8, 2021 at 8:53 pm
Classic tortoise and hare here.
Good at math work right away, answer/ask questions, seek clarification.
Poor at math, disinterested, need a reason to engage, very social…
Common, like to chat, work in groups, want to do well.
MemberJune 9, 2021 at 11:39 am
The “Good” at math group:1. – They have had more positive experiences with math…<div>
have been successful at the “Math Student” Game
Learned their Math Facts early in their school career
View themselves as “Good” at Math
Participate in Class
Do well on Assessments
The “poor” at math group
They act up in class, They won’t try a task or problem by themselves</div><div>
They won’t ask Questions
Need help getting started
Common Amongst Many in Both of These Groups
Ask “When am I ever going to use this”</div>
Are aware of who is good and who is bad at Math
Don’t like being graded or assessed
MemberJune 9, 2021 at 11:35 pm
Good at Math:
Confidence in their abilities.
Positive math experiences.
Not Good at Math:
Lack of confidence in math
Weak foundation – gaps in basics.
Negative experiences in math class.
Want to succeed.
Have the ability to succeed.
AdministratorJune 10, 2021 at 6:45 am
The big one that popped out for me is that all students can succeed. That is so key.
MemberJune 10, 2021 at 6:51 pm
Good: pay attention, follow along, ask and answer questions, show up and do the work, try/ persevere, solid prior understanding, ask for help, motivated, curious
Bad: the opposite of all of the above
In common: need math credit to graduate, have potential, enjoy success
- This reply was modified 4 months, 1 week ago by Camden King.
AdministratorJune 13, 2021 at 7:21 am
I think believing that students have potential is so key!
MemberJune 11, 2021 at 3:27 pm
Good at math: learn from mistakes, ask questions, attempt all problems, perseverance, willing to talk/share/learn with others
Poor at math: gives up, scared to make mistakes, afraid to asks questions, won’t attempt problems
Both groups: typically want to do well, may be listening, tries sometimes (just depends on effort of trying), capable
AdministratorJune 16, 2021 at 6:48 am
So true. And I think that those who may not appear to be giving a full effort or lack the “care” to learn are actually just stuck in a fixed mindset or negative feedback loop. We can help shift their perspective and get them “doing” if we are intentional about it.
MemberJune 15, 2021 at 6:41 pm
Here are some of what I was thinking for these questions:
“Good”- flexible, sees mistakes as learning opportunities, tenacious, makes connections between math strands and to real life, sees math as having purpose, numeracy vs procedure
Both good and poor at math may have a different mindset – both can have fixed mindsets, they may see math as procedures to learn and lacking any real purpose outside of a grade at school, both may work hard, Both may have a disinterest in math
“Poor” students lack some key understandings of numeracy concepts, may have given up and stopped being willing to try
AdministratorJune 16, 2021 at 6:50 am
So true that both groups can have a fixed mindset. Sometimes our “strongest” students on paper are the first to give up when they are given something as challenging to them as the day to day work is challenging to a student who is struggling.
MemberJune 19, 2021 at 2:47 pm
Students good at math learn by listening and can take good notes. Students not good at math have lots of gaps because they don’t learn by listening and therefore did not take good notes. Both groups of students look toward adults to tell them what to do and hate making mistakes.
MemberJune 21, 2021 at 10:59 pm
“Good” at math: Confident, feel smart when it comes to math, tend to give up quickly if they do not know the procedure
“Poor” at math: sometimes will stick to a problem longer, but often do not think about it in a different way, feel like a failure, feel “I’m just not good at math”
Common: capable of “doing the math”, have great ideas to share, may not like math
- This reply was modified 3 months, 3 weeks ago by Serina Signorello.
AdministratorJune 23, 2021 at 6:51 am
Both groups are capable is awesome and sadly, I agree some students in both groups may not like math. Why is that and what can we do to help change that ?
MemberJune 22, 2021 at 2:12 pm
Students in both groups: want to understand and do well, can apply “rules” to solve problems and follow specific steps to solve a math problem as directed when shown how to do so, do better when a positive relationship is established with the teacher, desire and appreciate praise and positive feedback
“Good at math” group: Have a greater ability to use problem-solving skills, typically have more of a “can-do” attitude and are willing to try, ask questions when they don’t understand
“Poor at math” group: Struggle to use problem-solving skills and need to have specific steps/rules to follow in order to complete math problems, often feel defeated in math class as they have a history of lower success and so believe that they can’t do it (“I’m bad at math so why try?”), need a lot more encouragement to try problems that require mutiple steps, often don’t ask questions when they don’t understand and just give up/stop working
MemberJune 23, 2021 at 7:13 pm
The “good at math” group understands the game of math class and listens to clues about what might be on the test or studies the review.
The “poor at math” group might like to understand the math but gave up trying. They might even think they are just not a math person to rationalize it.
Neither group actually understands why the proceedures work.
AdministratorJune 24, 2021 at 7:10 am
Great point for the “both” groups.
This is especially true as we head through 4th and 5th grades with ideas such as long division, Pi, area of a circle, and beyond.
Let’s help them make sense of mathematics along the way and merge those two groups into one big math community!
MemberJune 24, 2021 at 11:37 am
Good at Math:
1. High level of participation
2. Has math facts and rules memorized
3. Able to work independently
Poor at Math:
1. Low levels of participation2. Lacks confidence in their abilities
3. Terrified of making mistakes.
1. Carve positive feedback
2. Need to increase stamina to move forward.
3. Lean that proof of reasoning is more important. Than being right.
AdministratorJune 25, 2021 at 6:55 am
Craving positive feedback is a big one for both groups. Imagine not feeling confident in math and also not really getting much positive reinforcement due to the fact that you have such significant gaps / lack of expertise? Really tough place to be.
MemberJune 25, 2021 at 3:53 pm
The “good at math” group : confidence, persistence, positive outlook towards making mistakes.
The “poor at math” group : lack of confidence, gives up easily, harbors negative feelings towards math, and in my experience : often avoid doing the work (which leads to even less confidence).
Common characteristics among both groups : both want to succeed, both have the ability to succeed.
MemberJune 25, 2021 at 4:44 pm
Good: confident, willing to try, eager to answer, help classmates
Poor: lack of confidence, give up easily, dread class, don’t participate
In common: ???
MemberJune 28, 2021 at 11:42 am
Here are my ideas on the characteristics of Two Groups of Math Students:
“Good” at Math Students
Have a general good sense of number and how the place value system works
Believe that they can get the right answer
Appear to be engaged most of the time
Confidently attack problems and can apply an appropriate strategy (or 2, or 3, or more!)
Eager to learn the next step, and often ask for “harder problems”
Make connections between different concepts (ex: fractions and decimals)
Like to check in with the teacher when they get stuck
Have an excellent grasp of math vocabulary
Loves to challenge a concept to make sure it works all the time before truly accepting it
Only feel successful if they get all the answers correct
Or, if they get the wrong answer, they will keep at it, trying other strategies, until the sun goes down!
Want to teach others
“Bad” at Math Students
Can usually name a teacher or other adult who told them, “You’re just not good at math.”
Have a difficult time recognizing patterns in general, and in the place value system specifically
Feel lost most of the time, and will deploy avoidance behaviors
View math as a separate entity from life skills and daily interactions with others (ex: only think of math as problems to do during math class)
Lack confidence and are afraid to try
Have a belief that they will get the problem wrong
Afraid to ask questions because of looking “stupid”
Believe that everyone else in the class “gets it” and he’s the only one who doesn’t
Hide their ideas when it is time to share, maybe even try to sink into the background
If they get the “wrong answer” they add this as internal “proof” that they aren’t good at math
Want others to go away so that their “poor math skills” aren’t discovered
Common to “Good” and “Bad” Math Students
ALL students want to do well in math
Want the answers to come quickly, and may lack perseverance
Must have chances to employ productive struggle!
Need time to practice and to process through challenging discussions using as much mathematical vocabulary as possible
Need an opportunity to explain their thinking
MemberJuly 1, 2021 at 9:11 am
“Good” at Math-
-can work with a problem until they have a solution
-can see multiple ways to solve a problem
-can make connections between math topics
-can compose and decompose numbers to work with them
“Bad” at Math-
-wants a trick to solve the problem
-does not retain concepts from day-to-day
-waits for others to answer
-does not apply knowledge from one concept to another
-says they are bad at math
-does not see the connection of math to real life
-gives up when the problem requires a lot of work, or they don’t get the answer easily
-defeated by mistakes
-wants to please the teacher.
-can solve problems of different levels of difficulty in isolation.
MemberJuly 1, 2021 at 2:48 pm
Group “Good” at math:
*Do things beyond (eg. Hmwk)
Group “Poor” at math:
*Don’t Speak/Don’t Ask Q’s
*Not Happy/ Usually “Spoken To”
*Don’t do Extra (eg. Hwmk)
Common to both groups:
*Come to class (“good” to learn, “poor” because they have to)
*Listen(“good” to attempt to understand, “poor” to not be bored)
*Speak(“good” to show their knowledge or check if they’re doing it correctly, “poor” because they’re called on but are not following)
*Write/Copy Notes (“good” to have it for reference when doing homework or studying, “poor” so it looks like they’re being productive – but may not even copy it correctly or in full)
MemberJuly 5, 2021 at 10:18 am
Good at Math – parents likely are positive about math, strong work ethic, have supports in and outside of the classroom,
Common – want to do well, potential
Poor at Math – parents might not of had positive experiences learning math, less support in and outside of the classroom, had trouble seeing themselves in the math or relating to the math
MemberJuly 5, 2021 at 11:07 am
“Good at math”: Complete problems and show their thinking process. Ask questions that clarify the problem more than “tell me the answer.”
“Poor at math”: unsure of self. focus on getting problems correct and completed more than the conceptts. Ask “Is this right?” or “What is the correct answer to problem number 2?”
Both: Don’t understand everything in math. Both get frustrated sometimes. Both are capable to understanding and learning new things.
MemberJuly 7, 2021 at 5:11 pm
Good: persistent, growth mindset, problem solvers, motivated to follow through
Poor: fixed mindset, not motivated
Both: capable of learning
AdministratorJuly 8, 2021 at 8:29 am
Wondering about the growth mindset of the “good at math” group… is it really a growth mindset or are they possibly not challenged enough to see them truly model a growth mindset nor visibly see a fixed mindset?
MemberJuly 7, 2021 at 9:39 pm
Good: good at mimicking teacher, good at following instructions, good at self-advocacy, self confidence
Bad: not engaged, give up easily, lack of confidence
Both: want good grades, often know more than they think they do
AdministratorJuly 8, 2021 at 8:26 am
Both “know more than they think they do” is a big one and something that both students AND we as educators always need to remember.
MemberJuly 19, 2021 at 11:27 am
-want to feel successful in math class
-both types will make mistakes (how they react is key)
-will question their math strategies
-want to please teacher, family, and themselves
-Need Thinking Time
-Practice Time is needed.
Poor Math Students:
-low self esteem towards math (built from previous experiences)
-struggle with motivation
-reading skills are not used to their advantage
-hard time taking math with others
-give up quickly
-have struggled with calculations over the years
-takes longer to understand at times
-more practice is needed
-work is not always completed
Good Math Students
-enjoy problem solving
-apply multiple strategies
-learn from mistakes
-collaborate with others
-confident with math abilities
-learning sparks the curiosity
MemberJuly 25, 2021 at 1:04 am
Good: consistently does homework, asks questions, tries hard (perseveres), has academic resources (tutor, older sibling, parents)
Poor: doesn’t do homework, doesn’t pay attention in class, lacks support at home.
Both: want a good grade.
MemberAugust 11, 2021 at 1:46 pm
I don’t use “good” and “poor” but “good” students usually demonstrate most or all of the 8 mathematical practices and not always during every activity. “Poor” students don’t yet demonstrate some or all of the practices. What they have in common is that outcomes typically vary by standard or activity type.
MemberAugust 17, 2021 at 4:20 pm
“Good” at math: -show their work, active participants in class, eager to work, support at home
“Poor” at math: -students do not know where to start when tackling math problems, they are less likely to participate or ask questions whole class, can often show frustration, support is often lacking at home
“Common” at math: -in small groups most students will share their ideas, students want to learn and be successful
MemberAugust 24, 2021 at 1:45 pm
Good: have had positive experiences in a Math class, feel confident, willing to take risks.
Poor: not so positive experiences in Math, may have gaps in learning which erodes their confidence and willingness to take risks, assume they can’t ‘do’ the math.
Both: want to pass the course.
MemberSeptember 21, 2021 at 8:56 am
Students that are good at Math, are usually good at listening and pick those mathematical patterns quickly. Students that are believed to be poor at Math, lack understanding of strategies and in some cases, do not retain information.
For both groups, we can see students following information and have a need of support regardless of their level of understanding.
MemberSeptember 26, 2021 at 3:34 pm
When I was in school, there were the kids who just, “got it” and those who didn’t. There was a large gap between them. Those that “got it” often became disengaged because they weren’t pressed to think bigger. Those who didn’t usually sat and stared while the teacher tried to explain math rules and concepts. I think that, often, those who struggle with math are missing basic math sense skills, so they just try to memorize rules and apply them even if the situation doesn’t warrant those rules. Common ground: math is important in so many fields, that is important to help students early on to understand how math is concrete and how it is applied.
- This reply was modified 2 weeks, 6 days ago by Patricia Scheler.
MemberSeptember 27, 2021 at 10:26 pm
• Able to recall knowledge and apply knowledge
• Motivated: Grades, Extra Curricular Activities etc.
• Involved Parents
• Participate in Discussion
• Able to follow steps
• Willing to make mistakes
• Able to complete task while in class, and get frustrated at home when they forget a step
• Uninvolved Parents
• Do not participate in discussions
• Cannot follow steps
• Scared to try
• Want good grades
• Have the foundation skills
• Want to know more
• Love teacher feedback and praise
• Need boost of confidence
MemberOctober 11, 2021 at 6:18 pm
Good: Quick to answer, share thinking, solid mathematical foundation, confident in abilities.
Poor: Slow to speak, have gaps in their learning, lack confidence, won’t share their ideas out of fear.
Both: Could put in the effort, want to be successful, are scared of the unknown, struggle with critical problem-solving.
MemberFebruary 3, 2021 at 10:56 am
Good points! I resonate with the characteristics you shared.