The Blogs

Student Choice in Middle School Math

So, I am trying something new this year with my middle school math units. I am offering a choice of three. After I assess a unit, I am setting up the next unit, for three different levels of math, and then allowing students to decide what they want to learn next.

Full disclosure before I begin describing, in my middle school classes, I teach grades six through eight, in four different sections, all multi-grade.  The sections are also single gender.  I have two sections of girls and two sections of boys.  

So, I am trying something new this year with my middle school math units. I am offering a choice of three. After I assess a unit, I am setting up the next unit, for three different levels of math, and then allowing students to decide what they want to learn next. On the surface, it sounds like a lot of voice, and a lot of choice… new educational buzzwords. I’d like to defend my reasoning. I will do so by way of example as I think that is easier for us linear math-ies.

I start the first day of the new unit with a preview day. First up, ratios. The unit is a “typical” sixth grade level unit on ratios, understanding and application. I do three problems that the students would see in the beginning of the unit so that the students can ascertain for themselves if they have every seen ratio notation and can manipulate a fairly simple ratio table. I also set up a proportion, solving for a variable. The second level unit is proportional relationships, and is crucial, in my opinion for foundational learning of math. I always over-estimate to students that if they can master learning of proportions and how they work, they can solve 80% of all math problems going beyond the 7th grade. To preview the proportional relationship unit I give students three problems to try- scale factor, percentage decrease, and estimation of sales tax and tip (using number sense, not a calculator). Again, these preview questions were ones that would be found in the beginning of the unit, giving the students a sense for themselves if those are types of problems they could solve with ease, with or without a simple reminder. The last unit offered was an abstract unit on understanding numbers. On the surface it seems simple because it starts with sorting numbers such as fractions, negatives, and decimals into categories; however, at the heart of the unit it is about exploring sets of whole numbers compared to natural numbers, about closed versus open sets, about what makes a rational versus irrational number and how to describe them, etc. Most middle school students, even the most advanced ones, are able to calculate and manipulate the numbers, but are not able to describe and apply the vocabulary to numbers enough to truly understand them.

The preview lessons were interactive as students use their individual whiteboards to try their best to answer all of the questions presented. In the mixed ability, mixed grade classes, there were students who could answer most or all of them, and some students who had not even been introduced to ratios at their old schools. The challenge of using the class time wisely is not to get too bogged down in teaching the concepts, but also to allow for some validation of the dedication of work of the students. For example, after the first problem I put on the board: Write the ratio of stars to all shapes as a ratio in 3 ways: △ ★ ★ ⮹ ⮹ ★ ⮹ ★ . I gave the students only about a minute to answer because they either knew it or they didn’t. Then when providing the answer, I used language such as “remember there are 3 ways” and “colon is the most common” and “the word ‘to’ is the one most people forget” so that all students would begin to feel comfortable, even those who have never seen ratios before. After demonstrating the answer as 4/8, I ask all students to reduce to simplest form, as just about all do not. This task is something that even students who have never seen a ratio can do, and then they feel some success. All of this teaching takes 2 minutes, at most, which allows me to see who knows ratio, gives the students an idea of their understanding of ratios, and also provides a nice review or learning experience for the day before we move to the next question where more learning occurs. In this way, pre-assessment is also a learning activity.

After the preview of all three units, which took approximately 3/4 of our class period, or about 40 minutes, I encouraged students to decide where along the continuum they felt they would best be served, even if they would not be following the path of their previous unit. For example, students who just took a post-assessment on decimals and volume would next be studying ratios, if only following a sixth grade curriculum was the norm; however, if they have previously learned it, or feel confident doing that unit on their own without direct teaching, they can move “up” to proportional relationships. Similarly, if students previously studied and tested on square roots (a pre-algebra level class), but really missed studying proportional relationships and need the foundation, they can choose to do one or two units with direct teaching.

The practical- I had the students write their names next to the unit(s) of their choice on a public dry erase board in the classroom. From there I assigned their first lesson on our LMS so that the students could independently answer the questions and complete the learning activities. I knew that a few students would select units that were a little too difficult for them, and from this first unit they could adjust before starting the direct teaching and the more difficult, lesson two. I also knew that some students would choose units that were too easy, and some students did self-select to move on to other units, and others needed help to select other learning. A third by-product of allowing students to self-select unit was that some students chose to challenge themselves and also reinforce their own learning by doing multiple units- one that is self-taught that is reinforcing their gaps from previous years and one that is guided by the teacher and moving them forward in their curriculum. Utilizing the LMS helps me personalize the learning.

This isn’t the first time this year I have had the students self-select their learning or their units, but it is the first time I have been as pragmatic and, honestly, as thorough and personalized once chosen. I am challenged by the shift and I am excited to see where it goes.

As always, I encourage discussion, on this forum, or on the social media from which you found this post. I’d love to hear your feedback.

Time Management or Managing Time

A Ramble: What are we doing well as educators, as parents? What are we really helping our students and children learn through, and beyond, academics?

There are many ongoing debates in education right now. One of them that seems to pit teachers against parents and teachers against teachers, leaving students somewhere in between, is the debate over the value of homework. For that matter, there are plenty of conversations as to how class time is best spent, and how curriculum, instruction, and assessment can be utilized, in tandem, to guide students towards the ultimate potential. Sounds great! Sounds great?

In order to reach every student’s potential, units and lessons should be a combination of differentiated, personalized, and individualized (check out my presentation in the resources section). Learning should be engaging, active, rigorous, and relevant. Along with content, students should be taught executive functioning and social-emotional skills that will help form learners and citizens that will succeed in school and in society at large. No small task, of course. Is it possible for teachers to plan, implement, and assess in classrooms that are truly teaching and reaching students in a way that are society is expecting? How is there time in a 24-hour day, 7-day week?

Of course, my statements are slightly hyperbolic. No one can, or should, work 24-hours in a day, every single day of the week. And no one can possibly expect every lesson to be as described above. However, on the flip side, it is exactly the type of pressure educators are putting on ourselves, and the type of pressure that is driving educational movements today, in and out of school buildings. So, the questions arise- how are educators using time? How should we, as teachers, plan for students to spend their time out of school? How should we, as parents, expect our children to spend their time out of school?

It isn’t an exaggeration that time is limited. We are only given so many hours in a day, and so many weeks in a year. Knowing we cannot literally use all of the time available, how do we best use the time provided. I’d like to give my opinion at this point in my career, at this point in my life, and at this point in the year. I say it this way because I know that experience has changed my views. I also believe that as the year ends, and I am a reflective person looking towards a fresh start of sorts, I want to give another caveat to my point of view.

I encourage dialogue via the comments section below, and also via the social media outlet from which you may have been directed here.  Discourse is a way to learn.

The role of adults is to help guide children, to guide students towards becoming educated and productive members of whatever group and society in which they choose to live. Teaching our students and our own children to manage their own time is important, a skill, I believe, most people do not naturally learn on their own. We like to say that we can’t teach intrinsic motivation, but wish that all people had it, of all ages. I think we want students to be intrinsically motivated so that true learning can take place. When learning is authentic and genuine, time, and its management is often not a factor, only a constraint by our school system or our families’ busy schedules. It’s a dichotomy we need to teach our children to manage, for better or for worse. We need to help guide our students to love learning for its own sake through instruction that facilitates it and we need to explicitly teach time management.

Do we teach time management skills through the mundane necessities that often come in life, but we are wanting our children to experience less and less? Or do we teach them to manage their time and their energies to focus on what is priority at the moment, and what is fun and engaging? How do we balance learning for its own sake, with the stark reality that there are tasks that do need to be accomplished, and accomplished well, for their own sake, for the means to the ends, and also for learning how to be members of whatever productive society and culture in which we are happy and healthy participating members. Teachers and parents need to work together for the sake of a next generation that, unfortunately and fortunately, have so much more to learn, and can learn in ways that are beyond exciting and beyond fun. Students of today are able to have almost a customized education, of sorts (an oversimplification, best understood by knowing the difference between differentiation, individualization, and personalization), one that many parents are demanding, and schools are trying to find balance to figure ways to accommodate. However, is the push to find the potential in every child, every lesson, of everyday, leading us astray of skills that may be necessary to help facilitate learning, one of them being the management of time, and with it comes the management of mental energy? All of the new trends in education today, and all of the debate over whether homework is needed, or what type of homework should be given, or when school should start and what students should be doing while in school, may all come down to how well are we, as adults, helping to explicitly teach our students how to realistically manage their time and energy in a world that is 24 hours a day, 365 days a week in their demands.

I encourage dialogue via the comments section below, and also via the social media outlet from which you may have been directed here.  Discourse is a way to learn.

Faith, Family, Football:

Sunday Priorities? Perhaps.

How do we determine priorities?

It’s another Sunday. I am not planning for the week tonight, but I will probably assess some tests, if I can muster the energy. This week has been one of reflection, about education, its state, and my place in it.

So what are the priorities this Sunday? Family, for sure. We spent a lot of time together on this rainy Sunday. To me, some of the best days are the nothing days, the days when everyone is home, doing nothing, or avoiding what they should be doing, television on, and just hanging out. It’s even better with football games on, in today’s case in the background, with the big games to come tonight, and tomorrow night.

Was there nagging to do more chores? Of course! Was there even more encouragement to do reading and homework? Definitely! Not sure how effective I was today, but, then again, I know when to fight the battles, and today was not one of them.

On this Sunday, not motivated by a particular football team, it’s even more of a time to reflect upon the gifts of faith and family that push me to continue in the field of education. This week has tested me. I did not work directly with students this week and without the ultimate beneficiaries of my dedication I find it easy to start dreaming of what life would be like with another profession. What would my hours be like? Would I have more time to read for pleasure? Would I have more energy so that my house would be cleaner or I would exercise? Would I have saved more money so that I could be in my “happy place” on the water of CI, VA instead of dreaming of it?

The flip question has to be, what would education be without me? The same, for sure. I mean, seriously… I am just one person, easily replaced in a job, even in a career, as everyone is. If there is one thing I have learned in my 2 1/2 decades in the “real world,” it is one is only irreplaceable to their family. With that perspective, however, my reflection this week centered around career goals and what type of impact I want to make on the field of education. After 22 years in education, is it time to move on and find another field where I can utilize talents and potentially focus on other talents? A perfect storm of a pro-con list… but in reality, the cons outweigh the pros. I am not done impacting students. I just want to do it on a grander scale. You are all a part of my dream because you have taken the time to read my blog posts, and explore my presence on this site and on social media.

In future days and weeks to come, please visit back for resources, for more discussion, for information on my presentations, for my curriculum, for education. Faith comes in all forms, and this Sunday I reflect on a week that has led me to regain faith in myself. Thank you to my family and my like-family for always supporting me. And, well, football… thank you for my escape.

“I thought there would be no math.”

I was watching one of my favorite morning shows, Good Morning America, and the anchors were jokingly laughing off their inability to quickly calculate something that would have added to the light-hearted conversation with an off-handed quip we often hear, “I thought there would be no math.” In other words, ‘it’s okay that I can’t do math, because I can read and I am good at other things.’ One of my other favorite morning shows, Golic and Wingo, even has a button they push that sounds when the personalities become befuddled by the numbers. Theirs is similar, “I was told there’d be no math.” I always take exception to these sentiments because, obviously, we are sending the wrong message.

An even further wrong message was heard at a recent college tour we took with our son, a high school junior. As the admissions counselor was describing the requirements of their liberal arts program, hoping to hook the kids, she opened with, “Has anyone ever been victimized by math?” Victimized?? Seems a bit harsh. I always joke as a teacher when students tell me they are not fond of math (that’s a nice way to put it). I joke with them by asking in what ways numbers have actually hurt them. That gets a laugh, but maybe you need to hear my tone and see my corny face when I say it :). But, this counselor was actually trying to insinuate how painful math class and math with numbers can be, to the point that this college was going to replace all of the kids’ harmful K-12 experiences with a better, more fun class that will be more useful to them. I can’t argue with making math class more real and more meaningful. Whether something is fun, that’s for another conversation, I believe. What bothered me most was that our son, and seventh-grade daughter with us, already both not math-lovers, are once again hearing how awful math is, and in this context, from an educator.

Math educators have uphill battles, maybe more so than other subject areas, but what are parents to do? Society is not subtle about a preference for reading, for history, for science, for art, for sports, for almost anything besides math. Some kids start out with a natural propensity for counting and numbers, and continue a lifetime love of math, paralleled with success in math classes. The parents of these kids probably have an easier road through school, as many subjects and leveling, etc. are tied to math success or failure.

On the flip side, other students struggle with math concepts their entire lives. While still others are up and down depending on many factors, including the type of math involved. The parents of these two types of students may find themselves needing to support their children during their years in school, and at home, and most do not know exactly what to do. I have seen that many battles with math in kids, and probably adults, comes down to confidence, more so than any other subject. Due to many of our schools’ tendencies to tie their overall class structure and opportunity to math ability and/or successes, it is an unfortunate product that math confidence is tied to overall academic self-confidence. I believe I have counseled more children than I would have liked in what seems basic: one’s self concept should not be tied to math ability (perceived or actual). At the heart of the college described above, I do believe they are trying to find the math mind in every kid and try to build up those students who have lost their confidence, however, the message came across like all of the others we hear in society- you either know math or you don’t. If you don’t, it’s okay. If you do… well, you must be the smarter one because us here certainly can’t figure it out.

In our house, one of our the things we like to say is, “Math puts food on the table.” Both my husband and I teach middle school math, for many years. Both of our children are far stronger in writing and history (our son) and writing and science (our daughter). In fact, they will do anything possible to avoid math, and many nights have been a complete struggle to finish math homework. Some years, passing math class has been very close, and too many dinner conversations, car rides, and money have been spent making sure math is understood enough to pass the tests the school feels are important to pass. Don’t get me wrong, I support the school, and their assessments. I just wish, somewhere along the line, someone, or something had sparked a love of math, or at least something that would have provided a like for the subject and the potential that it can have. Math can be more than just learning concepts and completing assignments.

Will math put food on my grown kids’ tables? Probably in some form or another, but not in the way we have provided for them in our house. I mean, seriously, without math we literally would not have food as we have made our living teaching math to hundreds, if not thousands, of students. The most important students are the two that eat dinner with us every night. We do not hold class each night. We have already taught during the day. We have sparked, we have provided opportunities that will create critical thinking and joy, and we have followed our curriculum, and our own children have already gone through their day, exhausted also by 8-12 hours of learning and activities and practice and work and chores. Should we do more? Should we tutor in a way that will provide what we want out of math that ensures math directly puts food on the table? I am sure we will be greeted promptly with eye rolls like every parent gets. The best we can offer is to be there to support our children when they need help with all homework subjects. To make sure that every subject gets equal billing. To make sure that all subjects gets positive words, but especially math. That we “Yay MATH” whenever possible. We are role models by living the life of math, selectively nagging, so as not to push two teens away. We lit the fire of math and let it simmer, until one day it will come out as it is intended in our children, as this world, and our daily lives in it, cannot function with numbers, and at least a basic understanding of them.

It’s Sunday Night- Planning Time!

In my opinion, Sundays are one of the best days of the week. Although it is obvious and imperative to build upon the academic and SEL work that has been done last week, and the entire school year, it’s like a fresh start for a new week of learning, Whatever may have caused any stressors last week seem to fade to distant memory of Friday and Saturday with family and activities. Sundays are days of football watching, of straightening and organizing, and, of one of my favorite intellectual pursuits, planning for the math learning of my students, this year in grades four, and in grades six through eight.

I have always enjoyed the development of curriculum, and have never been able to just stick to the program that the school purchases. I use “the book” as a guide and a resource, combined with a the standards that students need to reach by the end of the year. I am blessed that I have always worked in schools throughout my career that have allowed me to utilize my creativity and my education to do what I feel is best for my students. I have added activities and ideas, from resources that I research or from my own creation, that I know will interest my students, or more importantly, be impactful to the students’ needs as math learners. As teachers, I know we have an intuition that sometimes supersedes data, we know what our students know and don’t know, and can use the “art of teaching” combined with the “science of teaching” to produce the perfect balance of challenges within a learning environment.

At this point in my career I am focusing on teaching math so that they get excited when they figure out problems, to excite students about numbers, to increase the confidence of all students, especially in mathematical pursuits. And… I personally strive to reach every student in a way that all of their gaps are filled without overlapping with prior mastery. My hope is that if I do overlap learning they have done before, I do it in a way that is more meaningful, more rigorous, and/or in greater context so that it builds numeracy, critical thinking, and appreciation. It is not easy to teach math in a personalized way, it takes time. And, as I am learning this year, and slowly documenting here, and in a notebook, and of course, in my mental notes, it takes prioritizing beyond just time.

Tonight’s planning for this week? Well, the middle school students, grades six through eight has been set with an upcoming assessment. My focus, as part of the prioritizing, is a new way to look at a fourth grade class of almost thirty students that I feel has not learned in a way that provides the education the students deserve- it needs to be more personalized. It needs to be more math. If I had my way, we would do math the entire school day! But, alas, I am only allowed so many minutes, so it’s about flexibility and thinking outside-of-the-box, and being grateful for the generosity of colleagues. Tonight, I am solidifying what I have been thinking about for a week- I am putting in a plan for hands-on, and face-to-face, and paper-and-pencil centers, all surrounding the topics of factors, multiplication and division, at a variety of levels. Let’s see how it goes!

Thoughts in the Trenches

New: I will have an occasional post of more journal-like blogs. An inside look into feelings, activities, thoughts, etc. of my experience as a teacher, or as a teacher-mom, or as a mathy-mom. Frequently, it is my hope, as I grow, to have them quickly followed up by a more professional post. It is not my intent to vent, so I hope you do not find that they are full of grousing. My goal is to share, while also providing a springboard to conversation, or at least of thought.

So, I have so many ideas of posts I want to share. I have been keeping notes in my classes over the past couple of weeks- when students get excited, and when they celebrate the little victories they didn’t even know they wanted to have in over numbers. I also have ideas from my recent trip to the NCTM Regional Conference in Boston, which I followed up with a couple of college tours. I will post them… soon. I want to document them, and I want to document how I am personalizing learning, and I want to document my curriculum growth. But first, I want to connect with something that seems to happen every fall…

Teachers, has this happened to you? Has your year begun to get away from you, and quickly? That is what is happening to me. Best intentions for success in all aspects, has quickly become a game of ‘which priority should I attend to today’? Is planning important? How about assessment? What about utilization of the assessment? Implementation??

I have chosen implementation. Of course, I plan. I have planning down as curriculum is my area of expertise, at least I am hoping so after all of this time and all of the money I spent on my degrees in curriculum. Plus, I just love planning. So, I plan, before AND during my implementation with students. But, the real priority is the learning of students, and with the miracle that is teaching that allows the students to have the power to push all of the teacher “stress” out of the window while I just teach them to love math and to learn math. I choose implementation over all else because if I leave nothing else in my wake after the sunset of my teaching career, it will be that math can be learned, and it can be fun!

I’d love to hear your thoughts, and welcome you to make this a collaborative venture.

Excitement over Content?

I mostly teach middle school math. It’s not usually the subject to which students look forward to returning from their summer. This year I tried to accentuate a version of what I have done in years past- engage students in how awesome numbers are, all while integrating the routines of the classroom. I mean, numbers are cool! So, this wasn’t too much of a stretch!

Early in a school year, one of the main routines that I think is critical to running a successful classroom is to teach what to do when students finish early. For me, if students are doing work that is meaningful, and math-related, for the entire period of time they are with me, the benefits will be plentiful- more teaching and learning time all around… and an exponential potential love for math!

However, teaching students the routine for finding interesting activities takes time in the first few weeks of school. I purposefully made lessons shorter than normal to provide time to practice going to the “extras.” I purposefully engaged the students in activities during the shorter lessons to make math learning fun, so that they would want math to continue after the lesson.

Sure, this year, I gave a few pre-assessments, and I also introduced my weekly skill assignments and procedures, however most of the time we kept it fun, we kept it new, we kept it about the numbers. For example, on the beginning of Palindrome Week, I showed the students a quick video about how this could be the last week until 2111, and then they were able to prove the video wrong with some eager thinking. That was exactly the lesson I wanted them to get out of the video, beyond what a palindrome was. I wanted them to learn to question the internet with their trust in themselves as math thinkers! So proud, so early in the year!! Then I taught them how to use addition to turn numbers into palindromes (403 + 304 = 707) and they were off to find the more challenging ones.

Two of my favorite overheard quotes of the day, from the middle schoolers:

“This is actually pretty easy. I’ve never done this before.”

And then when given the option of choosing what to do when finished my portion of the lesson, a student added, “Yes! We can continue the math!”

Mission accomplished. I have slowly moved into content, this third week of school, but my students are now engaged with numbers, and with math, and with themselves as math learners within our classroom.

There may be errors, but there was excitement… And the early middle schoolers, previously not excited about math, picked up on the concept, and became engaged. We are now ready for content.

Let’s Talk Math!

Welcome to my thoughts, and to this exploration of teaching and learning math, in school and at home. Welcome to my reflection, of education, of a career in transition. Welcome to my documentation of my own learning. Along the way I’d like to interact, to learn and reflect together, to provide you with new ways to approach math curriculum, and to open up a world in which we are all talking math! Thanks for joining me!

I invite you to explore the pages of the site and begin our learning journey by starting a conversation or signing up for updates. I will be posting about my first week soon.