See like a Coach: Considering the lenses we use in Formative Assessment

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Formative assessment

a process of gathering evidence within the stream of instruction in order to inform teaching and learning (Black, Harrison et al., 2004). To be considered formative, the evidence must be “elicited, interpreted, and used by both teachers and learners” (Wiliam, 2011, p. 43)

From the Joint Position Paper on Formative Assessment of the National Council of Supervisors of Mathematics & Association of Mathematics Teacher Educators (2014)

We hear all about the benefits of formative assessment but what is it and how do you do it…well.  The Formative Assessment Conference put on by the Center for Mathematics and Science Education attempted to answer that question for mathematics educators from across the state (and beyond) the past two days.  My contribution to the conference was a talk called “Considering the Source: The Lenses we use when we Assess” where I used an interesting situation from my own teaching to illustrate the idea of seeing like coach versus a critic. (As I was figuring out how to talk about this idea of different lenses to use in formative assessment I heard this podcast by Perry Noble on “Coach v. Critic”, so you will hear some parallels in this talk. Just want to give credit where credit is due.)

Here is a link to the slides that I used in my talk, which has links in it to the resources that I mention.

Love, Allies, and the Cost of Course…discuss.

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The Association of Mathematics Teacher Educators met in Orlando this week which provides the opportunity for fellow teachers of teachers of mathematics to discuss how to improve the field of mathematics teacher preparation.  Sounds like a niche field but the importance of preparing teachers to teach mathematics, a subject which is directly connected to the academic and economic opportunities available to students, has a potential to ripple throughout schools and the country at large.  My contribution to the conversation were presentations from two projects that I am engaged in.  Both projects have helped me consider what does it look like to lead teachers in loving others though mathematics education.  One in helping future teachers consider the world in which they will be teaching and one in positioning ourselves as colleagues with in-service teachers to influence the mathematical system in which we all are a part of.

The first project, which we call the Cost of Course, was inspired by the article Access to Mathematics: “A Possessive Investment in Whiteness” written by Dan Battey from Rutgers University. The data and analysis within the article was striking (please go read it) and we as a project team wanted to figure out how to share it within a mathematical task, designed for preservice teachers, to open up awareness and to instill a sense of agency around issues of equity and diversity in mathematics education for our preservice teachers.

The other project, Access, Agency, and Allies in Mathematical Systems (A3IMS), inspired a presentation around how to position yourself as an ally in a professional development program where the circumstances of the project created a lack of interaction between teachers and the members of the project until day one of the professional development.  Not ideal, but what do you do given that reality.  We discussed how we adjusted the logistics, how we created opportunities to build relationships in order to build a foundation to have difficult conversations and consider the teaching of a mathematics as a political act.

Below are the citations to the presentations and links to the slides (if available):

Marshall, A.M., Amidon, J., & Nance, R. (February, 2017). Moving Prospective Mathematics Teachers from Instruments of Inequity Towards Agents of Change. Session at annual conference of the Association for Mathematics Teacher Educators. Orlando, FL.

Koestler, C., Amidon, J., Wager, A. A., & Foote, M. Q. (February, 2017). Facilitating a Mathematics Professional Development Collaboration as Allies with Teacher-Colleagues. Session at annual conference of the Association for Mathematics Teacher Educators. Orlando, FL.

Sharing Learning from the Desert: PMENA 2016

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The theme of this years meeting of the Psychology of Mathematics Education- North America Chapter is Sin Fronteras: Questioning Borders in Mathematics Education. The purpose of a conference is to grow as a professional and one thing I can do through the magic of the internet is share what I learn through the notes I take at the conference and sharing the presentations I am a part of as well.

Link to PMENA 2016 Program

Link to PMENA 2016 Proceedings

Link to PMENA 2016 Notes

Amidon, J., Koestler, C., Harper, F., Herbel-Eisenmann, Wager, A. A., & Scroggins, A. D. (November, 2016). Negotiating an Equitable Mathematical System Through Professional Development. Proceedings of the 38th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Tuscon, AZ: University of Arizona.

Marshall, A.M., Amidon, J., Nance, R.. (November, 2016). Crossing Borders: Moving Prospective Mathematics Teachers from Instruments of Inequity to Agents of Change. Proceedings of the 38th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Tuscon, AZ: University of Arizona.

Wager, A. A., Larnell, G. V., Langer-Osuna, J. M., Bullock, E. C., Bartell, T. G., & Amidon, J. (November, 2016). Addressing Equity and Diversity Issues in Mathematics Education. Proceedings of the 38th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Tuscon, AZ: University of Arizona.

Larnell, G. V., LopezLeiva, C. A., Scroggins, A. D., Amidon, J., Foote, M. Q., Hand, V. M., Herbel-Eisenmann, B., Koestler, C., & Wager, A. A. (November, 2016). Theory and research methods: challenging and reenvisioning frameworks for equity in mathematics education. Proceedings of the 38th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Tuscon, AZ: University of Arizona.


The Orchard Oxford: Growing Deep and Branching Out in Haiti

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5471207_640x640The Orchard Oxford is headed back to Camp Marie, Haiti!

Again we are partnering with 410 Bridge to connect with our neighbors in Camp Marie.  Last spring a team of 15 was able to live, learn, and pray with the people of Camp Marie and we are excited to return with another 15 member team during Spring Break, 2017.  Here are the details:

When: March 13th – 19th, 2017
Cost: $1945 with a $150 deposit due by 11/6/2016

Team members will be given support to help with fundraising and to help prepare for living, learning, and serving in Haiti.  And also to figure out how to use the gifts we have been given to serve others (1 Peter 4:10). To get a peek at what we did during the last trip and an idea about what we may do during this upcoming trip, check out these blog posts from

AP in Haiti – Day One: Questions for Haiti

AP in Haiti – Day Two: More Questions

AP in Haiti – Day Three: Movement in Math and a Community

AP in Haiti – Day Four: Hoops and Math

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

AP in Haiti – Day Six: The Answer is Relationships

There are more ways to get connected with our neighbors in Camp Marie besides participating in the trip.  Most urgently are needed funds to help with relief efforts from Hurricane Matthew.  Other ways to connect are through child sponsorship, community sponsorship and just praying for the people of Haiti and Camp Marie.

Deposits (made out to “The Orchard” with “Haiti Trip” followed by the trip member’s name in the Memo line) can be turned into The Orchard Oxford on Sundays (in the basket) or mailed to The Orchard (295 HWY 7 North, Oxford, MS, 38655). In addition you (or one of your supporters) can use a debit/credit card to submit deposits/payments for the service trip to Camp Marie, Haiti by doing the following:

  1. Go to
  2. Set up an account
  3. When submitting funds enter in the amount then be sure to select “Oxford” from the drop down.
  4. After submitting, send an email (jcamidon at with the following information:
    • The amount submitted
    • The date submitted
    • The first and last name on the card used

Any questions about the trip feel free to check out this 410 Bridge page dedicated to Frequently Asked Questions or to  contact Joel Amidon (one of the trip leaders) via email (jcamidon at

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  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.