
A MiddleWeb Blog
I was talking with a teacher in my department about the best way to teach factoring. We were discussing the pros and cons of two different methods.
She said that she preferred a certain method because it made more sense logically and it was easier for her to see what the students were thinking. That was of first importance.
I really thought about that for several days. I agree about the importance of understanding what students are thinking and for them to be able to communicate what they are thinking through their work.
Ultimately, what’s most important though, is that they understand what they are doing and why.
Communicating math ideas through their work
At my school we have gone back to a full 5-day week with all the students coming to school each day, except those who have chosen to go fully virtual and avoid physical school altogether.
Now that most of us are face to face, I have had an opportunity to see more of their work. After learning virtually for several weeks, many students got in the habit of showing little to no evidence of the work they did to reach their conclusions. In general, they were out of the practice of writing anything down.
In the current climate, it’s more important than ever to remind them to communicate their thoughts logically and clearly. But how do you get students to think about concepts in a meaningful way and then communicate those thoughts clearly? I decided I’d start by asking students what they thought good math work looked like.
What does good math work look like?
When I posed that question to students, I was surprised by their responses. Most didn’t say anything. A few simply said, “Show your work.” Others were very adamant that in math it’s not necessary to show any work and that they work better when “they just do it in their head.”
Others said it this way: “I can do the math but I can’t write it down and explain it.” To be fair, I have had some students who could do a lot of work in their heads and get the right answer, but not many.
After listening to a lot of answers to my question, I concluded that my students don’t know what good mathematical work looks like.
I’m not sure I know exactly either, although I can easily identify bad work. And I do know that I haven’t explicitly taught or even expected them to demonstrate good work. In the past, I would say, to get full credit you have to “show your work” or “show your steps.”
What does that even mean to my students?
“Show every step” is vague and unhelpful. Besides it’s not always necessary to show every step. The point of their work should be to help them think logically about the problem, and to help me follow their thinking. I don’t want it to be a hoop to jump through or just something to check off a list.
So here’s what I did…
To start with I needed to determine what I consider to be good math work. What do I like to see when grading, and what helps me when I am personally working math problems? I decided that characteristics of good work would be:
✻ neat and organized, easy to read
✻ math symbols used correctly
✻ provides evidence that they understand the math concepts
✻ provides evidence that they have reasoned and thought logically about a problem.
Now that I had an idea of what good work looks like, I had to get this across to my students. I spent several days thinking about how I was going to accomplish this. (I tried researching what good math work looks like and I didn’t find a lot. I did find this website that had good suggestions: Teach Thought.)
I decided to focus on three areas: communication, rubrics, and studying examples of good student work. I have elaborated a little bit below.
1. Regular Communication
I plan to continue to gently remind students of the importance of creating good work in math class. Just talking about it with them and letting them know it should be priority is helpful. After we discussed what their work should look like for one day, I started to notice a little improvement in most of my students’ work. So just addressing the issue is helpful.
Also, I think it’s a good idea to get their feedback and their ideas. It helps if they can share in deciding what good work looks like. I also like to walk around the room and call attention to individual students who are showing good work.
2. Examples of Good Student Work
Students can’t just be encouraged to create good work. They also need to be shown what it looks like. Just like their English teachers explicitly teach them how to write a good paper, math teachers need to show students how to create good work and provide evidence for their thinking.
One way I plan to do this is by sharing exemplary samples of student work. It might also help to share examples where the work is not as good and let students provide suggestions as to how it could be improved. It’s interesting because when I teach AP Statistics I always use exemplary student samples to help students evaluate their own work. I don’t know why I didn’t think to do it in all my classes.
3. Rubrics
I plan to provide students a rubric so they can grade their work samples. For this, I am more interested in students thinking logically and reasonably and communicating than thinking they are working to get the right answer. I found many good rubrics dealing with problem solving and showing work in math class on rubistar. Here’s my rubric:
In the end I made my rubric by borrowing bits and pieces from several different rubrics. If you haven’t used rubistar before, it’s pretty easy and there are lots of pre-made rubrics. I have included mine, but I’m sure it will change as the year goes on. I know that I will need to discuss it with my students, and we will have to decide what each of the categories entails and requires.
Updates to Come
This will be one of those year-long goals, so I plan to write an update and share what worked and what didn’t. If anyone has any suggestions, please share. This is an area where I know I have lots of room for improvement. It’s important to me because I’m convinced that if students can learn to think logically and communicate their work clearly, that is a skill that will go beyond just math class and will be helpful in so many different areas.
where to buy viagra online http://viagrabng.online/# buying viagra online
where to buy viagra online: viagra online usa – viagra without a doctor prescription usa
cheap drugs buy generic drugs without prescription – tops pharmacy
ed treatment options buy prescription drugs without doctor – online med pharmacy
lisinopril 10 cheap lisinopril – lisinopril price
Thanks for offering this sort of very good written content. https://ketodietplanus.com/
plaquenil headache plaquenil 150 mg – plaquenil 400 mg
Nice web-site you have in here. https://ketorecipesnew.com/
ivermectin new zealand stromectol for humans for sale – ivermectin price usa
Hello to every one, the contents existing at this
web site are really amazing for people knowledge, well, keep up the
good work fellows.
ed clinics: ed pills online pharmacy – ed treatment drugs
viagra without a doctor prescription generic viagra – buy viagra online canada
viagra without a doctor prescription usa viagra over the counter walmart – viagra amazon
Extremely helpful look frontward to visiting again. http://ketodietione.com/
buy cialis with paypal buy cialis tadalafil tablets – buy cheap cialis uk
This post is worth everyone’s attention. Where can I find out more?
Thanks for sharing your thoughts. I truly appreciate your efforts
and I will be waiting for your next post
thank you once again.
Thank you for helping out, good info.
my web blog: FrioBreeze Air Conditioner
Ηi! Someone in my Myspace group shared this website with սs so I came to checқ it out.
I’m definitely enjoying tһe informatiⲟn. I’m book-marking and will be tweeting this tоo
my followers! Wonderful blоg and great design and style.
There is noticeably a bunch to know about
this. I assume you made some nice points in features also.
My site :: Compoise 360X CBD Reviews
This text is invaluable. Where can I find out more?
Also visit my web site – Jolt Alpha Ingredients
Thank you for every other wonderful article. The place else may just anybody
get that kind of information in such an ideal way of writing?
I have a presentation subsequent week, and
I’m at the look for such information.
My web page :: Ultra Cut Keto [http://vip5.moisait2021.ru/viewtopic.php?id=119810]
Howdy! Do you know if they make any plugins to
protect against hackers? I’m kinda paranoid about losing everything I’ve worked hard on. Any suggestions?
cialis .uk cialis ad – when does cialis patent expire
Thanks for one’s marvelous posting! I seriously enjoyed reading it, you are a great author.I will be
sure to bookmark your blog and will often come back sometime soon. I want
to encourage you continue your great job, have a nice morning!
Here is my page :: Coastal Hemp CBD Review
Great – I should certainly pronounce, impressed with your website.
I had no trouble navigating through all tabs and related information ended up being truly simple to do to access.
I recently found what I hoped for before you know it in the least.
Reasonably unusual. Is likely to appreciate it for those who add forums or anything, web site theme .
a tones way for your customer to communicate. Nice task.
Feel free to surf to my web blog; Erexzen Pills, http://wwwWa.L.R.U.Scv.Kd@lulle.sakura.ne.jp/cgi-bin/kemobook/g_book.cgi//g_book.cgi/index.php,
Howdy just wanted to give you a quick heads up. The words in your content
seem to be running off the screen in Chrome. I’m not
sure if this is a formatting issue or something to do with web browser compatibility but I thought I’d post to let you
know. The design and style look great though! Hope you get the problem fixed soon. Thanks
My page … Ultra Cut Keto Pills
viagra dosage instructions pills like viagra – xanax with viagra
viagra cvs free viagras yydnihu – viagra with out prescription
I am glad to be a visitor of this stark weblog, thank you for this rare information!
Also visit my blog :: Bio Shed Keto Slim Ingredients
Hey there! I realize this is kind of off-topic but I had to ask.
Does operating a well-established blog such as yours take a massive amount work?
I am brand new to writing a blog but I do write in my journal on a
daily basis. I’d like to start a blog so I will be able
to share my experience and thoughts online.
Please let me know if you have any kind of recommendations or tips for brand
new aspiring bloggers. Thankyou!
Also visit my page Compoise 360X CBD Reviews
Hello, its fastidious article concerning media print, we all understand
media is a wonderful source of information.
My web-site – Xoth CBD Gummies
viagra amazon viagra – where to buy viagra online
I love this site – its so usefull and helpfull. https://freegaychatnew.com/
Howdy very nice site!! Guy .. Beautiful .. Amazing ..
I will bookmark your site and take the feeds additionally?
I’m glad to search out so many useful information right here within the
publish, we need develop more strategies on this regard, thanks for sharing.
. . . . .
I am not sure where you’re getting your information,
but great topic. I needs to spend some time learning more or understanding
more. Thanks for magnificent information I was looking for this information for my mission.
bookmarked!!, I like your site!
Thanks in favor of sharing such a fastidious thought,
article is pleasant, thats why i have read it
completely
Hello, after reading this amazing piece of writing i am also cheerful to share my knowledge here with mates.
I will right away take hold of your rss feed as I can not find your email subscription link or e-newsletter service.
Do you’ve any? Please allow me know in order that I
could subscribe. Thanks.
prednisone 7.5 mg prednisone – prednisone 2 mg daily
I was wondering if you ever thought of changing the page layout
of your website? Its very well written; I love what youve got to say.
But maybe you could a little more in the way of
content so people could connect with it better. Youve got an awful lot of text for only having one or two images.
Maybe you could space it out better?
men ed weight loss pills from canada – buy drug online
natural herbs for ed buying ed pills from canada – natural ed
Hi! Do you know if they make any plugins to safeguard against
hackers? I’m kinda paranoid about losing everything I’ve worked hard on. Any recommendations?
quest bars http://j.mp/3C2tkMR quest bars
I’m truly enjoying the design and layout of your site.
It’s a very easy on the eyes which makes it much more pleasant for
me to come here and visit more often. Did you hire out a
designer to create your theme? Exceptional work! scoliosis surgery
https://0401mm.tumblr.com/ scoliosis surgery
I’m gone to inform my little brother, that he should also
pay a visit this web site on regular basis to take updated from most up-to-date gossip.
cheap flights http://1704milesapart.tumblr.com/ cheap flights
Hi I am so grateful I found your web site, I really found you
by mistake, while I was browsing on Google for something else, Regardless I
am here now and would just like to say thank you for a incredible
post and a all round entertaining blog (I also love
the theme/design), I don’t have time to go through it all at the moment but I have saved it and also included your RSS feeds, so
when I have time I will be back to read a lot more, Please do keep up the awesome job.
asmr https://app.gumroad.com/asmr2021/p/best-asmr-online asmr
This website was… how do I say it? Relevant!!
Finally I have found something which helped me.
Kudos! ps4 games https://bit.ly/3nkdKIi ps4 games
Do you have a spam issue on this blog; I also am a blogger,
and I was wanting to know your situation;
many of us have created some nice practices and we
are looking to swap methods with other folks, be sure to shoot
me an email if interested. scoliosis surgery https://coub.com/stories/962966-scoliosis-surgery scoliosis surgery
Wow! This blog looks just like my old one! It’s on a completely different subject but it has pretty
much the same layout and design. Outstanding choice of colors!
quest bars https://www.iherb.com/search?kw=quest%20bars quest bars
drugs for ed treatments for ed – ed drugs online
stromectol cream stromectol – buy stromectol online uk
stromectol tablets uk where to buy ivermectin pills – ivermectin usa price
ivermectin uk coronavirus stromectol price us – stromectol covid 19
clomid buy online clomid for sale – where can i buy clomiphene
http://edcialislove.com/# whats better viagra or cialis
cialis black 800mg
tab amoxicillin 500mg
best ed pills online cheapest ed pills online – ed drug prices
prescription drugs online erectyle disfunction – buy cheap prescription drugs online
ed treatment drugs supplements for ed – drug prices
ivermectin purchase ivermectin brand name – stromectol canada
Neat blog! Is your theme custom made or did you download it from somewhere?
A theme like yours with a few simple adjustements would really
make my blog stand out. Please let me know where
you got your design. Thanks a lot https://parttimejobshiredin30minutes.wildapricot.org/ part time jobs hired in 30 minutes
http://stromectolst.com/# ivermectin eye drops
buy stromectol pills stromectol xr – ivermectin lotion
I’m not sure why but this web site is loading extremely slow for me.
Is anyone else having this problem or is it a issue on my end?
I’ll check back later and see if the problem still exists.
magnificent submit, very informative. I wonder why the opposite experts of this
sector do not realize this. You must proceed your writing.
I am sure, you have a huge readers’ base already!
prednisone online pharmacy prednisone for sale – cost of prednisone 40 mg
ivermectin coronavirus ivermectin for humans – how much does ivermectin cost
stromectol canada buy stromectol – stromectol online canada
ivermectin generic name stromectol drug – ivermectin stromectol
Sustain the amazing job !! Lovin’ it! https://online-casinos-hub.com/
legitimate online pharmacies india india pharmacies shipping to usa – india pharmacy
discount prescription drugs prescription drugs online without – anti fungal pills without prescription
Wow because this is excellent work! Congrats and keep it up. https://sexygamess.com/
You’re a very useful website; couldn’t make it without ya! https://sex4games.com/
cialis generic overnite brand cialis online pharmacy
You have one of the greatest web pages. https://ketogendiet.net/
Many thanks for sharing your excellent web site. https://ketogenicdiets.net/
ed pills that work better than viagra viagra side effects
Wow, attractive site. Thnx … https://ketogendiets.com/
purchase cialis australia free sample of cialis
hydroxy-chloroquine plaquenil 200 mg oral tablet
prednisone tinnitus success can you buy prednisone over the counter how long for prednisone to leave body
ivermectin canada ivermectin tablets uk
wellbutrin sr generic wellbutrin xl – wellbutrin price without insurance
cheap valtrex online valtrex – valtrex 500 mg tablets
azithromycin and chloroquine zithromax for sale is zithromax sold over the counter how long does it take for azithromycin to work
lasix and chf lasix price uk how long does furosemide take to work how much potassium with lasix
plaquenil chloroquine plaquenil for lupus sulfasa;azine xeljanz plaquenil plaquenil how long to take effect
buying furosemide online lasix 250 what is lasix used for in horses how to convert mg furosemide to meq
cytotec buy pills online cheap buy pills online cheap nolvadex buy generic drugs online
scabies stromectol dosage stromectol ivermectin drug stromectol dosage for lice
viagra pills how to increase viagra effectiveness how to take viagra for maximum effect
dose of ivermectin generic stromectol how long does ivermectin work? ivermectin when taken with antibiotics
plaquenil fatigue plaquenil osteoarthritis is plaquenil-induced erythroderma reversible what is the maximum dose of plaquenil
Wow cuz this is extremely great work! Congrats and keep
it up. https://anenglishessay.com/
plaquenil in pregnancy plaquenil online does plaquenil cause you to crave sweats how to bill insurance on plaquenil
metformin 500 er metformin 1000 mg pill why do doctors no longer prescribe metformin what happens if i stop taking metformin
https://plaquenils.com/ plaquenil 2 mg
quando prendere cialis cialis ГЁ in libera vendita usare cialis a 30 anni cialis dove acquistare
http://bimatoprostrx.online/ bimatoprost buy
ivermectin vs permethrin cost of ivermectin ivermectin for heartworm positive dogs what does ivermectin do
I enjoy looking through your site. Thank you! https://criticalthinking2020.net/
Sustain the outstanding job !! Lovin’ it! https://topessayswriter.com/
Great internet site! It looks very expert! Maintain the helpful work! https://choosevpn.net/
levitra sold in canada levitra levitra 20 milligrams staxyn vs levitra
plaquenil toxicity oct plaquenil for rheumatoid arthritis plaquenil out of pocket coat plaquenil how long to take effect
coronavirus ivermectin ivermectin canada ivermectin and doxycycline heartworm treatment why does ivomec have a longer shelf life than generic ivermectin
cialis und ibuprofen cialis 10 mg 28 stГјck was ist cialis generika? wie lange brauch cialis um zu wirken
ivermectin pills canada ivermectin new stromectol 3mg cost
qxsrjb
You’ve very good knowlwdge right here. https://thebestvpnpro.com/
Great internet site! It looks really professional! Keep up the helpful job! https://speedgaydate.com/
cialis dose massima cialis senza ricetta in italia tempo effetto cialis 20 mg quando cialis generico
effets secondaires viagra acheter viagra pharmacie les effets secondaires du viagra cialis 20mg ou viagra 100mg
esiste cialis generico miglior cialis generico il cialis ГЁ anche ritardante come assumere cialis 5 mg
natural cialis lowest prices on cialis in usa viagra for womens where to buy what does viagra do to a man
Hey! I understand this is kind of off-topic but I had
to ask. Does operating a well-established blog like yours take a massive amount
work? I am completely new to operating a blog however I do write in my journal every day.
I’d like to start a blog so I can share my personal
experience and feelings online. Please let me know if
you have any recommendations or tips for new aspiring blog owners.
Thankyou!
order viagra australia viagra prescription can i buy cialis online what is levitra for
avanafil vs cialis ordinare cialis online cialis funziona per le donne quando inizia l’effetto del cialis
I don’t even know the way I ended up right here, but
I assumed this post was once great. I don’t
recognize who you’re but definitely you are going to a famous blogger for those who are not already.
Cheers!
viagra suisse viagra en ligne livraison rapide viagra pour femme au maroc combien coute le viagra en pharmacie
plaquenil drusen deposits plaquenil blurry vision oct findings in plaquenil toxicity how does plaquenil interact with percocet
viagra et autres vente viagra en ligne quels sont les effets du viagra combien coute viagra
plaquenil side effects plaquenil tabs hydroxychloroquine/ plaquenil for tmj who can do plaquenil test
buy cialis online ou acheter du cialis en france buy generic cialis 20 mg qui fabrique cialis
tadalafil cialis cialis homme cialis 20 mg mode d’emploi pharmacie en france qui vend du cialis
plaquenil manufacturer coupons plaquenil 200 mg twice a day what does plaquenil do to your eyes what will plaquenil do for me
viagra y cialis viagra comprar online como pedir viagra al medico como tomar viagra 50 mg
medicament viagra achat viagra belgique effets secondaires du viagra sur le coeur comment obtenir viagra sans ordonnance
vendo viagra zaragoza viagra femenina natural se incendia la fabrica de viagra como tomar viagra generica
viagra femminile shop viagra senza ricetta prezzo viagra boys just like you chi ha provato il viagra
plaquenil antiviral plaquenil weight loss plaquenil se puede mezclar con ibuprofen if allergiac to plaquenil when she i see reaction
Thanks for the purpose of offering many of these superior
subject matter. usa online casinos
gay college humor dating girlfriendvictim met
killer on gay dating site new yorkadam4adam gay dating hook
up site dating site’s bi guys dating gay guy
buy viagra generico de viagra precio operado de prostata puede tomar viagra viagra de cuantos miligramos hay
argument essay example pdf definition essay examples 250 word essay
page length following directions essay
gay addiction dating apps what’s the best site for finding a gay dating site for women when a
secretive commitment phobic guy you are dating is really gay older gay men dating sites
cialis rx viagra effect on women does viagra stop you coming what is viagra made of
cialis paypal payment vente cialis sans ordonnance cialis 20mg prix en pharmacie paris viagra ou cialis
accoutumance cialis cialis 20mg prix comment se procurer du cialis sans ordonnance pourquoi cialis ne marche pas
viagra et diabГЁte pharmacie canada viagra viagra pour homme pas cher cialis ou viagra ?
free slots for fun viva slots vegas free hit it rich casino slots free classic slots
grand win casino slots grand win casino slots old vegas slots no deposit slots
free slots home 12345 vegas world slots for free liberty slots casino free slots to play
free video slots my vegas slots free chips ff7 cait sith slots limit emils grayslake slots
aralen for sjogrens aralen cheapest price will aralen cause hair loss what is the generic name for aralen
aralen for lyme aralen 300 what is side effects of aralen how long will it taje to get used to generic aralen
merck molnupiravir ivermectin molnupiravir delta molnupiravir аёўаёІ merck covid know about molnupiravir
aralen and nausea aralen for osteoarthritis taking aralen without a diagnosis aralen how long does it take to work
sim slots free games free slots games for fun casino gem slots play slots
triple seven slots free free on line slots scatter slots horseshoe baltimore slots
slots free ashbringer relic slots free kronos slots for fun quick hit slots free coins
carnival in rio slots best slots to play lucky
slots 777 free play real vegas slots
clomid ovulation calculator clomid 50 mg buy online chances of pregnancy with clomid when clomid fails did injectables work
zanaflex interactions tizanidine discount possible reactions of weed and zanaflex what muscle relaxer is stronger out of baclofen and zanaflex?
latisse ophthalmic solution sandoz bimatoprost latisse or rodan and fields why do we care about latisse
molnupiravir cost per treatment molnupiravir merck covid merck covid pill is molnupiravir a new drug
le molnupiravir molnupiravir covid drug molnupiravir about that cuts covid19 hospitalization molnupiravir pfizer
molnupirivir molnupiravir drug molnupiravir kaufen amazon molnupiravir 800 mg
aralen cost quineprox 750mg can i take pepto while on aralen what class of drugs is aralen
nolvadex arimidex buy tamoxifen pill nolvadex-d vs clomid where to buy clomid or nolvadex
zanaflex plm buy zanaflex uk can you take zanaflex with cymbalta what is zanaflex used form
nolvadex xt reviews tamoxifen prescription nolvadex and arimidex on cycle nolvadex where to buy reddit steroid
I was just telling my friend about that.
This article is actually a pleasant one it helps new net visitors, who are wishing in favor of blogging.
Asking questions are really fastidious thing if you are not understanding something completely, but this paragraph presents fastidious understanding
even.
We are a bunch of volunteers and opening a brand new
scheme in our community. Your site offered us with valuable info to work on. You have done a formidable
job and our entire group will probably be thankful
to you.
Nice post. I used to be checking continuously this
blog and I am impressed! Very helpful info particularly the closing section 🙂 I care for such info a lot.
I used to be looking for this certain info for a long time.
Thanks and best of luck.
pharmacy canada school online pharmacy walmart
best european online pharmacy free pharmacy tech training online
canadian viagra pharmacy rx one discount codes
pharmacy tech online degrees genoa pharmacy