Prior to coming to class, students were given 2 equal sized fractions – 1 divided into 3 equal parts with 2 shaded and 1 divided into 4 equal parts with 1 shaded. (Actually, they were so lightly shaded the students were instructed to re-shade the rectangles. This comes in play later.) They were instructed to have at least 6 of each rectangle cut out and ready to use for class.

We met in an online room and the instructions were to take the rectangle with fourths and fold it so that each strip (or fourth) was divided into equal sized pieces. I didn’t tell them how many pieces or how to fold it. While the students were doing this, I drew rectangles on the white board and told the students to represent their new rectangle on the white board and write the fraction for the new rectangle. Below are the results.

I then asked them to look at the 4 representations and make an observation or statement about what they see. Student A said, “All of our new fractions are equal to the ¼ that we originally had.” I asked her how she knew. She went on to describe how the rectangles were folded differently but each of the fractions were equal to 2/8. I asked for other comments and Student K stated that “if you were to cut off the yellow portions of each of the rectangles and placed them on top of each other, they would all be the same size. That’s how we can say they’re all equal to ¼.” Student S noticed that “every time the numerator goes down one like from 4 to 3, the denominator goes down by 4 from 16 to 12. And then from 3 to 2, the denominator goes 12 to 8.” (I wish I had explored this statement further with a question of “Why do you think this happens?” But I was focused on my goal of this lesson and completely let that nugget pass me by. Maybe I’ll bring this comment back up in another class and we’ll investigate why this happens then.)

At this point I had a goal in mind and they were nowhere near that goal, so I decided to have them try this again. I asked them to get another ¼ rectangle and follow the same instructions as before but to make sure they folded it differently from the first time. I asked similar questions and received similar comments. This was not happening as I anticipated so I decided it was time to move on.

Next I asked them to get the rectangle divided into thirds with 2/3 shaded. I again asked them to fold the rectangle so that each third is divided into equal sized pieces. While they were doing this I set up the whiteboard with 4 rectangles.

This time I asked them to look at their new fractions, the representation of the new fractions and the original fraction of 2/3 and to see if they could relate these 3 to each other. Student N said, “Starting with 2/3, I divided the 3rds into 4 more equal pieces within each third. By adding those pieces it’s almost like I multiplied it by 4 more and 2 x 4 is 8 and 3 x 4 is 12.” Student A stated, “Like Student N, I took my thirds and divided them into 3 equal pieces. So like hers was 3 x 4 is 12. Mine was 3 x 3 was 9. It’s like everyone’s.” Student S said, “They were talking about division I saw mine as 2 times as many. Each third has twice as many so I divided each third into two. So I guess I divided too but I thought of it as multiplication.” YES!! This discussion was just what I had been looking for!

I then asked them to look through the K-5 fraction standard(s) and determine which ones we had been working with up to this point. I wanted to see if they ‘saw’ what I was hoping they would see.

This is what they came up with

3NF.3 – Explain equivalence of fractions in special cases…

4.NF.1 – Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Student S explained 4.NF.1 by saying, “We kind of did this with our last activity of 2/3 times a certain amount. We divided our thirds into more, we multiplied the number of parts in each third. So we did something with that kind of.”

I said that I thought I understood what Student S was saying. I then asked if someone could explain in their own words the same standard.

Student A said, “I can see how students can totally GET multiplying the numerator and denominator by the same thing; they could actually see it holding true. It’s not just something that we say, but they can see that relationship working…I think that this activity would explain why we say ‘whatever you do to the numerator you do to the denominator’ because it actually HAS to be that way when you’re folding the rectangles. You changed each third into 4 smaller pieces. You were doing it to each third. I see students get confused and just multiply either the numerator or denominator by 4 but this would help them see that the entire rectangle’s pieces are being changed.”

Bingo! This was what I had hoped would come from this activity! We then moved on to the second goal of the lesson.

They were instructed to take both rectangles – where 1 fourth was shaded and where 2 thirds were shaded – and fold both sheets in such a way that both rectangles were divided into the same number of equal pieces. This took a little longer for some. I went ahead and drew rectangles on the board while they worked.

I then asked them how they decided what they were going to do. Student A said, “I wanted them to be equal. I chose 12 because 12 is a multiple of 3 and 12 is a multiple of 4 as well.” Student T stated, “I thought about our previous problems and I had folded both of them into 12ths before so I knew that I could do it again.” Student K pointed out that one might also do this activity by trial and error. To be honest this is exactly how I solved it because I wanted to see what a child might do who didn’t know about common denominators. I first folded the thirds in half horizontally and the fourths in half horizontally. That gave me 6ths and 8ths. I folded the thirds again (just repeating the first fold) and then one more time horizontally. That gave me 12ths. I looked at the fourths that had been folded into 8ths and realized that I couldn’t turn it into 12ths; but if I started over with a new fourths rectangle, I could fold it into thirds horizontally it would also have 12ths.

After this discussion I then asked If we wanted to compare 8/12 and 3/12, which fractional amount is greater and why or are they equal?

Student A stated that they are not equal. “8/12 is greater than 3/12.” I asked her how she knew. “I’m looking at my models and 2/3 is 8/12 and there is more shaded than the ¼ or 3/12 on my other rectangle. But if you look at my drawing you can see that 8/12 is 5/12 more than 3/12.”

Again, we moved on to another problem. I asked, “Can you fold both rectangles in such a way that the shaded amount on each rectangle is divided into the same number of pieces?”

Then something beautiful happened. Notice that some students already have their drawings up while the 4th student is still folding her rectangles. I notice that Student K doesn’t have 2/3 shaded on her first rectangle so I asked a tricky question, “Hey Student K, did you do the actual folds on your rectangles or did you just start drawing it on the board first?” She used a technique she’s seen me use often – answered my question with a question, “did you ask us to fold it so that you have the same number of shaded pieces? They each have 2 pieces shaded; they’re just not of equal size.” I then repeated my question, to which she confessed that she didn’t fold the papers. After looking at the other drawings she realized that she didn’t shade in 2/3 of the first rectangle. So she went to correct it by shading in the 2nd third. I told her to go back and do the problem again with her paper rectangles.

Notice what happened. Again Student K did not use the paper rectangles. Instead she hurriedly divided the 2 eighths into shaded equal pieces because she already had 4 shaded equal pieces on the first rectangle. As a result she didn’t think to continue the new horizontal lines. This confirmed for me the importance of students using the actual paper rectangles and folding them. If you fold a horizontal line in the shaded section, it’s going to go all the way across the sections that are not shaded as well.

Once all 4 students completed their drawings and fractions I asked them to use words to discuss their 2 fractions? Student N said, “My fraction 4/6 was orinigally 2/3 and I went ahaead and divided it more so 4 out of 6 parts are shaded. And in the picture on right, it started as ¼ and I divided that ¼ further into smaller parts of fours. So it pretty much mulitplied itself by 4 going from ¼ to 4/16. So you can see how ¼ times 4 on both the numerator and denominator is 4/16.”

Student A stated, “Both of my numerators are 6 and I can see from the shaded parts that I have a common numerator. We can compare the 6/9 to 6/24. We know 6/9 Is greater but typically we compare with the denominators the same but now we are comparing the numerators.”

I then said let’s assume a student has had a week or two of doing similar activities to what we’ve been doing with folding rectangles, representing them on paper, writing the fractions, discussing them, comparing them. How might one know which fraction, 6/9 or 6/24, would be greater and why, without the rectangles?

Student S said, “In one of them you imagine folding the fractions into much more pieces. So they are all smaller pieces than in the other rectangle where you folded it only into 9 pieces. So the pieces are much bigger than the other pieces. So 6 bigger pieces (6/9) is much bigger than 6 much smaller pieces in 6/24.”

What standards are we addressing now?

3.F.3.d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, <, and justify the conclusions, e.g., by using a visual fraction model.

I was very pleased with how this lesson progressed with developing fractional understanding of equivalence and fraction comparisons. But I was also delighted that we were able to develop such deep understanding in an online setting. We were once timid about doing any of our program online because we felt that it would not be as ‘good’ as face to face classes. This shows that it can be done. My brain does not automatically think in an online format yet, but it’s getting better and I’m no longer afraid to try new things.

]]>It seems that everywhere I go, I either read or hear someone’s opinion regarding the Common Core standards. (As I’ve stated before I am ignorant of the English Common Core Standards, so I refrain from making any comment.) Please become accurately educated regarding the Common Core Math standards. Attached is an excellent video produced by Jo Boaler, mathematics educator from Stanford University. She clearly explains the intent of the Common Core Math standards as well as provides evidence to support its existence.

]]>*“…*I was incredibly frustrated when I could see the problem, but I was making a mistake that I didn’t notice, causing me to get stuck. At this point, if this problem were being completed by my students, many of them would quit trying. For me, though, there is a satisfaction of knowing I struggled through a problem and triumphed, a sense of accomplishment. This class and this type of experience make me want to be more vulnerable around our students and other teachers. If we share our struggles with our students and show them how to push through that struggle, maybe some of them will have the courage to push through the difficulty they are having when working out something in our classes. One of the biggest complaints I hear from other teachers is the lack of motivation in our students… [T]eachers [are] still learning how to teach conceptually, we [should] show students that there are things we struggle through just like they do.

“The problem that we completed last week with the various routes was interesting in that all of the people at my table attempted the problem in a different manner at first. Once we all got to a place of frustration with the amount of combinations, the pieces that we each had helped us to be able to get organized to make sense of the problem. This type of problem could be taught in school just as it is, but I wouldn’t extend it to the point we did in class unless I was working with high school students. Most middle school students would get extremely frustrated. I even got a bit frustrated, as my peak performance is not in the evening; I am a much better thinker first thing in the morning. This brings me to another observation of my classes lately: we need to remember that students’ peak performance time does not always match with the school day calendar. While I’m not saying we should let students sit back and take a nap during class, I am saying we need to be mindful of students’ energy level and if they are having difficulty seeing a problem through. Maybe they need a hint or to work with the teacher in order to find some inspiration or motivation; maybe a student needs to get up and stretch; or maybe a student needs to think the problem through in a quiet place.”

Heather Isenhardt is a middle school mathematics coach in Henry County Georgia. She is also a graduate student in K-8 mathematics education at the University of Georgia.

]]>I hope that you all will help me spread the word!The **K-8 mathematics education graduate** degree programs are now being offered on the Griffin Campus of the University of Georgia in a hybrid format. We hope to start a new cohort in August.

If you are interested in more information email me, tweet me, facebook me, or write a comment to me here.

Pass it On!

Robyn

]]>I came across a post on facebook today. Here is the link: http://www.bizpacreview.com/2013/12/18/arkansas-mom-destroys-common-core-in-four-powerfulw-minutes-89152 In this video a woman is talking about the Common Core State Standards for Mathematics to some people in her state. (I think they were the state school board, but again I will admit that I really do not know.) She claims that the standards are “not rigorous…not college ready…[and] not preparing our students to compete in a global economy.” She also states that the statements to the contrary are “empty sales pitches from corporations and government agencies to profit from our kids and sell them downriver at the name of saving education.” Below is the following 4th grade example she provided.

Mr. [X’s] class has 18 students. If the class counts around by a number and ends with 90 what number did they count by?

She claimed that the students were “expected to draw 18 circles with 90 hash marks solving this problem in exactly 108 steps.”

In her defense she only had 3 minutes to make her point; however, she did not read the standard from which this problem probably was derived. I will include it here for my readers (the notation is included for educators who should be familiar with the format).

CCSS.Math.4NBT6 – Find whole-number quotients and remainders with up to 4-digit dividends and one-digit divisors, **using strategies based on place value, properties of operations, and/or the relationships between multiplication and division**. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models.

No where in the Common Core standards would 4th graders be expected to solve this problem in the manner she described. The standard simply states that students should use strategies based on… A student could solve this problem

* using their understanding of doubles: 18 + 18 is 36 (that’s 2), 36 and 36 is 72 (that’s 4) and 72 + 18 is 90 (that’s 5). They counted by 5’s.

* using their understanding of divisibility rules: I know that the only way an 8 in the one’s place will give me a 0 in the one’s place is if I multiply it by 10 or 5. 10 groups of 18 is 180 (that’s too much). Since 90 is half of 180, I know that I need half as many groups. So they counted by 5’s.

The Common Core Standards do not say that students should **never** learn how to use a traditional algorithm for computation. The standards simply encourage that students develop a conceptual understanding of the operation before being taught the traditional algorithm. Parents (and teachers) are doing their students an injustice when teaching the traditional algorithms too soon. For many children being shown the algorithm too soon hinders their development of conceptually understanding the operation.

Please READ the Common Core Standards before sharing an “uninformed” opinion. I have provided links below to help make this reading more accessible.

http://ime.math.arizona.edu/commoncore/

(Note: I am creating an additional blog site where I will discuss my thoughts on just about anything. It will be titled “Robynisms On Things” http://robynismsonthings.wordpress.com/)

]]>If you use Cognitively Guided Instruction (CGI) questions in your room or if you would like to get started using CGI in your classroom please feel free to go to the following public wiki site that I just created. Please feel free to share and borrow.

]]>I want to thank all of you for taking the time to read my post. As you can tell I was discouraged for the teachers I know and I hoped that I could encourage them and (obviously) other teachers that I don’t know by saying that I understand and I support and praise you for all that you do.

I believe that all teachers go in to the profession because they love children and feel called to help educate our future. In addition I believe that that is also the reason why teachers REMAIN in the profession.

The title of my last blog was meant to catch people’s attention. I was NOT saying that everyone in education takes an antidepressant, nor was I saying that if the educational system was perfect NO one in education would be taking antidepressants. That is a personal decision that is between an individual and his/her doctor.

My final comment is that I AM in SUPPORT of the new Common Core Standards as far as the mathematics is concerned. (I say this only because I have not read any of the other content standards, nor would I be comfortable making a judgment about a content in which I am not as familiar with teaching.) There has been a lot of misrepresentation from those opposed to the CCSS by saying that Common Core is the cause for so much testing taking place in schools. This is simply NOT true. Common Core in Mathematics calls for students to develop a deeper understanding of mathematics; to make connections between different ideas in mathematics as well as between the classroom and the real world; to develop a confidence in thinking mathematically; to make conjectures; to reason abstractly; and to defend and make mathematical arguments. If you are interested in knowing more about the Common Core Standards please click on the following link http://www.corestandards.org/.

And my final response is that I purchased my t-shirt from http://www.signals.com/cgi-bin/hazel.cgi?action=DETAIL&ITEM=CL6271 but it is my guess that it can be found elsewhere. I typed the slogan into a search engine and there are buttons, bumper stickers, etc with the same slogan.

If you have the time, skim over the following comments provided by readers (current teachers, retired teachers, para professionals, pre-service teachers, parents, grandparents, and non-teachers). I have copied word for word (correctly or incorrectly spelled) every post except for one that contained a curse word.

- Love this Robyn! I am glad to hear you say that you are actually okay with most of the common core standards because that is one of the reasons I have been concerned about having Noah in public school. I agree the testing stuff seems ridiculous. I know I have been out of the classroom for 15 years, but now I wonder, would I even WANT to go back? Or could I even handle it if I did???? I don’t know what the answer is. I wish I did. I am just so abundantly thankful that I have been able to keep my kiddos at home and school them here, climbing trees and all!!! And I am thankful for those teachers who are in the trenches and are now teaching my son. I pray for them each day because my son and others NEED great teachers desperately. Thank you for shedding some light on this for me. I will be thanking his teachers TODAY for a job well done…
- Thank you!
- You are so right! How can we change it! I’ve taken my child out of school 3 times because of this crazy and how it is affecting her. I honor every teacher that puts up with this. This crazy needs to change. I’ve been saying this for 5 years every since my daughter started school. How do we take back OUR educational system?
- Step one…get all of the politicians and school district superintendents OUT of the restaurants where they hold their “so-called” educational conferences/meetings/professional development seminars, and make them SIT IN on classes, ALL DAY, EVERYDAY. Let them FEEL the stress along with the teachers and students, instead of CREATING IT over lunch and coffee…in between all the conversation about their golfing events. Trust me on this. While I’m not a teacher, I have been a waitress who has waited on these Educational and political big wigs. I’ve overheard their conversations. They are, in my own opinion, nothing more than extremely over paid, professional luncheon organizers.
- Another thing you can do – contact your legislators and school board members!!!!! Speak up!!!
- Thank you! I needed that today!
- SUCH A SAD TIME WE LIVE IN….. THIS BLOG IS SO TRUE. WHEN THIS COUNTRY STARTS LETTING THE CHILDREN BE CHILDREN ,THEN THE TEACHERS CAN ONCE AGAIN BECOME TEACHERS. I WILL BE PRAYING FOR EACH ONE OF YOU. AND THANK YOU !
- Where can I get that cool & totally true tee?
- Love it! Children are being “shoved into their heads” far too soon!! Great book: “Magical Child,” by Joseph Chilton Pearce. I read it decades ago and concur with 95% of it based on my own life experience, other reading I’ve done, and observation over the years. My grandmother taught 4th grade for 25 years. She was the best teacher in the world! It was a lot of fun and everyone learned what they needed to learn in the midst of enjoying it all. What can be better than that?
- As a 3rd grade teacher, I am so thankful to you. We are truly over stressed and underpaid, but we love our students dearly. Those who teach, love to teach, no matter how stressful things get. Unfortunately, it is part of the way our educational system works. I just wish we could let our kids be kids, and not be stressed out at such a young age. It makes me so sad to see my 3rd graders worried about these standardized test. I agree, something needs to be done.
- Thank you Robyn. This was perfect.
- Perfect!!!
- As a former paraprofessional, substitute teacher, and now a teacher, I say bravo to your blog!!! Teachers are severely under appreciated, and under paid. Why does a pro athlete make millions of dollars more than the person who teaches you how to read, write, add, and subtract? What message does this send to our nation’s youth? Not a positive one if you ask me.
- Will pray more for our teachers. Sounds more stressful than ever. Makes me glad to be retired before this new curriculum, even though I loved teaching very much.
- we can do more than prayer. We can hold protests and become political. If you’re a parent, please ask your teacher what they need help with… Parents are more powerful than teachers. A parent that goes to the district office can get a few things done for that teacher.The parent is more likely to get the air filter changed in the room then the teacher! The parents can protest the test and not send their child to school that day.
- wonderfully written and VERY truthful!!
- You hit the nail on the head!! Awesome job!!
- And we wonder why fewer college students are heading for careers in education. Or why so many first-year teachers don’t continue into second year. My terrific husband retired recently from 30+ years as an elementary music teacher. He had some fantastic years, and he still keeps in touch with some phenomenal colleagues. But everything you said above, about what teaching is like – and the toll it is taking on teachers and on children – is true true true.
- Thank you… and…political correctness.
- I’m glad that someone understands. While the rewards are priceless, the journey is exhausting.
- So very well written and so very right. Thanks!
- When I retired I had an ulcer, was on Xanax, had high blood pressure and panic attacks. After retirement I was diagnosed with PTSD. I had planned to teach 2 more years but my health could not take it. I felt worthless, incompetent and depressed. Now, a year and a half later I feel much better, I sleep at night, I am no longer on Xanax and haven’t had a panic attack in well over a year. Not only that but I remember when I loved teaching, when I felt like I was making a difference and changing lives. I miss that. However, teaching as it is today was joyless for me and I would not return for anything.
- Well said, you really captured the environment in which many teachers work in across our nation. Thank you for posting.
- Many of us speak up and no one listens, which leads us to believe “they” don’t care. Sad isn’t it. So much for the legislation of No Child Left Behind. That’s exactly what “they” are doing!
- I am a 13 year vet teacher. Every word you have written is true. I stay in teaching because I love it, but over the past few years I have gotten the distinct impression that it doesn’t love me back.. If I hadn’t gotten a job in a charter school this year, where I am given more autonomy as a teacher, I might have thrown in the towel. We still have to adhere to standardized testing, but those tests are not considered the BE ALL of teaching and learning. If this nation is going to retain the teachers it has and attract a new generation of teachers, things are going to have to change..
- Awesome !!
- so well stated and I agree 100%~I stopped teaching 8 years ago basically as a result of pretty much everything you have written. I miss it, but not enough to feel that emotional pain.
- Thank you. I am 27 years in and all I can think of is that I want out. I have been on anti-depressants for over ten years. I can’t do this anymore. I am glad someone understands.
- Most people have to deal with these type of expectations at their job. The difference is most people didn’t grow up next to someone performing their occupation, allowing them to develop a child’s view of what that job entails.
- Don’t forget to add in severe behavior problems, behavior plans for individual students, referrals, counseling, before and after school duties, lunch with students, and PLCs.
- Amen!!! About the only things left out were working all those sporting events (gate, concession stand, crowd control), and our ESL students. I have ESL students who work from 10 pm to 6 am, come to school, go home and nap, and start again. Their learning is limited to classroom.
- This is simply the truth!
- Wow! is all I can say…………..
- Thanks for writing this. It’s nice to know that someone is actually paying attention. When you’re in the situation and can’t say anything for fear of losing your job, it’s nice to have someone else raise their voice and question what in the world is happening…
- I think you’re exactly head-on! I’ve been teaching for 12 years and I love it but I spent most of yesterday and will spend a good bit of today working on reports that I couldn’t finish during my “work hours” because I was trying to TEACH!!
- I feel your pain. I taught first grade for thirty four years, retiring 4 years ago. Over the years I taught I went from not having a complete set of books to teach from my first few years, to watching the administration jump on every new program possible if it was recomended by some higher paper pushing “expert”. There is WASTE in education.. We need fewer experts, lots of people with good common sense, more input from the classroom teachers who are there fighting the battles, and if you find something that works don’t throw it out to jump on some glossy program that an “expert” will say solves all your problems. That program does not usually exist. If you have given your best don’t worry about the rest. Education is just a reflection of our society today. Everyone is stressed. When they have a problem the first thing to do is blame someone else. Thus all the pressure on teachers to produce a perfect product at the end of 12 years. Forget all the others who touch the student’s life daily and screw up. Through out my career I felt so sorry for the little kids who were there trying to do the best with so little support from the outside world. Sometimes you as a teacher are the only security that a child may feel Please hang in there and remember when you have done your best then that is all someone can expect of you.
- This article is great. Where can I get a t-shirt?
- Excellent article!!! I retired from teaching 3 years ago, just in time to avoid the CC mess. My heart breaks for my fellow teachers – and their students – who are subjected to this stress and insanity which is loaded onto them not by the education system (and those who really know about how kids learn), but by politicians who want to make themselves look useful. The only way to get out of this mess is to vote OUT all politicians who supported CC and replace them with ones who truly understand what learning is all about. Require all candidates to spend a week in a classroom….that’ll open some eyes! Bless you for the job you’re doing. Keep the faith.
- I absolutely love everything you said! !! It is all soooo true!!! Maybe some people will read it and do something!! Thank you!!:
- Before saying what I am about to say, I am not in any way undermine a teacher’s duties, as I myself will graduate with a bachelors degree in Elementary Education in the next year. I have several friends who are already teachers and one of my three jobs is substitute teaching. Now, the further I read this post the more I realized that this attitude is actually contributing to the problem in our schools today. I completely understand the need and right to be upset about the new standards and, like I said before, am not trying to regard your point as invalid, but where is the passion to teach? These children have nothing without a good education: no hope for the future, no chance to change the course of life their family has chosen for decades… Nothing. And to complain about professional development?! Your post is full of propaganda and by simply reading the title one can see that.
- I could not have said it any better. Children are no longer allowed to be kids. They are expected to start some kind of school the minute they come out of the womb. At one time I wanted to be a teacher, but now I don’t think I could handle all these rules. It truly is sad.
- Thanks for saying this. retired because I couldn’t do it anymore .
- AWESOME!!!!! I WANT TO CRY. TEACHER OF 30 YEARS!!!!
- Until the public understands and believes what you posted, nothing will change. Their view is all too often, thanks to the media, that we sit with our feet up and hand out worksheets. We get all this “paid” time off and then complain about how unfair our job has become. We would all benefit from walking in each other’s shoes before we criticize. I have been a political conservative all of my life and I am now appalled at what the Republicans are doing to education. Here in Tennessee, we have a Commissioner of Education who taught one year in the Teach for America program and is making the decisions to test these kids to death. I am judged by tests that are invalid and irrelevant. I am judged by a one size fits all rubric that was designed by people who haven’t a clue what it is like to teach children with special needs and language barriers. And on top of that, my final score is only based on 50% of what I actually do. The other half of my evaluation is based on how students I never taught perform on tests. Are relevant assessments needed? Of course. Do we want the best of the best to become teachers? You bet. Powers that be, please talk and listen to us. We entered this profession to help make our nation strong through educating our children. Trust our intention and ability. General Patton once said; “Tell people what job to do, not how do it, and they will surprise you with their ingenuity.” It’s just my opinion, but I don’t believe the primary failure in education has been because of a lack of effort and dedication of educators, but of a rapidly changing culture in this country that values entertainment more than preparation for the future. Let’s ALL pull together for the betterment of our children.
- Wow. Thank you. You said it all PERFECTLY!
- Amen
- Thank you from teachers everywhere.
- I have sisters (2), both of whom are educators. Both of whom are very passionate about teaching. Both whom are in specialty areas (Math & ESOL). Many hours and a lot of their personal money is spent to motivate their students. However, based on many of the things you state in your blog, both have decided to retire early. I am a grandmother of two beautiful girls — a 2nd grader and junior in college. Since the time they each entered school, I have always been involved in their education. Reading is fundamental is not just a catch phrase, it is the very foundation of the success of any child in school — especially testing. My girls had learned to read by the age of 3 and both are still very avid readers. What too many parents don’t do is “partner” with their children’s teachers, offer to volunteer to help them during testing, help them with setting up a bulletin board change. Parents take no accountability for their children’s learning, nor their failure. My opinion of course is biased because of my sisters and the long line of educators in my family, but how well your student does is a partnership — the parents need to pickup on a daily basis where the teacher ended during the school day. If a child fails a standardized test, the parent is equally responsible. I applaud you for the courage to write and the candor of your blog.
- AMEN!!!!

For the most part I really like and support the Common Core mathematics standards. But how can teachers provide the new rigorous curriculum in ways that are most effective when they are having to stop every 4 or 5 days to give some kind of test? No, I’m not talking about a ‘test’ on the unit they may be teaching. I’m talking about the benchmark tests, the Writing test, the mock Writing test, the CRCTs, the mock CRCTs, pre tests, post tests, screening and monitoring tests, STAR tests, etc. These are just the ones I know of and it makes me tense just typing them. I’ve been told by numerous teachers that they give some form of mandatory testing about 40 days in the school year! If students go to school 180 days then they spend almost 25% of their ‘learning’ time testing.

Why are students being tested so much? Because someone somewhere decided that all students should score at a certain level on a certain test on a certain day, regardless of anything else that may influence their results. Are you kidding me? What if her parents got into a fight that morning? What if he had to stay up late to take care of his little sister because his mom was working until midnight? What if she freezes up on tests simply because that’s all she’s heard about since the first day of school? What if his mother is fighting breast cancer? What if she has attention problems and needs to regroup every 20 minutes but must remain still and quiet for an hour straight? What if he was born at 24 weeks instead of 39 weeks? What if she was already 3 years behind before she got to this class? What if he didn’t have anything to eat for dinner last night and got to school too late to eat breakfast? My niece almost chewed a hole in her mouth the week of testing her last year in public school – all because of one test that someone thought should be the be all and end all of education!!

Some of you may be cheering while others of you may be thinking “Doesn’t she believe that all children can learn mathematics?” Duh, of course I believe ALL students can learn mathematics – but not the exact same amount at the exact same time of every other child their age. How many adults can do that? What made someone who ‘can’t teach’ powerful enough to ‘pass laws about teaching’? We’re creating students who hate school as early as 6 years old simply because they feel and suffer the stress that the teachers feel and suffer. Five year-olds are not even taking naps in kindergarten any more. Did you all know that? When I was five kindergarten was an option. Now if a child doesn’t go to preschool for at least one year, they are considered behind when they enter kindergarten. How can a child – a kid – be behind academically at five years old?! Something is wrong with our priorities in this country. Why not let children climb trees, ride their bicycles, play imaginary things like baby dolls or cops and robbers, play on swing sets in the backyard, play football with the neighbor kids? Instead they’re spending 8 hours a day from the time they are 3 in most cases in some form of organized learning.

So, how does all of this affect teachers? Teachers are being judged on their performance based on how their students do on the one test on that one special day. I know what the ‘guidelines’ say. Student performance is only a ** portion **of a teacher’s performance report. Yet teachers are being treated as if these scores are the only thing that matters. They are given pacing guides (often written by someone who doesn’t understand the content) that they must stay within at least a day or two. This truly doesn’t make any sense. Many schools group students based on their levels of performance – low (special ed, EIP, etc); high (gifted, over achievers); and regular (the leftovers) – regardless of what the research says about grouping. But that’s the topic of another blog later. How can a teacher with all of the ‘lower performing’ students in one classroom possibly stay at the same place on the same pacing guide with the other classrooms? They can’t. But they’re still expected to.

And all of that is just the pressure of testing. Teachers are also expected to CYA. If you don’t know what the acronym stands for ask a teacher. If their students don’t score well on a benchmark test (again often written by someone who doesn’t understand the content), they have to complete documents justifying why and a plan for what the teacher is going to do to get that student(s) caught up. In most instances they have to do their own scoring of all of these tests I mentioned earlier. They have to fill out paperwork for all of their students with an IEP or a 504 plan (my number may be wrong). They have to make accommodations for all students who legally require one.

Teachers have to be at work 8.5 hours a day 5 days a week. I know what non teachers think – “yeah but they only have to do it for 190 days.” Bull! Actually for the last couple of years they had to do the same amount of everything in even less days because they were furloughed. Furlough to a teacher just means “work without pay”. Rarely are teachers ONLY at school for 8.5 hours a day. Many come to school an hour early because that’s the only time they can get things accomplished. Even more stay late – for tutoring (without extra pay), for IEP meetings, for RTI meetings, for faculty meetings, for parent teacher conferences. And then on some of these days they are expected to come back to school at 6 for a PTO meeting, or open house, or academic night, or math bowl, or fall festival, or some club or sport that they have been bullied into leading. Then what used to be called “work days” when I was a student are now called “professional development” days. This means that teachers are supposed to be in some kind of class in which they are learning ways become a better teacher – when all they really want is time to change a bulletin board or type up those standards they are required to post, or clean the student desks because many schools don’t even have someone who keeps students’ desks or the board clean. AND most of them work during those 11 weeks of summer ‘vacation’, fall ‘vacation’, Christmas ‘vacation’, Spring ‘vacation’ getting their rooms ready for fall, grading papers, writing lessons, etc.

Now because of the wonderful world of technology they get emails all day long from their administrators, system leaders, grade level chairs, subject lead teachers, content coaches, or parents. Probably only 5% of those emails are positive and thanking the teachers for what they are doing or have done. Most of them include reminders of something that they must do, or complete, or turn in, or go to. Parents complain about what the teacher is not doing for their child, or because they got a note home that was worded in a way that they found offensive.

In order for any teacher to successfully do ALL that is expected of them they would no more than 12 children in their classroom. Yet, due to financial constraints their classroom sizes are becoming unbelievably large.

Are you tired and stressed yet? I am. I can guarantee you that my blood pressure is higher now than when I first started this blog. Have you noticed that nowhere have I mentioned that these teachers are parents of their own, have aging parents they are taking care of, do volunteer work, go to graduate school, have health problems (mostly caused by stress), are single parents who are working a second job because they aren’t getting enough child support and make too much to get government assistance, are active church members, or Lord forbid – have a hobby?

I guess this all explains why I have seen 6 teachers cry in the past week. Most teachers have not even been able to finish reading this post because they simply don’t have enough time. So that means that those of you who had the time to stick with it needs to figure out what we can do as a nation to change things.

Yet, as an individual there is something you can do. Love and appreciate teachers. Tell them thank you. Show them kindness. Send them cards. Consider what their day may have been like before you criticize something that they have written or said. Pray for them.

(Disclaimer: I realize that everything I have written will not be considered politically correct by some. Sorry.)

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The center circle is what a child can do by herself. The middle ring is called the Zone of Proximal Development. This is where a child can learn but will need some help. The outer ring is currently out of reach for this child. And if you consider moving from the inside circle towards the larger ring, one must pass a mathematical wall or any other kind of wall (discussed in the previous blog).

Ok, so what? Well, let’s say that a child is being asked to practice the subtraction algorithm with regrouping over and over. If this concept is one that this child can do by herself (in the center circle) then the practice will help this child become more adept at correctly solving these types of subtraction problems. [Does this mean the child ** understands** subtraction? This will be saved for a later post.] When a child practices what is within that center circle, the concept will eventually become automatic. Children are happy within this circle of comfort. Teachers are happy when their students are within this circle. And to be honest, teachers as students are happy when

What if a different child is being asked to practice the subtraction algorithm with regrouping over and over and this concept is not inside their center circle? They are faced with a wall and have 3 choices: Stop (and wreak havoc in the classroom); go around it to just get by (which means that they probably practice all of the problems but make numerous errors and do a pretty good job of solidifying ** their** version of the algorithm inside the little circle); or they can start climbing over the wall with the help of others.

This is where the teacher role (and parent role) is so important. So the teacher is careful to not assign practice too soon; and the parent is careful to not ‘teach the way I learned it’ too soon. The teacher must know at all times what her students truly understand and what they need help with. This doesn’t mean that the help has to come from the teacher. Students can learn from each other and create knowledge together. In order for this to happen the teacher needs to provide numerous opportunities for her students to develop an understanding of what subtraction really means. (This is why the new standards have moved the subtraction algorithm to the 4^{th} grade – so they have time to hang out in the ZPD with their peers for a while until that wall is no longer a wall.)

As I mentioned in my last blog, there are many walls I would have never climbed ** by myself**. Being in that center ring is uncomfortable. We are raised in a society to be independent and do everything by ourselves. About as soon as a child begins to speak, he/she also begins to say “I do myself”. We need to teach our students (and ourselves) that it’s ok to be uncomfortable and it’s ok to need others.

Teachers seem to be afraid to make students uncomfortable – maybe for fear of students whining, or of parents calling to complain, or of simply moving out of their own comfort zone by pushing their students out of theirs. Teachers (and parents), if your children are NOT having trouble with mathematics, ** that’s** when the teacher is NOT doing what she/he should do. The only time a child should be in a comfortable place is when he/she is doing meaningful practice of a concept they already understand. They are just practicing until they can do it automatically.

And what’s in the outer ring? Probably the idea of multiplication as a way to add large groups of the same amount, or rational expressions, or quadratics equations…

Guess what happens when students spend time together in the ZPD developing understanding together. What ** was** in the ZPD for the child will move to the center circle and something that used to be completely out of reach before moves into the ZPD (this is what I have labeled as ZPD 2).

With a thoughtful and intentional teacher, mathematics students will begin to see walls as a bump, not a skyscraper. They will develop the belief that they will eventually cross that hurdle. It will probably involve working and talking with their peers. It might involve reading what someone else has written. It might involve the student asking questions. But they know that whatever they are struggling with now will eventually become comfortable.

So I will close with my question from the last post: Are you comfortable with being uncomfortable? Are you comfortable with making others uncomfortable?

As you can probably tell ‘making others uncomfortable’ has been moved from my Zone of Proximal Development to my center circle of comfort.

]]>My experience has been that most teachers go into education because they want to help students learn. Yet, as stated in the previous blog, we live in a society where we avoid making others uncomfortable at all costs.

The ‘best’ math class I ever had in college was Introduction to Higher Mathematics – a proof class. We had no homework, no tests and no final. As long as you participated in class adequately you got an A. We all loved it…until I discovered that I was actually supposed to learn how to mathematically prove something and I would be expected to do so in every math class that followed. I liked the easy path and did not complain about it while I was in the class. But you can bet I complained in each of the subsequent mathematics classes. I did not have the necessary foundation upon which to build future understanding.

I am quite sure that many of you can relate to “lacking the necessary foundation upon which to build future understanding” when it comes to mathematics. It is my belief that everyone will hit a wall at some point when it comes to understanding mathematics. The only question is ** when** the wall will show up. Even full time mathematicians may spend years trying to understand a piece of mathematics that’s just beyond their reach.

When faced with the mathematical wall you have 3 choices – stop, go around it, or climb over it. Those who stop are the ones who develop self-helplessness, fear math, hate math, and/or avoid lifelong dreams because of math. Those who go around the wall are those who choose the easy way out – either intentionally or unintentionally. These are the people who seem to do well in mathematics. They are not afraid of it; as a matter of fact, they might even like it because they feel successful. I was this type of person. When I hit a wall I found success at just paying close attention to the rules that the teacher was giving. I knew that if I tried to follow the patterns just as the teacher had, then I would be able to get around that wall. The last group of people is those who choose to climb over the wall. Just like there are some people who are born with an athletic desire, there are those who are born with a desire to understand the relationships between mathematical concepts. I was not born into this group.

I believe people can learn to make a different choice. I have a family member who was the stopper. She was able to go around some walls, but always dreaded the next wall and rarely believed that she could get around it. As an adult she was faced with a dilemma – stay stopped in front of a mathematical wall called ‘The Test’ or she could choose to try to climb over the wall and follow in the career that she felt called into. She chose to climb, developed the understanding necessary to scale that wall and ‘The Test’ no longer stood between her and her dreams.

I am an example of the person who always walked around the mathematical walls until I arrived in graduate school. It was at UGA when I discovered that I would not make it through the PhD program by walking around mathematical walls. I was going to have to climb over some of them and boy were they hard to climb. I quickly learned that I couldn’t climb by myself, I needed help. We would spend hours (and sometimes hours and hours more) working together to understand a concept and guess what would happen when we found ourselves on the other side of the wall? We would rejoice! We would high five. We had worked hard, fallen, gotten scrapes, and sometimes even fights but we would always end rejoicing together. Then we would take a deep breath, start again and moan when it was time to climb another wall, but we didn’t stop. Mathematically I have stopped climbing walls but I have gotten so much better at understanding the relationships within mathematics in the early grades that I can pretty much leap over the old walls without much effort.

My cousin and I had a reason to try to conquer these mathematical walls; we had a long term goal that required us to. Young children usually do not have those long term goals to motivate them to try to climb over mathematical walls. In many cases these same children are also in classrooms of teachers who mean well but who try their best to protect their students from struggle, from discomfort, from frustration, and unknowingly from understanding.

This blog has become much longer than I thought. I have not completed my thoughts, but I need to stop. Look for the next blog where I continue my thoughts on discomfort and understanding…

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