math tutoring without a tutor

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Do you tutor?  

It is a common question someone who has a career centered on math may hear from time to time.  When I hear the question I don’t want to turn someone away without giving them some way of obtaining what they need…help with developing their relationship with mathematics.  Something I always suggest is using Khan Academy.  Videos have been created by Sal Kahn and his team around many areas of mathematics and other STEM subject areas as well.  Students can then create a login (or use their Google account) to keep track of their progress in learning mathematics and computer science (with more being added daily).  Teachers, Parents, and even tutors can use the “Coaching” tool.  Teachers or Tutors can keep track of their students progress, or parents can use it to set goals for their children (Coaching Resources are available via the website).  I have written about Khan Academy earlier to reiterate what I like about Khan Academy is that a user is always learning through the hints, videos, and exercises that are connected to the multitude of content on the site.

Khan Academy is available as an app for the iPad (my preference because of the touch interface) and an app for the iPhone as well, though the iPhone app can only play the videos…as of yet.

Also worth a look is Smarthistory presented by Khan Academy which is a website that merges art and history.

Another site that I do not know as much about but is also free and keeps track of your progress through some math content is ck12.org.  I look forward to checking it out in the future.  Until then feel free to submit a comment below.

Here is a link to a little tutorial sheet I created for teachers wanting to use Khan Academy.

teaching problems and the problems of teaching

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Teaching Problems and the Problems of Teaching by Magdalene Lampert is the best book I have read about teaching math well.  Dr. Lampert was a professor at Michigan State but kept teaching in a elementary classroom.  The book contains thick descriptions of how she set up her classroom, how she encouraged kids to engage in the doing of mathematics, and even discussions that were facilitated in her classroom.  A great book for teachers looking to move away from the traditional math classroom.

complex instruction: group worthy tasks that show we are ‘smarter together’

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Complex instruction.  Great stuff with an intimidating name…at least when I first heard it.  Complex instruction is a highly structured form of group work that is especially useful in mathematics classes.  The purpose of complex instruction is to balance participation within groups.  I can think about those times when I was put into groups and someone didn’t participate (or I didn’t participate), someone dominated the conversation (or I dominated the action), someone took over all of the materials (or I took over all the materials, and I know that everyone did not receive the same opportunity to learn within that task.  Again, complex instruction is a means to interrupt the disproportionality in participation and increase everyone’s opportunity to learn.

I was able to learn about complex instruction through a conference in Atlanta, GA, where we learned more about how to structure a classroom to accomplish the goals of complex instruction, and to write tasks that are ‘group worthy’ and ripe for complex instruction.  Below are some key resources regarding complex instruction.

Smarter Together! Collaboration and Equity in the Elementary Math Classroom Book that describes the principles of complex instruction and contains sample tasks for use in the elementary classroom.

Strength in Numbers: Collaborative Learning in Secondary Mathematics Book that describes principles of complex instruction and contains sample tasks for use in the secondary classroom.

CIMath: We are smarter together! Complex Instruction Mathematics Website for teathat contains Group Worthy Tasks (e.g. the Ordering Numbers Task) and some more information about complex instruction.  This site was put together by the authors of the Smarter Together book.

Designing Groupwork: Strategies for the Heterogeneous Classroom The original book that describes complex instruction, complex instruction tasks, and contains strategies to interrupt imbalances in participation.

Group-Worthy Tasks Article that succinctly describes the essential elements of a group worthy task (essential for enacting complex instruction).

demos: free graphing calculator application

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Desmos is a web-based graphing calculator application for computers and also an iPad app.  The iPad app is not web dependent and gives me the “touchable” graph that I wanted with my TI-85 back in high school. What I love about this app is that it is free and available to everyone and you can create an account (or login with Google) in order to save and share your graphs.

Desmos can be accessed by using the link above or downloading the app from the Apple App Store or on Google Play.

Click on the graph on the left to go and manipulate the parabola and the line. (Another cool feature that you can embed a graph into a webpage or an electronic document for someone else to go and view.)

tinkering by the bay

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us-iphone-1-nctm-2016-annual-meetingThe National Council of Teachers of Mathematics are holding their annual meeting in San Francisco this week.  It is an exciting time where mathematics teachers are coming to learn about how best to serve their students in the classroom.  This year I was invited to talk in the New Teacher Strand, which was assembled to provide talks aimed at the interests, needs, and challenges of being a new teacher. When I considered what I might offer new teachers I thought about my own experience as a new teacher and how I would use the energy generated by the conference along with the new things I have learned to make adjustments to my teaching during the final weeks of the school year so I could consider how best to enact the strategies, problems, lesson structures when the school year starts up in the fall.  My hope is that this process is something that new teachers would appreciate hearing about and considering as they take in this year’s annual meeting.

Here is the link to the slides from my presentation

Another thing I like to do at meetings like the NCTM Annual Meeting is to share what I have learned and seen at the meeting. Here is the link to my notes from the Research Conference/Annual Meeting. Enjoy!

We Talkin’ Bout Practice

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Allen Iverson might not have wanted to talk about practice but it seems like mathematics teacher educators cannot get enough of it.  This week at the NCTM Research Conference I joined several colleagues to talk about how to represent the practice of teaching within LessonSketch. These representations were then used in both mathematics methods classrooms and mathematics content classrooms.  The thing that excites me most about what was said during the individual talks was the evidence that engaging in representations of practice was a productive way of promoting best practices, which is a good thing.  I have attached the presentation and the citation for this presentation below.

Here is the link to the slides for the portion of the presentation that Stephanie Casey and I were responsible for.  Enjoy!

Aaron, W.R., Alibegovic, E., Amidon, J., Crespo, S., Milewski, A.M., Bannister, N.A., Casey, S., Hanby, K., Kalinec-Craig, C., & Lischka, A.E. (April, 2016). Research on Math Teacher Education in an Online Multimedia Environment. Research Symposium at annual research conference of National Council of Teachers of Mathematics. San Francisco, CA.

teaching with khan academy

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I am a fan of Khan Academy.  As a mathematics educator I am often told about people who are struggling or know someone who struggles with mathematics and they are looking to hire a tutor and I ask them to give Khan Academy a shot.  I see Khan Academy not as a replacement for teaching but as a way to enhance teaching through a free resource that can bridge home and school, grade to grade, and subject to subject.

Khan Academy started out as a guy making videos for a family member to help explain mathematics concepts and procedures.  Now you can not only watch videos but demonstrate competence in those same concepts and procedures through differentiated exercises that are embedded in the site.  What is exciting to me is the emphasis that Khan has made on the idea of growth mindset, that we all can learn.  That seems pretty simple but how often have we heard people profess their own limitations before they have even tried to do something.

In addition there is way more than just mathematics on the site.  I especially like the work they have done in Computer Science and providing entry level exercises so that anyone can learn how to code.

Anyway, I decided to create a little tutorial sheet that is designed to point teachers to resources that will be helpful for starting to use Khan Academy in their own classrooms.  Here is the link.

AP in Haiti – Day Six: The Answer is Relationships

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IMG_0648Our time in Haiti has come to a close. Crazy to think how fast it went. Our last act was the Jericho Walk, where we were led by the leadership council up a large hill (mini-mountain?) that gave us a bird’s eye view over the Camp Marie community. The purpose of the Jericho Walk was to help us picture the leadership council’s vision for the community and allow us the opportunity to share in that vision and pray for God’s guidance in realizing their hopes and dreams for the community. The walk ended with a gathering in the church where the leadership council shared with us their appreciation for our visit and how our team connected with the people of their community. Finally, we had a chance to pray for the leadership council to provide them with discernment, patience, and resilience in the work they are doing for Camp Marie.

At the beginning of this week I had a lot of questions about this trip.  Some questions I mentioned in this blog and some just lingered in my head during the week. The answer to all of them lies in relationships.  Over and over again I saw the design of the trip and the mission of 410 Bridge come alive in how we did life with the Camp Marie community.  The Jericho Walk was the perfect ending to our trip, but not the ending to our relationship with Camp Marie…only the beginning.

Kenbe Fem!

AP in Haiti – Day Five: Kenbe Fem (Stay Strong)

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Today our first task was to head to Camp Marie and complete a service project. There was one problem. The people of Camp Marie completed the service project the day before. When I try to communicate the mission of 410 Bridge, I talk about how 410 Bridge helps communities help themselves. The fact that they took it upon themselves to fill the community need so that we could spend more time in the community building relationships, was evidence that the mission is becoming reality. The community visits happened in Charlene, which is a community that is up the mountain from the main part of Camp Marie. During one of our home visits we met the mother of three children who upon greeting us started saying the phrase “Kenbe fem”, which means “Stay strong” and in the context it was to “Stay strong in the Lord”. Our conversation with her ended with her praying for us, singing to us, and exclaiming “Kenbe fem!”  She was encouraging us as we continued the work we were called to do. It had become clear, in our last full day in the community, that this trip was not about doing some short term project where the paint will fade, or the fence will fall, but about building relationships. Because relationships will outlast any paint job.

IMG_0621-e1458390547200-1024x633Another event that happened in the afternoon was the women in our group decided to lead a bible study for any of the women in the community who wanted to attend. The theme for their study was “God Reigns” talking about God’s sovereignty over the world and over our lives. They used 1 Peter 4:10, which is the passage that inspires the work of 410 Bridge, to introduce the idea of how God has provided everyone with spiritual gifts to use in the service of others. The women of our group talked about the gifts they have observed in themselves and then asked the women of the community to share the gifts they have observed in each other. This impromptu bible study served as a way for the women of our group to use their gifts, encourage the women of the community, and strengthen the relationships between our communities. So cool to see!

Kenbe fem!