During the past several weeks after yet another school catastrophe, this time in Florida, I have been quietly contemplating as we wait for the reaction that comes. What doesn't surprise me, that seems to surprise most of the public, is the impressive nature of the students who survived. It seems that, as adults we seem to forget how smart our children are. We allow them to be smart as young children, hope they become more than we are, and finally get annoyed when they come back from college believing they are smarter than us. This is all fine when they are "our" children. When they are someone else's child who is trying to tell us what to do then we don't seem to believe they know enough to do that. Rather ironic isn't it.
The thing is, as teachers we know how smart all of "our" children are. Even those students we struggle with are really quite intelligent. "Our" children work, often not as hard as we want them to until they find a reason to show what they are capable of. "Our" children speak, often not as well as we want them to, until they find a cause that forces them in front of an audience. "Our" children show passion, too often about things that we don't want them to be passionate about, until they show us the true power of passion.
"Our" children mean a whole lot to me. Most of my energy goes to trying to figure out how to harness their potential and create the best child they can become. Because of that, it bothers me that I don't know how I would react to a similar catastrophe in my building. Would I do whatever I could to save their life? I have jumped up and saved a choking baby on a plane. I have done CPR to a referee at a basketball game. I have given the Heimlich to a choking adult. It seems I have had too many opportunities to be around when a life is on the line.
But none of these were my life...
Would I give my life for another student? I really don't know. My thoughts go to my family, my two boys who I have yet to finish raising. My thoughts go to my wife, whom I look forward to growing old with. My thoughts go to myself, and the experiences I really would like to have. Am I willing to sacrifice those for the sake of someone else?
Is this what I got into education for...
The answer is clearly no. Educators are educators because they want to empower students through the use of their mind. One of our biggest assets is trust. We gain the trust of our students through a long, focused, and persistent process to get to know them and show them we care. Can I gain a students trust with a gun strapped to my hip as I am now told I, or a few of my colleagues should do? It seems that would get in the way of a trust building exercise. If given the choice of being by someone with a gun or without, I would always choose without. Wouldn't some, if not most of my students feel the same way? Arming schools is not the solution to fixing this problem. Making our schools "tougher" is not the solution. Each of the children who have executed these shootings wouldn't respond well to tougher or more strict schools. It is not discipline that fixes this.
It is compassion...
We need to listen to our young adults speaking in front of the microphones. It is interesting that what we hear on the news is all about the officer outside the building, the lack of a gun in the building, etc... What we don't hear is what the true problem is, and there are several. Why do these weapons exist? Why do we have such easy access to them? How does a child obtain them without one, if not many other people knowing? Who do these children confide in? How do they plan something like these acts and not tell anyone? Who did these children trust?
We need Congress to help us equip our teachers with the time and talents to get to know the children they have in their classrooms. We need parents to be an active part of the learning process, not just trusting that teachers can teach their child everything they need to know. We need Congress to look in the mirror and consider that part of the problem may be themselves. Finally, we need everyone to open their ears and minds and learn from the same children we have been trying to teach. The generation we have heard so many concerns about is telling us they have learned. They have learned and are now ready to teach us.
Tuesday, January 3, 2017
For as long as I can remember seeing in pictures, reading in books, and watching old TV shows, the standard algorithm has been the staple of mathematics during the elementary years. These algorithms are burnt into our brain through images of the old school house, blackboards, and crummy movies. However, they have maintained in instruction for an assortment of reasons.
1. They help most students calculate math.
2. Our parents learned through them so therefore, children have also.
3. Teachers tend to teach the way they are taught…thus the algorithms continue.
4. The Common Core has them stated as necessary parts to instruction in grades 3-6.
Recent instructional pedagogy has produced strong data to support no longer using the standard algorithm as the main form of instruction. The changes started in the late 1990’s and are now being pushed further by people such as Jo Boaler. Their efforts are based off an understanding of mathematics rather than just calculation. With all of our advancements, the United States continues to be one of the few remaining developed countries that use the standard algorithm as the main form of instruction.
Personally, I couldn’t agree more with the changes being pushed in recent years. Since starting as a K-12 Math Coordinator we have been discussing, developing, creating, and presenting alternatives to these algorithms that have more to do with understanding than calculating. We have been working against traditional math trying to encourage students to do more than calculation. I believe we can expect so much more from our children than rote mathematics. I believe we need to focus on the “why” rather than giving students the “how.”
Lets go on a journey through some of the biggest reasons why teachers keep emphasizing these algorithms and why we as professionals need to make the decision to move on.
The methods in the algorithms are needed to learn the upper levels of mathematics
Forgive me but I started with my favorite reason most people give to keep the algorithms. It is not enough to say that after grade 6 or 7 calculators are doing the vast majority of the dirty work in calculating math. It is more important to understand that the methods used in the algorithms are not used in upper levels of math. The only algorithm that reappears consistently is the division algorithm, which comes back when dividing polynomials. Even that method for dividing polynomials is an inefficient method as compared to synthetic division or graphing solutions. In all of these cases there are apps that can do much of the computation for us. This doesn’t mean it isn’t important to know how to do these steps but that its’ importance is minimal as compared to the much larger picture of what the outcome of the division means.
The standard algorithm for multiplication is purely gone. For some time area models have replaced the algorithm. Even that is an incomplete comparison because we are comparing polynomials with multiple terms, not numbers. Polynomial multiplication is closer to the partial products method than the standard algorithm. Furthermore, the methods used emphasize the meaning of multiplication. Not just calculating for a solution.
It is the methods parents know so we must teach it that way to help with home-school communication
It is ironic that statements similar to this one surface about math when they don’t surface about reading or writing. I believe it has much more to do with the procedural drill and kill approaches taken when current teachers/parents were learning math. In schools, we used to teach keyboarding at the high school level. We taught students lattice multiplication in the late 1990’s and early 2000’s. We went through phonics, to whole language, and back again.
This goes to show that times change and we need to move with them. With the technology of today we can communicate our methods of instruction with parents and more importantly the reasons why instructional methods are changing. We need to emphasize instructing parents as much as instructing our students.
To be clear, we own this problem. The problem is communication, not knowledge.
The algorithms work. Why change what is working?
I would argue that the algorithms are not working. In third grade, students learn to add multi-digit numbers together. This addition should be fluent by the end of the year. However, in fourth grade teachers are always re-assessing and arguing that the students don’t know how to add multi-digit numbers. The same is true in fifth grade, sixth grade and so on.
Is the problem that students don’t know how to do it or are not retaining the knowledge? The answer, based on student performance is obvious. Students are proficient at the skill in each grade level but when reassessed the following year no longer show the same level of proficiency. The students don’t retain the process. However, when using alternative methods such as partial sums they not only retain the ability to add they perform it at a fluency level doing much of the calculations in their head. They learn that adding the hundreds, tens and then ones makes it easier to get the solution. It also gives them a much better understanding of place value which means when the students transfer into multiplication it makes more sense.
I leave this blog with a final thought. Watch a student as they progress through Kindergarten to first and then second grade. Students don’t naturally develop the traditional algorithms for addition or subtraction. Instead, they focus on concepts that deal with place value. The traditional algorithm must be learned through a teacher that directly teaches it. That alone should tell us what we should be doing. I believe there is a place for these algorithms. However, only if they are taught after the sense making methods are discovered.
As always, I don’t consider my opinion to be fact. Because of that I have linked a few articles that support both sides of this story. Enjoy the reads and come to your conclusion. Please share it with me. Hopefully we can learn together.
Do we Really Want to Keep the Traditional Algorithms for Whole Numbers? John A. Van de Walle
Thursday, December 8, 2016
I have the opportunity to talk to prospective Elementary teachers at the University of WI - Stevens Point today. The talk is focused on problem solving and how it integrates into the classroom. However, we are going to talk about much more than that. I am bringing a few examples of things with me. Such as a few articles I wrote, some Math Thinkers to demonstrate problem solving, some sample assessments, and a basic form that I use to evaluate instruction in a classroom. I am also bringing a few books that I feel are important for every new (and existing) teacher to read. The goal is to expose these current students to what we are going to expect from them as they become professionals leading our future students.
- How to Teach in a Group Centered Classroom
- Elementary Math Instruction "Look-For's"
- Task - Picnic Lunch for 3rd Grade
- Task - New Fish Tank for 3rd Grade
- Task - How Much Does it All Cost for 5th Grade
- Formative Activity - Going to the Movies for 5th Grade
- Grade 1 Assessment - Adding and Subtracting Multiples of 10
- Grade 3 Assessment - Place Value and Addition and Subtraction
- Grade 3 Performance Task - Arcade Tickets
- Grade 5 Assessment - Multiplying Whole Numbers and Decimals
- Grade 5 Assessment - Multiplying and Dividing Fractions and Mixed Numbers
- Task - Who is Correct for 1st Grade
- Task - IPod Usage for 3rd Grade
- Grade 1 Assessment - Working with Equality
- Unfinished Task - Shriners Donation from the Packers - Grade Unknown
- Book - What's Math Got to Do With It by Jo Boaler
- Book - Accessible Mathematics by Steve Leinwand
- Book - Principles to Actions by NCTM
This is a whole lot of stuff. However I want the future teachers to understand thinking at different grade levels. The key to the whole conversation is not the tasks but the thinking the tasks promote and how a teacher promotes it. Something that cannot be explained by a sheet of paper. This year I have been lucky enough to be able to be in more classrooms than ever. It just makes it more obvious that as teachers, we think a whole lot more than our students. At first read that sounds like a "duh" statement but the reality is it needs to be the other way around. In fact, we don't even let them get to the thinking because we "save" them from failure.
We, as professionals need to realize that the sage on the stage can no longer be a viable instructional method at any level. We need to realize that the more math (please don't confuse this word with calculation - instead read it as pattern finding) students are doing in the classroom the more math they will learn.
My hope with these conversations is the new instructional force coming into the field understands the expectations and can hit the ground running. The reality is this will take some time. If you are a prospective teacher just reading this blog for the first time, check out some of the links on the right. They are resources from great teachers. More than anything, be creative and try something new. If you have talked for 10 minutes or more while teaching a classroom...you have talked for too long.
For the experienced teachers reading this blog, post a comment that you feel new teachers could benefit from.