Wednesday, January 31, 2018


Do Multiple Ways Matter: Using Tech to Make the Connection

Let's be clear counting in small quantities is a skill most kids do naturally without much prompting or coaching needed, in fact the region of the brain we use for counting includes the same portion of the brain that controls our fingers. Research suggests this may be attributed to the fact that our ancestors first experience with numbers involved the fingers (Devlin, 2000).  However counting and calculations that go beyond our friendly finger tips are likely to result in errors. 

When it comes to calculations students need strategies and not just one.  Research suggests students will most likely use a particular strategy that they find to be a more efficient solution for a particular type of problem (Sieger & Jenkinds, 1989). Take for example the problem 6 x 42 . Students who have proficiency with breaking apart numbers can determine they will need to calculate 6 X 40 (240) and 6 X 2 (12) and mentally calculate the total of 252, but when these numbers become much larger 656 X 3245 the standard algorithm may be more efficient. 

Common core mathematics shifts the focus from learning one-way and one-algorithm to understanding the underlying principles of a concept and applying multiple algorithms.   This approach certainly lends itself to going deeper with math through multiple representations and ways of showing what you know.   

The idea that students don't begin with the end in mind but begin with understanding and developing concepts is at the heart of the common core. 

This shift in standards does not guarantee a shift in learning, this will only happen when teachers change the way they teach and curriculum evolves from focusing on some learners, to all learners in the classroom.  From gifted and talented to students with special needs and English language learners, our approach and modes of instruction need to be flexible and supportive of our classroom population.  Students need a variety of pedagogical approaches from number talks that support discussions of strategies and mental calculations, to manipulatives that allow students to construct models and make meaning of concepts.  

So when parents ask, "Why can't they just memorize their multiplication facts"  we can assure them that memorization does not promote understanding and automaticity will develop with practice.  Elementary teachers should begin introducing concepts by building on what children already know and albeit this may be intuitive, it can lead to a deeper understanding of the concepts.  

Rooting math in the lives of the students we teach can support building conceptual understanding as well as transfer the learning of math  (number words, symbols and quantities) into their informal learning experiences such as the park, playing games and with friends.  Take for example the idea of using arrays to introduce the concept of multiplication.  Arrays are all around students but this knowledge needs to be brought forward during instruction and through practice.  It's not enough just to talk about where you might see arrays kids also need to  construct , discover, apply and identify. We should understand that what works for one kind of learner might not work for another.  Woodward and Baxter found that students with disabilites in math tend to make significantly less growth in discussion-oriented classes (1997) than traditional ones.  

Technology can be a great mediator to support, and challenge students with open ended tasks and flexibility.  It can also be useful to move from the abstract to the real-life connection.  
Available as a Google Slide here

Repeated addition is the knowledge students can start with to build an understanding of multiplication, but some students in your class might not have developed automaticity of their addition facts.  Working with arrays that are highly contextualized and not just on a piece of graph paper can provide practice in addition while also introducing the concept of multiplication.  In this video a second-grader works on a Google Slide presentation his teacher made to drag and drop cars into a parking lot.  


If our ancestors first counting tool was their fingers then digital devices might be consider the cultural tools for our students today.  

 Using this digital lesson teachers can scaffold instruction and allow students to work at their own pace.  While some students might work with benchmark numbers 2's, 5's, and 10's to construct an array, students who understand the concept of multiplication and have strong number sense in this area can move to more complex equations.  

Are you using technology to support students conceptual understanding in your math class? Share your ideas here and join the conversation on our Facebook Group


Tuesday, January 16, 2018


Connecting Students Lives to Math Across the Curriculum

The excitement of school vacation doesn't end just because students have return to school.  From family trips to visiting relatives, students are filled with life experiences percolating in their mind. This excitement builds when they finally see their classmates and teacher with whom they want to share these experiences with.

Have you thought about ways you might build on student excitement and refocus their energy? Creating learning activities that build on life experiences and reinforces skills might be necessary before moving forward with new skills and standards.

Take a second grade class that has been working on writing addition and subtraction equations, they can practice this skill in the context of surveying classmates about activities they engaged in over winter break. 

While students are collecting data they also have an opportunity to share with their friends about their experiences. They can use this data to write addition and subtraction equations and create a word problem for other classmates to solve. As a whole class you can record all student responses into a larger graph for greater values. This activity reinforces test prep questions that often appear on the smarter balance where students need to read graphs and interpret information. You can bridge this activity across the curriculum by having students write a personal narrative, letter to a friend, thank you letter, or journal entry about one activity they engaged in over break. Here is the activity and remediation strategies for Graphing Winter Activities.

 As this activity was created using word it can be easily adapted for spring break or summer vacation. Furthermore teachers might use this with older kids to create a bigger sample size and collect data outside of their classroom. Rather than having pre-selected activities, older kids can create their own responses for the survey so that results represent multiple data sets.

 What strategies are you using to build on life experiences and share students interests in your classroom?

Join the conversation on our Facebook group

Thursday, December 21, 2017


5 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 number talks 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 in their tool box 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 number talks can be incredibly time consuming.   

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 not just those who volunteere to share their answer.  

Here are 5 Fun Ways To Go Digital with Number Talks: 

1. Google Voice:
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.

2. 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

3. 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

4. Recap: 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 from Recap and shared on Youtube

5. 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.  

Are you using webtools in your mathematics instruction? Share what you are doing and how it works! 

Join our Facebook Group for more conversations, freebies and best practices:


Friday, December 15, 2017


3 Reasons to Use Virtual Manipulatives in 3 Easy Steps

Manipulatives come in all shapes and sizes, from base ten blocks that support number sense concepts to geometric shapes that dispel the myth of a solid being flat.  We love manipulatives because it provides students with the tools to make sense of math concepts and model with mathematics in an intuitive way. What we don't love about manipulatives is they get lost, need to be organized, we may not have enough, and perhaps they are being used for something other than what we intended.  

Virtual Manipulatives can become somewhat of a panacea to the woes of tactile manipulatives.  There is plenty for everyone, no need to organize and you won't see one being thrown across the room or lost in a student's backpack.  Virtual manipulatives also may include a mat to organize students placement and self-checking features to give students instant feedback.  

Oh yes~whether their real or virtual, manipulatives should and must be a part of instruction and this belief is echoed in the Standards for Mathematics Practice which informs teachers on how to teach math, and explicitly states students should "Model with Mathematics" 

Beyond the drag and drop attraction of virtual manipulatives (VM) students really get into the flow of learning with virtual manipulatives. Perhaps for the same reasons as to why kids love to play video games, virtual manipulatives have some of the same appeal: competence, autonomy, and relatedness.  

Competence: When students use VM tools they get instant feedback and have the capacity to keep trying until they achieve mastery.  

Autonomy: When students work with virtual manipulatives they have the control over what they use and how they use them.  They don't need to share, and they are free to make mistakes without someone telling them it' wrong and why.  They may get feedback but it's not a real person!   

Relatedness:  Virtual manipulatives have some of the same features as videogames with choice in tools and how they use them.  They sometimes get points and rewards just like videogames do too! 

Teaching with VM is very similar to how you would use real-life manipulatives.  Here are my quick three steps: 

1. First, plan how you will have your students use the VM and what you will have them do with them.  Some tools provide problems for students to solve others will not.  If problems are not provided create a worksheet that students can record their response.  If problems are provided have students transfer the skills and ideas they are learning about with VM into the procedures and processes they are using without VM.  This might include either recording the problem and solution or writing out the steps to solve with VM.  If students receive a score at the end of play have them record so they can track their progress over time (growth mindset).

2.  Second, you model with the students the way the tools can be used and what each of the tools represent. Not all VM tools are created equally and you will need to explain and demonstrate how to use the tools. Solve a few problems and demonstrate with your students before they work independently,

3.  Check in on students and determine misconceptions and areas for support.  After you set them free walk around the room and help troubleshoot then bring everyone back together to address misconceptions and share out how students are using VM.  

Okay so now you want to know what VM I recommend.  Here we go: 
    National Library of Virtual Manipulatives: create a worksheet of  problems to solve. Go deeper with concepts in visual form; I love the equivalent fractions tools.  
    National Council of Teaching Mathematics Illuminations has a variety of tools across k-12 span.  The algebra tiles tool is my favorite to build equations and solve.  
    Glenco Math Tools: these tools are fun and provide much space for students to explore, create and craft situations around math in the real work.

Got a Virtual Manipulative tool to share or way to use it that has captured your students attention please LEAVE A COMMENT!