Monday, December 6, 2021

 

Harnessing the Power of Technology for Real-World Math Connections


Throughout the Common Core Mathematics State Standards, students should be making sense of mathematics in the real world.  In fact, the word ‘“real-world” appears across the math domains from “solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem (5.NF.B.6) to “solve real-life and mathematical problems using numerical and algebraic expressions and equations (7.EE.B.4)”.   Real-world connections are rooted in the experiences we’ve had whether shopping at a store and calculating the discount price, to planning a road trip and determining the time, distance, and cost given a budget.  Experiences make us mathematize in ways a traditional textbook problem does not.  Moreover, doing the math is driven by our needs and interests, and that is what makes the utility of math something of value. 

This approach to teaching and learning math can be as simple as using a Data Talk (see below) at the onset of instruction to engage your students in math discourse or creating a real world problem for your students to grapple with over a series of days or weeks!

Think about how engaged you were when planning a holiday party and having to scale up or down a recipe online or applying for a loan and determining the monthly cost given your interest rate.  Of course, in these situations attending to precision really matters. Seldomly do we need to be reminded to “check your answer” when math is personal. Creating that kind of interest, excitement, and perseverance in the classroom, will take more than just presenting our students with problems involving a real-world situations, or asking “ Would You Rather” questions.  As teachers, we need to provide our students with an opportunity to put themselves into the experience (aka immersive math).

Here is a video clip of me working with a group of sixth graders introducing the project of building a house.  https://youtu.be/M45VT4UHzcI

Build a house project on Google Slides for Reuse: https://bit.ly/3u2LN8Z

What kids lack in context we can provide with digital projects.  Digital projects allow us the teacher, to build an experience that will drive our students’ passion for doing math.  Students can share their interests, passion, and creativity in a real-world digital project.  For example, building on my second-grade students’ love of the Roblox game, Adopt Me, and their passion for animals,  I crafted a second-grade digital project in which students pick a pet to adopt, shop for items, and create their own animal.  This became an immersive experience similar to a video game, while students were adding and subtracting money, building three-digit numbers with base-ten blocks, and ordering and comparing costs of pets on a number line.

To further students' confidence in this skill have your students create short videos explaining their thinking and how they solve the problem. Check out this video of a student engaged in a digital math project where she reads, writes, and compares three-digit numbers https://youtu.be/GNBM4f2HjPY



Digital projects work across grade spans and allow students to see connections across math domains and other subjects. They can give our students an opportunity to use the academic language of a concept and have students explain their thinking through video, or text as shown in the above video. 

But best of all with digital projects we can hyperlink to awesome tools that allow our students to really connect math concepts to the real world.  For example in the “Plan A Holiday Party” I created for my sixth graders, they were selecting recipes from the site “All Recipes” for their holiday meal and had to scale up or down the recipe given the number of people they invited. 



In the digital project “Plan a Camping Trip” students not only were tasked with exploring a campsite in California but, calculating the mileage for their trip by looking up the gas mileage for a car they selected.   When given this situation, the mathematizing started to happen from students comparing the poor gas mileage between a Lambrogini versus a Hummer to determining the electrical charge they would need if they decided to drive a Tesla instead.  The beauty of mathematics appeared when students were allowed to be creative and explore possibilities which is what makes a good math project.


 Students can efficiently model with mathematics using digital tools and connect big ideas in math across important concepts.  In fact, the 2022 California Framework will require teaching “big ideas” as a way to support students in seeing how concepts are connected and deeply exploring fundamental ideas.  As teaching math continues to evolve towards are more student-centered and less teacher-directed approach, digital projects provide you with an opportunity to approach instruction with an emphasis on connections and ideas.  Projects give your students the time to link multiple practice and content standards in a comprehensive way with real-world connections.  Want to see my thinking process and “must-haves” for Digital projects check out this video in which I walk you through what I consider before creating a digital project and what are must-haves for project success.  

How to create a digital math project: https://youtu.be/ZkdWH_2mndE


 



Technology holds much promise for the future of math and certainly will prepare students for college and career readiness.  Collaboration, critical thinking, creativity, and communication are part of students' experience in working on a digital project.  The 4 C’s are 21st Century skills that have been in education for quite some time, as a staple for the future workforce.   As teachers however we are challenged to bring in the fifth C of compassion in our work with students as well. With compassion everything is possible and we can reimagine our world and our children’s future.  




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Sunday, September 13, 2020

 

6 Fun Ways to Go Digital with Number Talks


One of the cornerstones of a solid elementary math block are activities that support students in developing numerical literacy. Developing numerical literacy in the elementary classroom will support students in being confident problem solvers, and engage in mathematical discussions at a higher level.  Number talks are one such activity that builds students numerical literacy and are taking place in classrooms on a daily basis.  

If you are not familiar with number talks here is the gist of it.  The goal of a number talk is to give your students an opportunity to use mental math strategies to solve a problem.  That's right no paper, whiteboards or pens, just solve the problem in your head.  

The conversation that occurs after the number talk is teacher facilitated with students sharing answers and their strategy.  This process supports students learning from each other and teachers assessing students thinking and what strategies they use naturally.

       Teacher says: How can you solve this problem by doing it in your head? Give me a thumbs up when you have a solution!



One thing I love about a Number Talk is students are provided with a problem that can be solved in a variety of ways.  This allows students to be flexible in their thinking and develop a variety of strategies that will support them when they are faced with cognitively demanding math tasks.   


       Get these slides here

One thing that is a struggle with this process is number talks can be incredibly time-consuming if you are in a class with 30 plus students who all want to share how they found their answer.   As a teacher, I want to honor all of my students' voices and give them an opportunity to express what they know, but logistically this is not always possible.   

This is where technology can come in to support you in making number talks accessible to all students and useful as a formative assessment tool to see where all your students are at and give them a chance to share their thinking.  

Here are 6 Fun Ways To Go Digital with Number Talks: 

1. Google Slides: During a synchronous meeting with your students share this slide deck in edit mode for students to record their solution to a number talk problem.  Students can drag the icon to indicate they would like to explain their thinking or to show agreement with another student's explanation.





2. Google Voice:
For asynchronous collaboration post an image and/or your question in a Google Doc.  Students can work with a partner or independently to share their strategy. All you need to do is create a Google Doc and Share with your students.  Then have your students go to the Tools Menu in the Document and click Voice Typing



                                       click here to get this document

If you want to see how quick and easy this process is just check out my 8 year old son demonstrate how to use Google Voice Typing.
                                   


3. Padlet: Post your question on a padlet board.  Students can access the board with a URL and automatically post their response by sharing a picture, text or video.  Try this out by responding to my number talk wall below with your response.  If you have fun doing it imagine what you kids will say! 
Made with Padlet


4. Google Drawing: teachers can illustrate student responses using Google Drawing either on their IPAD or computer.  The Scribble tool is a quick way to make illustrations and the student can also illustrate their response using this web based tool .  Google Drawing can also be used inside Google Document and it even features math symbols as images.  
                          Click here to view in Google Drawing

5. Flip Grid: Create a video word problem with a student response system that records students thinking in an instant.  This process can ensure that students voices are heard and recorded. You can also leave feedback for your students with this process.  The videos below were created shared on Youtube



6. Shadow Puppet: This tool can be used by you to make video number talks or by the student to share their response. Students can illustrate their work with paper and pencil then take a picture with an ipad or iphone.  Then they can audio narrate their response.  This can be a center activity that students complete and provide feedback and comments to their peers.   This is an app and not accessible on a computer 



If you are an elementary teacher looking to improve your students number sense than number talks are a must.  This process instinctively allows me to see where my kids are at, who has grasped the concept and who needs some extra nudging and support.  With number talks the nudging and support does not necessarily come from me it can be found in how their peers respond and with web tools I have the power to capture their answers.  

Want a book that can put it all together for you with over 100 digital resources and tools then check out my book on Amazon



Check out these digital number talk images I have collected and be sure to share yours with me. 

How much for one (unit rate)? How much for 13?


Join our Facebook Group for more conversations, freebies and best practices: https://www.facebook.com/groups/mathconnects/



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Friday, June 26, 2020

 

Ratios and Insert Learning



Math Warm Up: Which One Doesn't Belong? 


Look at the Graphic below and decide "which one doesn't belong" 

What justification could you use to say that 8 doesn’t belong?
What justification could Student B say that 64 doesn't belong?
What other justifications could student A have used to decide that 27 does not belong?

How can students A, B, and C all be correct even though they each chose different values?

Today's Lesson: Ratios
Ratios are used to compare values. They tell us how much of one thing there is compared to another. For example, ratios can be used to compare the number of cars to motorcycles on the road. If we have a total of 12 cars on the road, where two are motorcycles and ten are cars, we can write that in ratio form as 2:12 (motorcycles:cars). We can also write it in factor form as 2/12. To compare the number of cars to motorcycles, we can simply rewrite our ratio with the number of cars first as 12:2 (cars:motorcycles ) or 12/2.

3 Acts Math Task: World Fastest Dog
What do you notice and What do you wonder?





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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
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