Monday, August 19, 2019


Are you Teaching Outside the Box with Technology Infused Math Instruction?

Technology that promotes 21st century skills are essential for the classroom today. But if technology use consists of students working in silos while staring at a computer screen they are more likely modeling the 21st century skills seen at Starbucks, than the skills students need to thrive! The opportunity to partake in experiential learning, ask questions, compose an argument and justify your stance, must extend beyond a typical twitter post and exist within the realm of social engagement.
Image result for starbucks everyone on their cell
Learning happens when students' experience a shift in their thinking (scientist call this disequilibrium) and this happens when we collaborate, create, communicate and think critically (the four C’s); notice click was not included. Teachers and peers provide the perfect context to challenge our current ways of thinking so that students can stretch themselves cognitively. Using technology as a means to avoid printing out worksheets for students to complete would be what Dr Ruben Puentedura (founder of the SAMR Model) would say is the Substitution stage. Using technology to “redefine” a traditional tasks and create a novel experience is where we want to go with technology (think of Bloom's Taxonomy and the higher levels of learning). If kids are just using technology to answer test questions, then we are going to turn them off to technology just like teaching to the test turns kids off to school. 

Brubaker image
Image created by Jonathan Brubaker (@mia_sarx)

Is it obvious I am writing this blog post while sitting at Starbucks? If teachers are using technology purposefully and with the intent of having students be co-facilitators of their learning then the future of education technology will revolutionize the classroom and move education beyond the 21st century. 

Technology is a tool for student learning, just like a utensil is a tool for eating and we can still eat without it. As a classroom teacher you need to know your students as well as your subject matter to decide which tool is best for their needs.  Considering how PE teachers are typically outside the class; they can use QR readers and a recording sheet to get kids using technology to support their understanding of a skill, or demonstrate what they can do via video recording is a great way to integrate technology meaningfully.


As a math teacher I love using Google Docs and Google tools to create my own activities for students to play with and explore math concepts.

For example I created a Google Slide show for students to understand the concept of dividing fractions using the shapes tool where students can divide up parts of the shape to find the quotient of 2 divided by 1/4. This is much more meaningful than teaching students the standard algorithm which is multiplying the dividend by the reciprocal of the divisor. None of this makes any sense to students especially if they don't have a conceptual understanding of dividing fractions.

There are a plethora of tools and innovative approaches to utilize technology such as using Flip Grid with students for a video-based response to a questions. Having students create a podcast in your English Language arts or a Social Studies class can be an innovative way to approaching an oral report on a topic as it be shared in your class and beyond.  For math solving a 3 Acts Math Task, or using Desmos can transform student learning into active problem solving and critical thinking. I have curated a list of over 100 free tech tools to use immediately with your students

The biggest tech innovation is the ability to put the technology in the hands of your students which was not the case twenty years ago when I started teaching. I went knocking at company's doors in Los Angeles to get enough computers for my students to have access.  Now that students have access as teachers we need to use technology to create personalized learning for all learners. You can reach and teach all with technology and that's the best innovation of technology. From having students create their own video to explain a concept, to using virtual manipulatives to develop conceptual understanding, innovation comes from the teacher and the choices they make in using the technology to support student learning. 

Filling the gap between math pedagogy, content knowledge and technology integration was the inspiration for my first publication "Teaching Outside the Box: Technology Infused Math Instruction".  I spent three years working alongside math teachers across the K-8 grade span to examine how technology can be used intentionally to support student learning in math and the results were amazing.  
The book focuses on five instructional practices in math: Daily Routines, Open-Ended Tasks, Project-Based Learning, and Problem-based Learning and how technology can be used intentionally across each pedagogy.  Moreover the book specifically focuses on technology as a tool to support English language learners and students with learning disabilities. Most curriculum material focuses on separate activities and approaches for teaching different groups of learners but this book supports real inclusion by making content and pedagogy accessible for all with technology. The book has a ton of resources and examples that teachers can use in their classroom the next day. 

That is one thing I learned about being a Math Coach and presenter, is that teachers want something they can use in their classroom immediately and this book does just that.

Want to learn more about how technology is shaping the classroom culture join our Facebook Group: TeacherPrepTech

Sunday, May 19, 2019


Would You Rather: Spark Interest or Keep Your Students Quiet?

By Guest Blogger: Heather Szabo
In my classroom I commonly use “Would you Rather?” questions as a warm-up or an appetizer. Students usually choose an option and are asked to be able to support their argument with mathematical reasoning.
Question: "Would you rather have your weight in pennies or your height in quarters?"
This particularly days question sparked a powerful debate so we decided to explore the problem deeper. Students identified that in order to prove which they would rather, they would need to know the weight of themselves and of a single penny as well as the height of a quarter and the height of themselves. I collected the materials and student table teams explored. In the moment I did not know that a simple question would turn into our whole unit of study on linear equations and writing/solving systems of equations. This lesson driven by students was much better than the storybook problems I have used in the past.
Set Up: Each student in the grouped followed the same protocol and we collected data as a whole class to prove which would equate to a larger value, the weight of a student in pennies or the height of a student in quarters.

Students first weighed themselves using a digital scale in pounds. Students then used a kitchen scale to weigh pennies. Each group weighed a different number of pennies. The mean penny measurement was 10 pennies with a measurement in grams. Students then used conversion facts to calculate the number of pennies that would be equal to the weight of each student.

Once students had a total number of pennies they calculated the value in dollars.
Students used 10 pennies and divided to find a unit rate. Students noticed that they were getting different measurements for weight of the pennies based on the image on the penny. We researched this and found that pennies minted after 1982 have two different weights.

Following the penny/weight measurement students did a height/quarter measurement. Students first measure their height in inches using a measuring tape. Students the converted that measurement to meters. Students measured the height of a stack of 10 quarters and recorded the measurement in mm. Students then used conversion facts to calculate the number of quarters that would be equal in height to each student. Once students had a total number of quarters they calculated the total value in dollars.

After collecting all of the data students realized that for some students choosing pennies would be most profitable and for others choosing quarters would be most profitable depending on their height and weight ratio. We then extended this activity to figure out at what height and weight you would rather choose pennies or quarters. We used this example to cover topics of linear equations and systems of equations.
When finished students asked questions like: What if we chose dimes instead of pennies? Since dimes are smaller but have more value students were interested to see if the outcome would be the same. So we embarked on the same journey led solely from student questioning and facilitated by the teacher.

Reflection: This appetizer turned entree was rewarding for both the students and myself. It truly embodied the five key aspects of project based learning including: real world connection, academic rigor, student driven, multifaceted assessment and structured collaboration

First the question was real to them. They chose to seek the answer out which was the driving force. Second, the rigor was embedded within the lesson. Once students had their own data, they shared it with the class. We then looked to the class data to make predictions and generalizations. We used this time to create graphs and solve systems of equations which is the next chapter of our current curriculum. I let them ask genuine questions and pursue the answers themselves and that is where it led. Some student groups were more ambitious than others. Many groups struggled with the unit rates and conversions so we took time to discuss proportions via a mini lesson in class. The rest just fell together. In this lesson, I was really able to take on the facilitator role and let the investigation be student driven. This is not to say that the lesson was without struggle but the struggles students faced were productive struggles that they persevered through.
When the students asked if this situation would hold true if we used dimes instead of pennies I responded, “I don’t know! Let’s find out!” Due in part to this the finding out became an adventure for students which caused them to buy in more to the lesson itself. 

Saying yes to student ideas in this instance was easy because students were so inquisitive. They wanted to know more which paved the way for much deeper understanding.  

I wholehearted believe that we as math educators are responsible for creating students that are comfortable enough with numbers to challenge and question the authority of numbers. I want my students more than anything to be well prepared to be consumers in a market that is out to take advantage of the mathematically illiterate.

As stated in the video, “without mathematical literacy career opportunities shrink and students become easy prey for credit card companies, payday lenders, the lottery and anyone really that has a dazzling statistic. Because when we aren't comfortable with math we don’t questions the authority of numbers.” I want my students to question and to seek answers and during this lesson that is exactly what they did! 

Heather Szabo is a 7th Grade Math Teacher. She is learning different approaches to math instruction in the course The Math In Our Lives which focuses on designing instruction based on real-world application. 

Wednesday, April 10, 2019


Going Google with Hyperdocs

The agony of leaving your class with a substitute for the day is gone when you "Go Google" with Hyperdocs. A Hyperdoc is a digital google document that contains links and directions to student learning activities in a colorful and playful way that get's your kids excited about showing what they know about subject matter. Think about a table in your document where each section has an activity and instructions on what to do and how to do it. It's like you are right there in the classroom telling them what to do, except your really not there and hopefully on a fun tropical vacation. 

Creating a Hyperdoc is easy with Google Docs.  Just create a table where each section includes short and sweet instructions (i.e complete the Desmos activity) and what to do to show they have finished  (we call this "evidence").  Your evidence might contain a screenshot of their score or a reflection of what they learned.  The fewer steps and the simpler the better.  

 As a Hyperdoc is simply a Google Doc with a URL you share with your students be sure your "Share" settings are in "View Only" this forces the reader to "Make a Copy" and work on their own. Did I ever tell you about the time when I left my Google Doc in "Edit"? Oh the places your kids will go, and yes they went there ( I work with 6th and 7th graders). I always include this directions on the top of my Hyperdoc, and to "share" with me so I can see evidence of their work.  

Hyperdocs are perfect sub activities because you can allow your students to work autonomously and encourage them to "be on task" all the while you are tracking their performance with digital tools and online websites.  Some of my favorite webtools such as FlipGrid, Desmos and Khan Academy include a teacher dashboard where I can see how my students are performing and where they struggle.  Check out my Google Doc on Webtools for lots of resources for online tasks.

The key to a successful Hyperdoc is differentiated activities with a "low floor" and high ceiling".  What I mean by that is creating increasingly challenging activities that begin with tasks that all students can do without any support.  This might be watching a video about a concept, or playing a game and recording their score.  Thinking about how tasks can become increasingly challenging are easy with a framework such as Bloom's Taxonomy.  
Your first few tasks should promote students in "remembering" the concept and big ideas and "understanding" how things work to make sense of the skills and strategies they are learning in class.  Once you've activated prior knowledge then students can "apply" the skills and strategies in a context that requires more cognitive demand.  Finally your students should reach the highest level of Bloom's by creating a product of learning that shows mastery of the standard.  This might include "creating" an Educreation video that shows how to perform a task, or a Digital poster with a tool such as Canva that allows them to synthesize big ideas.  

Want to see what this looks in action for a 6th Grade Math Standard on Equations and Expressions? Check out my video below and be sure to Subscribe to my channel to receive a copy of this Hyperdoc so you can start creating your own.

Join my Facebook Group Teacher Prep Tech or Making Math Connections for more freebies and best practices in teaching with digital tools! 


Friday, March 15, 2019


Creating Open-Ended Math Tasks

Regardless of your class size, designing instruction for everyone’s ability is a complex endeavor, students come into the classroom with different funds of knowledge, experiences, and beliefs about themselves as a learner. Despite these differences, you must prepare students to meet grade level standards and access state adopted curriculum.

While traditional math textbooks often provide the structure for students to practice procedural skills, they often lack the flexibility to scaffold instruction based on students' needs and interests.  Just like a doctor needs to focus on the patient's needs, lifestyle, and symptoms, so must the teacher individualize instruction based on their students. This is where designing open-ended tasks for your students can move your instruction from "why do we need to learn this" to "when can we work on our task." 

There are two main types of tasks: close-ended and open-ended tasks. Close-ended tasks are predictable, focus on one way of thinking, and have a single right answer. In contrast, open-ended tasks are unpredictable, provide students with opportunities to explore ideas more broadly, have multiple solutions, and incorporate many ways of thinking and decision-making. There is often ambiguity in open-ended tasks, as such they are frequently referred to as ill-constructed questions or problems. Open-ended tasks require more cognitive effort from students and therefore engage them in higher levels of thinking and learning. Students must draw from their knowledge in broad ways to figure out potential solutions.

Another difference between open-ended and close-ended tasks lies in the type of thinking required when determining a solution. Close-ended tasks often draw on narrow ways of thinking that rely on procedure or previously memorized information, while open-ended tasks draw on students’ broad conceptual knowledge (Stein & Smith, 1998). The path to the solution of an open-ended task requires effort, multiple steps, and application of broad conceptual knowledge, rather than rote memorization.  

So are you ready to infuse Open-Ended Tasks into your classroom practice? In this video I am demonstrating how I introduce an open-ended  task of a Scavenger hunt to identify arrays in this second grade classroom.  Students have been working with arrays by constructing models using a variety of manipulatives.  In this activity they are extending their thinking to identify an array in their class. 

The flexibility of open-ended tasks allows students to work in their "Zone of Proximal Development" (ZPD) while providing you with the knowledge of where student understanding lies in an authentic task.  

Technology can also support students in ways of showing and expressing what they know about a concept.  Using free tools such as SeeSaw or Flip Grid students can create a video to explain their thinking.  This type of activity also allows students to create, apply and synthesize learning in a meaningful way.  As an extension of this activity students were required to identify arrays in their home. 

When creating Open-Ended Tasks you must ground the task in students' interests, funds of knowledge and ability.  This will support you in creating a hook, that will capture students' attention and support them in making mathematical connections.  Holiday's and school events are also a perfect way to build on students' fund of knowledge.  In this gift giving guide activity, students were able to select a gift to get ratings from their peers.  The concepts of ratios, percents, and division were all included in this open-ended task.  Once students completed a hard copy of their gift guide they then completed a digital version which was shared with families.  
Ratio Gift Guide

Creating open-ended tasks are a perfect way to keep students motivated to "do the math" and apply the concepts they are learning about in a meaningful context.  When the recess bell rings and kids are still motivated to work on this open-ended task, you know it's worth the investment. Create your own open-ended tasks with this planner and invited Dr. Dickenson to your school for Professional Development in curriculum and design.  

Join our Facebook Group for more Freebies and share your best practices on making meaningful math connections.