Is there a debate: Are students behind in math?

To be behind insinuates there is a line, someone must be first, and someone must be last, with everyone else lined up in order. As parents we want our kids to be near the front of the line, and anything else is difficult to watch.

Before diving into the debate, and more serious discussions on matters related to education, math, and the future of our children, let’s set up an analogy. Are you behind in the laundry? I know it’s not exactly the same, nor is it “worth” the same. I get it, because I love math, and I live math. But, this is also a family blog, so hear me out.

Laundry (or fill in the chore of your choice)… some weeks I feel so caught up, it’s glorious. But, in reality, it just keeps coming, and if I am being honest, I should never rest because there is always more clothes to wash, or fold, or put away, or organize. There is always something new to do with clothes to make the laundry situation better. Most days and most weeks, it is good enough. Sometimes, though, it is overwhelming, and all of our bedrooms plus the laundry room are overflowing with clothes in multiples stages. Am I behind? I think the questions really are: Am I not up to my standards? I am not keeping up with the other people in the neighborhood? Am I disappointing people in my family? Is my mother-in-law judging me? Am I behind the laundry chore timeline that earlier generations of laundry care have set?

You have probably seen some of the articles about students being behind in math because of being out of the classroom since March, in whatever fashion that looks like in your schools. Or, maybe you have seen some discussion about it on social media. Here are some resources for background:

So, are students really behind?

Due to Covid-19, most of our kids have been schooling differently for almost a year now. Will that make a difference in their education? In their futures? In our collective society? No one really knows the answer to these questions. There is a lot to conjecture, but I think it is clear there are concerns about students falling behind academically. As an expert in learning gaps, I can examine the impact of remote (or hybrid) learning might have on your children, and give you some advice moving forward.

The opinions in articles have used test scores as evidence for lack of growth, as in every other school year. Among other findings, a highlight is that math scores “slipped 5 to 10 points” compared to 2019, while reading scores have remained stable or have increased. Further investigation, in my opinion, needs to be done surrounding the assessments. Granted a very small sample size, my own children have been in a school building with any consistency since March, and I do not know how they would have taken any standardized assessment of the caliber or validity needed for data to determine the progression of learning this year. On some tests they take, their cameras and microphones need to remain on, so distractions from every home is abundant. Other assessments allow for both cameras and microphones off. Not sure how any test results can be valid in that situation. The impact of internet stability, computer accessibility, and home environment are variables that cannot be overlooked when determining progress. Best practices in recent years has shown that for K-12 classroom assessments, a low-stakes test is preferred, especially in our current climate, but if we are trying to measure progress, we cannot rely on taking online assessments at home.

But, there are articles, opinions, and some data. So, what does all this mean?

Reading scores are doing well, according to the reports. My hypothesis is that students are most likely performing better in reading than in math because the majority of students can read at home with little to no adult assistance, at least by third grade. It’s an independent activity, and also does not necessarily build on the skills of the previous year. For example, let’s say last year your child was supposed to learn idioms, but did not do that due to the schools closing and remote learning is difficult. While there is a gap in his learning, one that will need to be filled eventually, it may not be inhibiting him from learning about sentence structure or protagonists now. Parts of learning in language arts are linear, but it isn’t as dependent on prior concept understanding as math. 

Math is a less- less independent of an activity, less understood by parents, less liked by children, but also it is more linear. It is more important for students to have mastered (or at least been exposed to, and actively participated in) a previous concept before moving on. For example, let’s say now your child is learning to solve for x in what you think are simple algebraic equations and she is struggling. The issue may not be the remote learning, per se, but that it may be hard for her to learn so solve all problems for x if she either never learned or never was exposed to adding and subtracting with negative numbers, or does not understand inverse operations. Some parents try to teach the current skill, in this case, solving for x, but it is harder to really understand what is missing that is most challenging for the student.

There are many issues, educational and otherwise during this pandemic. I am not minimizing them, and certainly not trying to compare them to dirty clothes. Students who struggle in math have been struggling prior to last spring, and may be continuing to do so now. Parents worry about their kids, that’s our job. We feel the pressure of so much now, and when data is coming out that math scores are lagging, and we know we alone might not be able to catch them up, it feels similar to the experience of when the laundry is piling up. Do we give up or do we panic? I’d argue, somewhere in between, or really neither. When the laundry starts to feel overwhelming, as wonderful as it may be to just throw our clothes out and start over, we certainly can’t give up. It’s not practical, and definitely unrealistic for most of us to do that. We just need to take it one task at a time, and get caught up. The laundry will get done, at least for the moment, and then we will get to a place where we will feel the pull of being behind and then ahead. For laundry, like learning, there is always something to do, for all of us.

Obviously it is easier for most kids to learn in the classroom. Under all of the debate out there, I don’t think anyone is disputing the school setting is what is best for students, where kids and students are not solely on their computers, regardless of the location, where interaction and discussion, and real learning can happen. I envision that education will change in 2021 and beyond, as we address priorities, learning styles, advancements in technologies, societal shifts, harsh realities, etc.

Learning gaps will need to be filled, and I am hopeful, and passionate about that. The questions are many, and should be asked now by educators and administrators at all levels: If students learned less, what skills do they need to learn? Are they missing skills, and how do we make sure they “fill the gaps” before moving on to learn concepts that require foundational concepts? Can we do this concurrently? How is the best way to fill gaps? And most importantly, when can we get started? Remote learning has some benefits, that I will call silver linings. No one is saying it is ideal for everyone. However, we can fill gaps virtually, with targeted lessons. All teaching and learning is valuable, and any time we can get our kids to log on and be engaged, even if it is with the ceiling in view and not their faces, it is critical to do so. But, more than just logging in and teaching math, which is more than a challenge now, but an uphill battle, let’s do it, target gaps and personalize the learning for students. Let’s let technology be our co-pilot and help our students with lessons they can use. And, when we return to the classroom, let’s continue to be patient. If we readjust the expectations, and then rise back to our levels of normalcy, in every facet of our lives, including math education and math learning, I know we can be back on track. The future of our kids’ education is dependent on how we handle the transition back to school. Sometimes slow and steady really does win the race, filling the gaps and sealing the holes along the way.

Photo by Mateusz Dach on

The laundry will always be there. Learning will always be here, and no time like the present to start filling gaps. But, the debate remains: Are students behind? To be behind insinuates there is a line, someone must be first, and someone must be last, with everyone else lined up in order in the middle. As parents we want our kids to be near the front of the line, and anything else is difficult to watch. We want to do anything we can to help our kids. But, my fear, as a math educator and as a parent, is that we are doing too much comparing and labeling right now, at a time when a better strategy might be to take each day as it comes, and work through each task. Learning, like laundry, will always be there in the sense that there is no end, it’s a journey towards our own destination, whatever that may look like. There’s no end to learning, as there is always something more to learn.

Is there a debate? Yes. But, are students behind? No. Not really. I guess that’s for you to decide whether we can use relative terms to determine students’ progress. In my opinion, even though we might be able to use arguments of curriculum position (“My kid isn’t where he should be compared to other years”) or scores and grades are lower (“My kid’s GPA is much lower than when all the kids were in school), all of these, we must remember, are also constructs created by educational institutions to build the journey towards an end destination (promotion, graduation, school advancement, etc.). It is important to remember that math learning is a journey, and even though it may seem different now, it’s the impetus we need to change the way we teach and learn.

However, I will leave it up to you, my readers, to decide, and to debate. I encourage you to comment, or to go to my my Facebook page or website for resources on education.


The Gaps…

Finding and filling the gaps are the critical missing pieces… to student success, to curriculum development…to how the whole child is truly learning.

So my life has become about gaps now. At least my professional life. I promised in my last post that I would explain my new professional venture and here it is. I am filling gaps. A passion of mine, or it has become one.

In the latter part of my two plus decades in education, most of which was teaching mostly math, I spent a great deal of time researching and practicing personalized learning. I was wondering how personalized learning differed from individualized learning, as they seem really like synonyms until you dive deeper. And, I also spent an even greater amount of time unpacking the years we were drilled as teachers on differentiated learning. I did a lot of drilling myself, that differentiated was the way to go. Differentiated learning seemed to work, especially for a whole class, and especially for one teacher with a lot on her plate. But, then as education seems to do, it cycled to different ways, along with different words, and one is left to decide are the new ways just new words or are they worth trying?

Without diving too deep into educational practice, as this isn’t a post about that, when I think about differentiating a math lesson, I think about making sure that each student has something at their level or their interest, for whatever portion of the lesson that may be. When I think about individualizing a lesson, I am making sure individuals have what they each need, but in a way that really understands the individuals and gives individuals attention. This is not an easy task, when compared to differentiation, in both planning and in implementation, for any size classroom. Think about differentiating versus individualization for an ice cream bar for a kids’ birthday party. Differentiation would be comparable to providing a range of choices based on different abilities and interests, gauged prior to the kids’ arrival at the party. The adults would then be available by walking around and making sure that the kids are able to enjoy the party. The choices were available to the kids and the adults were there to guide them to what was better for them. This would be easier than an individualized ice cream bar that may look like every child receiving their favorite flavor and in a vessel they are able to eat out of, which was accomplished by the same pre-party survey.

Personalization of learning is a buzz word recently, but for me, in math, it is one of the hallmarks of best practices. All teachers personalize to some extent, just as they differentiate and individualize at times. Actually using a combination of the three is an excellent way to run classrooms, and knowing when to use techniques for which students and which subjects is the true art of teaching. Personalization is knowing that groups of students may need the same skill, but may need it presented in different ways, or vice versa. Groups of students may be able to learn in the same way, but may need different skills. Personalization of learning is understanding that while all students are individuals, their course of learning does not need to be individualized, and while choice and differentiation is often a great way to organize input or output, it always required. Using the birthday party analogy, at a personalized ice cream bar the guests would be grouped upon arrival based on previous experience with ice cream, again either gauged by a pre-party survey or by the adults knowing their experience through relationships built with them. At those stations the students would enjoy the flavors and toppings presented at the station, and adults would be at the station to help make sure the kids were making the most of the options presented. No child was at their own table, and once the ice cream station was complete the students could then move on to the next activity at the birthday party. The tables looked relatively similar but each one was personalized for the group assigned to each, with flavors that were around their liking, and toppings and vessels that they could handle for their age and understanding, etc. Each table had a different type of creation to build, guided by an adult.

When planning the ice cream party, and figuring out which kids to put into which groups, often you realize that kids don’t have all the experiences they need to to truly enjoy the dairy deliciousness to its full extent. Grouping helps, of course, filling the lessons with help from adults, and peers to some extent, also helps, but if students don’t know that how to construct a perfect sundae, or that the salty-sweet of pretzels adds an extra dimension, there is really only one way to go… back- to fill the foundational gaps… allowing true success to open up for children during the lesson, I mean the party.

Obviously, overly simplistic in its nature, the ice cream party example of gap filling is very small. However, if a student is in sixth grade and trying to learn complex operations with fractions, maybe even with variables, but never truly was able to add fractions back in elementary school, or never really understood that a fraction was part of a whole, the student will struggle. Sure, the teacher can try to patch the gap, or push ahead with computation procedures in hopes that the student will get it enough to manage some level of success. But, what the student really needs is to understand. The gap needs to be filled and the hole needs to be sealed, in this case, on fraction understanding. Does this take time? Sure. Does it take a lot of time? Maybe not. Is it worth it? YES.

So, circumstance aside, I created Filling the Gap Educational Services. I made it official, with an LLC. We do it a lot of different educational “things,” all virtual now so we can reach a wide audience. I have a good colleague-turned-friend off of which I bounce a lot of ideas, who is gracious enough to be providing her services for free. I have a husband who is allowing me to play entrepreneur right now, as I build all of the foundations of curriculum, assessment, and instruction for my “brand.” And, I have a few educational peers who have joined me on this journey, waiting for the time when education and families move beyond the daily grind of will or how will schools reopen.

What we do and how we do it is certainly not all unique, but some of it is in the way we not only believe in personalization as an educational best practice but we also personalize, and at times, individualize, our educational plan for our clients. We aim to help students, parents, educators, and schools. We offer a wide range of services, all centered around our why- finding and filling the gaps are the critical missing pieces. And there are many ways to fill the gaps, and then seal the holes, through diagnosis and detective work, through education and tutoring, through family and educator education, through curriculum development and alignment, through lesson design and modeling, and more. We want students to experience success and feel confident, and we want to make sure students are not pushed forward without the foundation and true understanding to do so. As a team, we work to make sure that our service is the right one, and then as a team we find the right path towards success.

As readers, new and old, of my words about talking math, I hope you can join me in filling gaps too. I believe that teaching math through talking about it is important. How else can anyone understand math, the why, not just how-to, without talking through problems? The future of our education and our careers are about discussion, real discussion, and being able to explain understanding is preferred to completing pages of computation problems. Teachers understand students’ challenges in current math skills and they find them through daily interactions or through formal assessments. My goal, through Filling the Gap Educational Services, is to bring awareness that the challenges in learning (math and other subjects) could actually be gaps from content introduced years prior. The gap finding and gap filling are critical pieces to student success, to curriculum development, to lesson writing and implementation, and to overall thinking about how the whole child is truly learning.

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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.

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!