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Lesson 12: Discussion Prompt
Posted by Kyle Pearce on May 1, 2019 at 11:39 amAfter 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?
Kyle Pearce replied 3 weeks, 4 days ago 58 Members · 78 Replies 
78 Replies

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 1 year, 2 months 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: Resiliant
Poor: lacks confidence and resilliance
Both: Want to do well

Good at math:
 Are validated
 Think they are smart
 persevere
 pay attention
 rule followers
 are placed in advanced math (or given the option)
Poor at Math:
 Struggle in other areas
 distracted
 lack of home support
 gives up easily
 disinterested
 Think they are not smart
 are placed in remedial classes for math and other subjects.
Both:
 Same age group
 similar math exposure
 same peers
 like validation
 like praise
 want to do well

I agree with all of Lizzie’s comments here. Mine are:
Good @ math:
– Often have support at home
– Good at seeing/recognizing patterns
– Learned early math easily
– Believe they “can”
– Connect with the learning/can apply it to real life.
Poor @ math:
– Often don’t have support at home, or have chaotic homelife
– struggle to see patterns
– struggled with early math, maybe due to no connection to it.
– believe they “can’t”
– often struggle in many subjects at school
In common:
– age alike peers
– capable humans
– can choose to practice or participate
– use math in real life, whether they recognize it or not.
– have me willing to help if they reach out at all.
– are valuable, interesting, and not perfect.

Good at Math:
 Are validated
 Think they are smart
 Persevere
 Pay attention
 Rule followers
 are placed in advanced math (or given the option)
Poor at Math:
 Struggle in other areas
 distracted
 lack of home support
 give up easily
 disinterested
 think they are not smart
 are placed in remedial classes for math and other subjects
Both:
 Same age group
 similar maths exposure
 same peers
 like validation
 like praise
 want to do well.

Thanks for taking the time to share here. The piece I see consistently and that jumps out to me is that both groups want to do well – even if sometimes it feels like they don’t or are intentionally sabotaging their own chance for success – they would jump at the chance to be successful if the risk was low enough.

Attached is my 12 Venn Diagram, this was a great reflective exercise to think about how our various students feel in math class. As I did it, I could think of those students in my class who probably feel one way or another.
 This reply was modified 1 year, 1 month ago by Tarini Arte.

Thanks Tarini,
I tend to agree, fluency and mindset are big barriers to feeling confident with math. Let’s help address these in our students.

“Good” at Math: 1st to finish, loves to participate in class discussions, listens attentively, recalls number facts, good problem solving skills, positive attitude, enjoys math
“Poor” at Math: Last to finish, not motivated, offtask or avoids participating in class discussions, struggles with number sense or concepts, guesses or leaves problems unanswered, struggles with number facts, doesn’t enjoy math, doesn’t complete or turn in work
“Both”: Completes assignments quickly, upset when gets answers wrong, enjoys use of manipulatives and math stations/games/handson, enjoys small groups, partner work, and independent help, tries to solve problems in head, loves positive feedback, doesn’t show work at times

What are the characteristics of students in
 The “good at math” group: Generally they take risks, understands that a math question is like a puzzle and take it as a challenge knowing they are able to solve.
 The “poor at math” group: Believes things are more complex than how they actually are, they believe the class examples have nothing to do with what is taught in class and they think the effort is too big to even try
 common amongst any in both of these groups: Humans are curious by nature, all students should feel challenged and motivated when they are asked to solve a task in a way that engages them.

Hopefully throughout this workshop, you’ll build the tools to spark curiosity in all students regardless of where they see them fitting into math class!

“Good” at Math: Will be engaged with almost any lesson format, seem to “get it” after a few examples, selfmotivated to complete all work
“Bad” at Math: Typically missing some foundational math skills, have experienced feeling defeated repeatedly even after giving effort, typically do not have math support at home
Both: Want to know how what they are learning will connect to their real lives, want a feeling of success, can experience “math anxiety” due to grades and the right vs. wrong nature of math class

Thanks for your thoughts here!
I wonder about those “good at math” students. Is it self motivation or is it that they know they are “good at it” and don’t look at it as difficult or hard? Such an interesting discussion!


Good at math: Often more exposure to math, generally more fluent, strong conceptual understanding, confident in ability, not necessarily deterred by a wrong answer, can keep rules/tricks straight in their head over time
Poor: Lack confidence in math, assume they won’t understand, low conceptual understanding, helpless hand raisers, eventually start to confuse rules/tricks, poor numeracy
Both: Like validation, similar experiences in life, want to do well, can have good relationship w/ teacher regardless of opinion of math, can be afraid to take risk, can be teacher centered, know rules and tricks they don’t understand, worry that others may judge them (middle school)

“Good” at math: Embrace the challenge of math, are flexible with their thinking strategies, make sense of the material, often see structure in the content.
“Bad” at math: Believe that math is something to be memorized, struggle with persistence, believe that they don’t have control over their mathematical success.
Both groups: Seek validation, would like to succeed, often do not see the beauty of math (even successful students aren’t exposed enough to this in school mathematics).

I agree with a lot of what’s said here, but what first came to mind for me (particularly as a HS teacher) was:
Good: have been told they’re good at math for a long time, and have generally positive emotions associated with math class; want to keep doing the things they’ve been doing that have given them those positive “rewards” First to finish, 100% correct, good mimics of teacher methods
Bad: have been told they’re bad at for a long time, and have generally negative emotions associated with math class; have significant (and understandable) barriers to trying
Both: Want a comfortable safe environment; want to be recognized

Love this especially your part about wanting to be recognized. So true. Often students play the part of not wanting that, but it is usually well after they’ve realized that they aren’t going to be recognized for anything 🙁



The “good” at math group–Willing to try, willing to ask for help, wants to learn new things.
The “poor” at math group–Way behind gradelevel, lack of knowledge of basic math facts, thinks math is a waste of time, wants to keep on doing what they already know how to do.
Common amongst both–Like to succeed, like to impress others

I wonder about the “think math is a waste of time” part. If we dig deeper, would this be because they were left behind so long ago that any effort (it seems) they put in gets them little to no result afterwards?

I think that is a really good possibility, as almost all of my students are showing between 4 and 6 grade levels behind.



“good” at math: can be flexible with numbers, understands how concepts are related, quick calculation skills, good at memorizing
“bad” at math: longer processing/think times, don’t see how math is important in their lives, think math is “magic tricks”, number relationships don’t feel intuitive
Both: often see math as a set of rules, focus on the answer, want to do well

Agreed that often both groups have an overemphasis on the final answer. I wonder how we can help push students beyond that?


1. Good at math: positive experience, positive thinking, open mindset, had and felt what success is and looks like.
2. Poor at math: negative experience, anxiety towards math, poor selfesteem, feeling like math is beyond their reach.
3. Common amongst both groups: need to learn math in school, both would like to succeed, both need to feel valued and good at math.

The commonality that all students want to feel successful has come up a lot. Even though many students have given up, helping to shift their mindset can br incredibly helpful.



Good: Not afraid to “try” and fail, seeks to understand the “why”
Poor: Easily distracted, think they are “dumb”
Both: Want to do well

Good: successful in class, math facts memorized, believe in themselves
Bad: don’t believe in themselves, disengage, don’t know math facts
Both: need math in life, come to class, want love, aim to please

I am reading the points others wrote, but this task was extremely difficult for me. As a new teacher, I don’t make these groups. I don’t think any of my students are bad at math. I approached it trying to think from the perspective of the student that believes this about his/her/themself.
Good – motivated to work, likes to try because they “know” they will be successful.
Bad – sits and waits for an example problem to be worked out for them because they are afraid to attempt it, or believe they will not get it right “anyway.”
Both – Genuinely want to learn.

Good at math: Ask questions when they don’t understand, perseveres through thinking through about the end goal
Poor at math: Memorizes steps to solving a problem, wants help with each step of the problem
Both: wants to do well and doesn’t like to make mistakes

Thanks for sharing!
So many consistencies from the different groups being shared here. One that is standing out to me is how all students want to do well… let’s continue learning how we can reach more of them!


Good Math Group: Rule followers, organized, Strong Math sense, and strong mental math skills.
Poor Math Group: Disorganized, inconsistent, lack of confidence, and no interest in material.
Combo Group: Struggle with why are we doing this and will write correct answers and work down with zero understanding of why or how.

Students who are good at Math
They have confidence
Able to conquer multiple step problems.
They have found validation at some point in their Math career
Students who struggle with Math
Lack confidence
Not struggling in just Math class
They don’t know the unwritten rules of Math class
They quickly erase mistakes
Students in the Middle
They want to do well in school
They want to succeed in Math
They have a desire to engage and have fun

I agree with so many here! I kept updating my Venn as I went through.
“Good” at math: ask questions/seek to understand (inartistically motivated), confidence/growth mindset, engaged no matter the modality, general enjoyment of the “puzzle” of math, ask for opportunities to extend their learning, memorize well, regular attendance.
“Bad” at math: fall asleep in class, don’t engage in purposeful practice, give up quickly (little to no stamina), lack of confidence (fixed mindset), lack of home support (either parents not caring about their schooling at all, parents being absent/home life being unstable, or even just parents acting like mathematics is a genetic trait), lack of fluency/”bad” at memorizing, poor attendance
Both: Feel an obligation to be present and working (though some buck against that obligation), generally want to do well and receive praise/experience public success, think that there’s a right/wrong way to do math (I think the difference between students after they think this is whether they think it’s in their power to achieve that right/wrong), play the comparison game with their peers (am I doing as well as the majority? Am I doing better than the majority? Am I at least doing better than the person over there who I despise?)

good: are resilient, can make connections easily to what they already know, confident in what they know,, they enjoy a challenge they know their maths facts so they don’t get bogged down with calculations and they have number sense
poor: the fear failure : challenges makes them anxious, they get easily confused, they don’t process speech easily, don’t make connections easily, have little or shaky background knowledge to make connections with.
Both: are kids, they like to have fun, they want to succeed, they are curious

BOTH: usually don’t know/understand WHY they are doing the math

Good at math: consistent attendance and effort, engaged, rarely distracted by phone, rarely request bathroom pass, they know “how” but not “why” …
Poor at math: poor attendance, inconsistent effort, not engaged, often distracted by phones, often request bathroom pass, they rarely know “how” or “why” …
Common ground: short attention spans, dislike being challenged or asked to think about the math they are doing …

Great brainstorm here.
Which parts here do you want to focus on changing / challenging the most?

I really want to get my students engaged. I teach at a Title 1 [free and reduced meals] school in Colorado. My students are used to failing in math class which seems to make it easier for them to give up. I know that if I can get them engaged, they will be successful.



Good at math: Confident, willing to take risks, see failure as a chance to learn and grow, see relationships and make connections
Poor at math: Not willing to think, consumer vs. producer, low confidence, wants stepbystep instructions, is concerned with what the right answer is and not as much with the process
Commonalities (at least for my students): learning the same standards since Kinder, have been told the importance of math facts with emphasis on memorization, have experienced “I do, We do, You do” framework, have had good and bad experiences with math


Thanks for sharing. Are there any of these ideas that you think you could influence through the use of the 3 part framework?


Good at Math: know math facts; attentive; perseveres; learn from mistakes; willing to try different methods.
Bad at Math: don’t know math facts; unattentive (bored); give up easily; mistakes are detrimental to the student; the student will only try the method the teacher has shown.
Common for both groups; want to do well; capable of doing the math.

Good: Have confidence there is a solution.
Poor: Easily frustrated.
Both: Like activity, want material that is engaging.

I always say that my “good at math” students often got frustrated too when they didn’t immediately know the answer or what to do right away. I just wonder if I never challenged them enough to see the frustration often.


Good at math: Able to access concepts, able to memorize, flexible with strategies, good number sense
Bad at math: They want to understand but the way math has traditionally been taught they have trouble accessing the concepts, they have gave up on math, they have learned to hate math
Both: curious, problem solvers, love of learning

“Good” at math group: Parents/family enjoy math; support at home; growth mindset; strong foundational skills.
“Poor” at math group: Parents/family don’t enjoy math; less support with math concepts at home; fixed mindset; poor foundational skills. Additionally, students may have learning disabilities or other personal factors affecting their performance and may not have received the supports they need to be successful at school.
I frequently hear students say “I’m just not a math person” and even parents echoing this same concept: that both they and their students are just naturally bad at math.
I believe that both groups of students have some traits in common: a natural curiosity about the world; the ability to learn math; and the desire to succeed on some level.

Good: Think/try before asking for help, ask detailed questions to help solve the problem, practice skills (either in class or on homework), positive
Bad: Ask “how do I so this?” Read questiondon’t get itgive up, Unwilling to try, large mathematical vocabulary gap from peers, negative.
Same: Enjoy working with others and talking, afraid to fail

This is hard. Do I really know what goes on in the minds of any student AND do I know what their experience both in school and out of school may
“Common:” unknown support at home, wants to do well and to learn, wants to be understood and accepted, frustrated, strives
“Good:” comes naturally to student, does not necessarily want or need to follow all procedures, when frustrated changes approach
“Poor:” does not know why math is hard, may feel there are too many steps and feels confused, does well with one area of math (facts) but application is frustrating, struggles to communicates wants/needs/understanding, gives up when frustrated

Good at math students…
memorize algorithms, many times without true understanding
confident in their answers
want to share thinking with their peers
Poor at math students…
think there is only one way to do math
think math is hard and they will never understand it
hate math
disengaged
would rather fail than appear stupid in front of their peers
want to learn but don’t want to ask questions for fear of feeling “stupid”
Both…
can learn anything/concept with the right motivation
want to do well in front of their peers
with the right environment are willing to take risks


Good at Math: Ok with trying different approaches and often ask “why” questions about procedures
Poor at Math: Fear of failure, want to be shown procedures but don’t often seek to understand why the procedures work the way they do
Both: capable of learning

Good at math – willing to take risks
Poor at math – afraid and unwilling to take risks
Common – want to do well

The students who are “good” at math usually enter class with strong number sense, and they are comfortable with computation, both facts and algorithms. They are able to focus and pay attention to examples and usually follow and understand the process being modeled so they can use those examples as a starting point when solving problems independently. They are willing to try problems on their own and take more risks and to apply their own logic and strategies, too.
The students who are “poor”at math usually enter class lacking number sense, and they struggle with fact fluency and computation. They struggle to see and understand the logical processes in examples through teacher modeling, so they are not able to apply it independently later. They often lose focus because they don’t understand why this matters, and they can’t follow what the teacher is saying, and they assume they will get it wrong anyway, so they give up easily or do not try at all.
Both groups of students have a lot in common. They all want to feel successful, and they all want to understand both the how and the why of the math we are teaching. They want to feel seen and heard and like they are a respected member of the classroom community. They enjoy working in groups and collaborating with peers on work that they feel is interesting and important. They like to have fun, play games, and put their own creative spin on things. And they are all worried about getting it wrong — not just answers, but everything. They all feel pressure to do well, and that pressure can get in the way of learning at times.

I totally agree for a middle school student and above.


Good at math: eager to learn more/something new, want to help peers, looks for different strategies for curiosity.
Poor at math: dread class, unengaged, frustrated.
Both: want to be successful, want to understand the concept they’re learning

The good at math group are confident, have positive attitudes about math and their skills, and are fearful of making mistakes.
The poor at math group tend to have a more negative attitude towards math, have a poor selfimage, and are used to making mistakes so they expect to be wrong.
Both groups do what is asked of them, want to understand what is going on, and appreciate positive teacher/peer feedback.

“Good” at Math: higher confidence, feel supported by teachers/respected by peers, engaged, know facts, growth mindset, think they are good at math
“Poor” at Math: low confidence, negative vibes from teachers/parents/peers, disengaged, math facts are more challenging for them, fixed mindset, think they are not good at math
Both: capable students, deserving of effort from teacher, smart, influenced by parents/peers/teachers, want to learn and do well

Good at math group: has resilience and can wait to get an answer.
Bad at math: often already lost all confidence in knowing math and therefore, they get overwhelmed as soon as they don’t know one thing.
Both groups: have the ability to understand math

Good at math students are the ones that “just get it”
Bad at math are the ones that don’t get it even after intervention

“Good” at math – have discovered how to apply the ideas sitting in their math toolbox
“Poor” at math – look at math as independent, unrelated concepts
Both – have the potential to grow, to be creative, to connect math to their own life expereince

Good at Math: Grit and perseverance. Recognizes patterns. Multiple entries point to a problem. Ablet to extend learning to other facets of real life. Makes sense of a problem and is able to estimate a reasonable answer if applicable.
“Good” at Math: Fluent in math facts. Accepts the rules and procedures at face value.
Poor at Math: Accepts failure almost immediately. Little or no confidence in ability. Lacking number sense. Major gaps in previous learning targets.
Common Characteristics: Honestly, every student walking into my class has the capability to get good at math, not just “good” at math. I wonder what happens to create a good math student or a poor math student? Certainly, there are myriad experiences that influence those two groups of students. At some point, are not all of the students in the middle and then slowly migrate one way or the other?

Great points and questions. Ironically, even students we often would put in the “good at math” category wouldn’t put themselves there. If students aren’t sure why they do what they do in math class, this lack of confidence perpetuates.



“good” at math: motivated, participate in discussions/lessons, persevere, can see many ways to do things (which is why I up it in quotes: if they are good at math, they see many ways to solve problems; I have some students who will earn an A, but do so by following a certain step sequence each time and don’t see alternate solution patterns) so maybe a better term would be “Flexible Thinker”
“bad” at math: not always motivated, do not participate, trouble making connections, tend to be rule followers; just looking for the one way they were shown a particular problem
Common: capable, seek approval

“Good at Math” Do well in most classes, work hard and persevere even when it gets tough, ask questions, know where they are confused.
“Poor at Math”Don’t do well in other classes, don’t ask questions, don’t know where to start asking questions, give up easily. Don’t think logically when solving problems.
BothEnjoy working with partners (sometimes), Enjoy talking to peers, like it when the routines change and are not the same everyday. Like to get up and move.

Good Math Group: attentive, persevere, asks questions, understands how concepts relate to one another and can be applied to different scenarios, good at “doing school”
Poor Math Group: reluctant to ask questions or seek clarification, disengaged, mentally overwhelmed
Both: Want to succeed, have questions and need clarification/feedback, are capable

Good at math, a positive collaboration with teachers and students make them to enjoy learning mathematics.

Good at math:
High fluency
Beter focus
Better number sense
More “risk takers”, willing to do something that might not work.
More likely to “think” and engage with the process of being wrong and figuring out why
Overlap:
Tendacy to rush through things (but also a bit normal, they’re seven!)
Question “why” we need to do things, and want to follow through procedures so it’s “done”
Copy patterns or adults
Impatient about how long things take
Poor at math:
Don’t understand how strategies work
Low fluency
Give up easily
Low attention span
Anxious about making mistakes, tend to make a “freeze” response to problems

“good” at math: confident, willing to explore and try strategies, rule followers, able to “do school” in a traditional way
“bad” at math: assume they don’t know what to do before they start, lack confidence, do not believe they can do it, have already decided or have been told they “can’t”
common: want to learn, want to do well, want to have/share ideas

Great ideas here. Thanks for sharing your thinking!

I like how you’ve clarified that sometimes students haven’t been ‘told’, but they’ve ‘decided’ that they’re not so great at math. We need to help students realize the mathematics potential they all have inside of them!
