For many years I have had a collection of useful documents curated from a variety of powerful resources buried in my Drive. I had a moment of inspiration to make this more available to anyone needing these resources, so, like me, they are more accessible and ready to use just a click away.
"Mathematics is not about numbers, equations, computations, or algorithms: it is about UNDERSTANDING," said William Paul Thurston.
What if we considered literacy in the same way we considered mathematics in that there are four fundamental, interrelated components that we recognize as essential for a person to be successful in understanding this process.
Mathematics utilizes addition and subtraction, multiplication and division.
Literacy utilizes speaking and listening, reading and writing.
We have to provide opportunities for students to engage in mastering their mathematical literacy with greater urgency than we have them practice their arithmetic.
Dave Derby, the man responsible for showing the power of cognitive coaching always says, "Understanding comes at the point of articulation..." If we wish our students to understand mathematics, to improve in their abilities we have to give them opportunities improve their mathematical literacy.
As William Thurston said, if we want students to experience math, to understand, then we need to provide students opportunities to speak, listen, read and write about their mathematics.
Entering the last day of the busiest month of blogging to date, I thought I would try to get one more entry done. There are several items I could report on, some more interesting and powerful than others, but I want to focus on this idea, Ten Minute Math, in particular. The concept is solid and easy for me to follow, which means it is probably unclear to most and hard to see its value, which is why I am wanting to revisit this idea (I posted about this topic here), and explain in more detail.
The opening slide is a clickable Index of all the current 10 Minute Math strategies, and provides an overview, you will also notice a home button on each slide corresponding to returning to the main index. Our first foray is a nod to Michael Fenton for sharing this idea and inspiring such rich mathematics, and it is about completing the missing story given two chapters. To complete the missing chapter, you begin by dragging dots into the missing chapter to complete the missing chapter. Creating your own chapter stories is a ton of fun as well, and giving students the opportunities to create their own fun.
The second 10 Minute Math strategy is the classic Which One Doesn't Belong with this one created from a variety of shapes playing different roles. Adding additional pieces like having students write their reason for the one they chose, or pushing students to find a reason why each one doesn't belong adds dimension to the scale. Another great layer to WODB is Daniel Kaufmann's Convince Me That for the two most popular choices or to launch a discussion if 2 and 4 the equivalent representation.
One of my favorite ideas Dan Meyer talks about is the idea of perplexity and creating situations with perplexity built in, typically by removing information and having a series of questions asked by the facilitator to make sense of the content. The image shown is a typical example of a data display, and by removing the labels, the viewer is forced to pay attention to the details of the image. The content is slowly revealed to the viewer, each time adding layers to the conversation.
The next three 10 Minute Math tasks are variations on the ideas of sequencing and different ways for students to interact with this process. In the first case, there is a series of steps in a solution in a random order that either an individual or pair must properly sequence with justification of their steps. The second and third tasks are essentially the same in that individuals look to match their corresponding result trying to connect a certain number in a row. The major difference between the two formats is one is whole class, the bingo version, while the Tic-Tac-Toe is for pairs to interact with.
Taking our first example (the dragging of steps into a solution) above to the next level, we have a Frayer solution, with multiple interpretations that may be highlighted based on content and desired learning. In this example, students are given a multi-step algebraic equation and they are asked to solve for the unknown quantity. Sequencing through the solution at each point the learner dives a bit deeper into mixing both the procedural knowledge with the conceptual knowledge.
The last two 10 Minute Math tasks are related to their openness of the task itself. While each one has some guidance, the essential exploration of the task is open for the user to define. Giving students these valuable tasks to dive into for 10 minutes will get them excited about math, while not letting them feel defeated if they don't get it during the allowed time. Revisiting this structure over many days will provide fresh insights and a much deeper understanding of these topics.
Thank you for diving into the 10 Minute Math with me, please feel free to explore here, or https://tinyurl.com/10minutemath
About this time, we were asked to take a problem and present it to our class and report on the results. The problem I had chosen was called The Locker Problem best explained in the linked video by Nuno1014's Youtube channel (careful the answers are revealed in the video). I use a snippet of the video in the lesson I created, I love how this person approaches the explanation and models the concept in this 9+ minute video.
Anyway, as a first draft students were having a very challenging time accessing the problem, but I saw a student trying a process of elimination with the locker doors and the students changing the state of each door. The array the student was making were reminiscent of a multiplication table, which we had plenty of in our math class. So I gave each student a 20 by 20 multiplication array, and I asked if the lockers numbers run around the top and the student numbers run along the side, how might that help them access the problem?
The change in the room was palpable as many struggling learners were able to access the problem, this tool allowed the students to go from hating math and this problem to a shouting with joy. When we give students a task that is challenging, but give them tools to help access the problem we create better, confident mathematicians.
From this point, The Locker Problem has taken on many different formulations and iterations. Most recently, we had the opportunity to start off the 2018-19 school year in an 8th grade math class with this problem. The problem creates the opportunity for exponents to come about in a natural conversation. The beginning of the lesson is shown in the slide deck below:
The power of this approach is that the problem experience immediately provides a shelf for the students to put the learning about exponents on, and it also gives context for using language about a concrete object to make more sense of the problem. When we move on to discussing exponent rules, factors, rational and irrational numbers, and other content students are able to articulate their ideas with The Locker Problem acting as their backdrop.
Resources are here:
Six years ago I left a community I cared about, an awesome group of math teachers, and students I loved to find out two things: 1. How do humans learn mathematics? 2. What constitutes a "good" teacher?
To answer my first question, my journey has allowed me to work with students from TK to 12, from age 4 to 19, from the most studious of learners to the most resistant of learners, where each moment provides learning opportunities. I cannot say it has always been easy, but few things worth knowing are rarely easy; however, I have caught glimpses of how we learn through being able to work with this span. Understanding when we are exposed to different concepts and tracing how those concepts evolve through the grade levels, connecting this to why students still seem to show up year-after-year acting like each concept is brand new, and finding ways to combat that process. While I am so very, very far from a satisfactory answer to this question, I have developed a solid foundation for how and why.
My second question I originally thought would be the easier question to answer, but I have found that I still do not have as solid a foundation as I do with the first question. As a new teacher, I thought a "good" teacher looked like the photographs below:
The teacher at the front of the room, every student quietly hanging on every word I say, because the students were hungry to learn, and I was THE TEACHER, the dispensary of knowledge. These images quickly faded as I got into working with kids because they didn't have this same image of what their classroom should look like or that this is how I envisioned their learning.
Making a long story short, I found that my journey changed when I could have fun with students, I could be myself with them, and we could still have some sort of learning environment moving forward. After five years, I felt I was ready to really dive into answering my two questions. I didn't consider myself a "good" teacher, which is why I had the question. I knew that I cared about kids, I knew that I developed connections with them and I was always curious how they were doing. I knew that most of the time I was listening and dealing with helping them get past their "friend drama" or other types of drama in their life, which is their reality and they wouldn't, no couldn't, learn math if they were in the wrong mindset. I knew that I could laugh with kids and those disruptive, not afraid to be themselves, loud, and challenging students were my favorites. I like authentic people, people who tell you that you have something in your teeth, who call you on your BS, and who challenge you, but I didn't know what a "good" teacher looked like, sounded like, or did. My perception at this time moved from the images above to something amorphous and unclear, but with one important characteristic.
The message I was receiving said that the only thing that made a good teacher were the results the students were getting on whatever the measurement tool was, and it was almost entirely related to some sort of test. My effectiveness and worth as a teacher, my only criteria to determine if I was a "good" teacher, or not, was based on a single number. What's worse is that this single number only had to be high enough as compared to my colleagues to make me stand out as a "good" teacher. Not only does this not set the stage well for collaboration because I don't want any of my colleagues to know the "secret sauce" because they'll be just as "good" as me (I have to pause and say how much this sucks for our kids sitting in your's and mine's classrooms).
Although the notion that I was judged based on a single number didn't feel right to me, the gravity of importance related to the sacred number indicated that my notion was misguided at best. This process led me to seek out what makes a good teacher, and what might we pay attention to, because I was convinced there has to be more...that being a "good" teacher was more than determining if my milkshake was...well...you get it.
As my understanding about the learner grew, I noticed that most students respond to and desire their teacher to care about them, the individual, and seem to care less about the effectiveness of strategies or the preparation the teacher put into their lesson plans. Kids care about their relationship with you, they don't care about the learning you want them to master. From a kid's perspective, a good teacher is:
The educational system has this other focus which is results based on various measurements, but mostly based on a standardized test that inevitably is used to mark if a teacher is a good teacher or not. From this perspective, all the relationship and people side of things only matters if this helps produce better test scores, if we are machiavellian about our approach here then really any ends will justify the means provided our results meet whatever criteria we meet. Now granted, it is as dire as all that, but our current state I already see that approach coming back as the thing that matters is scores. It may be obvious by this constructed narrative where I stand on this issue, but personal belief aside, I am not really closer to answering my second question.
Granted that a balanced approach seems the most logical in terms of wanting measurable results from students that exist in an educational learning environment that promotes and cares for them. I believe all reasonable adults would agree with this middle ground, and the problem I still have is that this feels a like a great compromise, I don't see it as a meaningful answer to my second question. Perhaps input from others would be helpful in parsing out some sort of truth from this conversation:
My dream of starting a Twitter chat happened two years ago when I started #MathConceptions with the help of my buddy Shane Ferguson. Since that time, I have had the dream of starting a chat with the folks I work with, to grow and learn with those closest to you makes the most sense. As with so many signs I am reading and learning about, if you want to see something happen you should jump in and get moving on whatever that thing is...so I am starting another Twitter chat to tell our story from Burton School District.
Our team of coaches has grown significantly this year, with a lot of folks being new to their roles, having a centralized location to pull info and share stories seems to make sense. Our first topic is on Growth Mindset, as we all benefit from fostering a growth mindset. Each week we will have different topics and hopefully different educational leaders from our community jump in and we all learn about a common passage. Our first chat starts on 9/10 at 7:00 p.m. Pacific standard time. I am excited for the new journey and the amazing folks that will be there, or will eventually be there.
One of the things I love about teaching is how we continuously grow, learn, evolve, and become better at the crafting of learning experiences for our students. Inspired from a variety of amazing educators from within my personal learning network (PLN) I have compiled a series of game like structures for all learners to access and I call the whole kit Ten Minute Math (#tenminutemath). The sequence the various games are shown below, with a clickable index to follow.
One of the blessings of my current position is being able to model lessons and concepts in all grade levels from Kinder through high school and I've tried a variety of these at various grade levels to showcase their value and impact. Well if you'd like to try, please make a copy of this slide deck and get to work. I only hope you share your experiences and modifications so we can all learn a little more and get better together, or you can type tinyurl.com/10minutemath and have fun!
We are always on the hunt for resources that make our teaching lives easier, and I love to curate and share. To this end, I am showing some of my favorite and richest collections of resources for powerful mathematics instructions. Starting with a collection of powerful uses for one of my favorite ways to capture student voice, Flipgrid, through a collection of some of the amazing, sharing educators in my PLN, with over 40 ways to capture student thinking. The clickable Flipgrid PDF is has a variety of ideas to spark your creative teaching practices and let students voices shine. The second clickable PDF I am sharing is a link to several other clickable PDFs depending on what you are looking to do with your learners. The Math Coordinator in me wanted to share some ways for you to access instructional strategies that allow you to go deeper with students. The MCs Top Six clickable PDF is for you if you're looking for empowering students through meaningful math experiences.
The next two clickable PDF resources may be confusing if you're not careful with understanding their intent. The one of the left below (Single Serving) target is for single lessons, if you are looking for powerful single lesson ideas then this is the clickable PDF you need. If you are looking for deeper learning experiences, then the clickable PDF on the right (Multi-Servings) is the one you need. Please note, like the MC Top Six above, these may lead to additional clickable PDFs depending on the resource type. For example, on the Multi-Servings (on the right below), if you clicked on the Clothesline Math resource it would lead to another clickable PDF with the various clothesline math resources linked there. There is too much on either of these resources to go into in any more detail here, but I encourage you to jump in and start clicking away. The resources are linked below.
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