So, I was invited to the White House…


In late November 2016 I was invited to a summit in Washington D.C. that was organized by the U.S. Department of Education’s Office of Educational Technology and focused on educational technology in teacher preparation.  The summit took place in mid-December with one day of meetings hosted at the offices of the American Association of Colleges for Teacher Education and a second day of meetings at the
Eisenhower Executive Office Building of the White House. It was an honor to be included on the invitation list to this event, and I was very happy to be able to attend.

The second day of the summit coincided with the release of a policy brief, Advancing Educational Technology in Teacher Preparation. The brief, and our summit, focused on four guiding principles:

  • Focus on the active use of technology to enable learning and teaching through
    creation, production, and problem-solving.
  • Build sustainable, program-wide systems of professional learning for
    higher education instructors to strengthen and continually refresh their capacity to use technological tools to enable transformative learning and teaching.
  • Ensure pre-service teachers’ experiences with educational technology are
    program-deep and program-wide, rather than one-off courses separate from
    their methods courses.
  • Align efforts with research-based standards, frameworks, and credentials
    recognized across the field.

During the summit experts from around the country were asked to share descriptions of their work that align with the principles. The list of presenters included: Dr. Teresa Foulger (Arizona State University) who discussed the work her team is doing to develop teacher education technology competencies and how educational technology is being integrated into the ASU teacher preparation curriculum; Dr. Jeff Carpenter (Elon University) who described his work using Twitter to develop community in Elon’s teacher education program; Dr. Royce Kimmons (Brigham Young University) presenting about the work he and his colleagues have done with technology in teacher preparation, including PICRAT; and Dr. Kyle Peck (Penn State) and Dan Randall (Brigham Young University) who discussed their work on badges and microcredentials. There were other presenters, but the ones I have listed here are working in areas that most closely align with my work context and/or research interests.  The summit attendees also heard remarks from Mario Cardona, Senior Policy Advisor for Education to the White House; Dr. Ted Mitchell, Under Secretary of Education; and Dr. Joseph South, Director of the U.S. Department of Education Office of Educational Technology.

Teresa Foulger, Jeff Carpenter, Royce Kimmons, Kyle Peck, and Dan Randall are all doing important work, if you are a stakeholder in teacher preparation and/or educational technology.  I encourage you to give their work an in-depth look.  The work with badges and microcredentials may be new to you.  When I talk to people about badges in education I often sense a lot of skepticism, but I believe this topic especially has the potential to change a lot of what we do in Education in terms of pre-service and in-service teacher education.  You may see me write more about this topic in another blog entry soon.

As the summit was concluding we were given the opportunity to join affinity groups around the four principles from the policy brief.  Thus, we will all hopefully hear more about these efforts from the affinity groups rather than having the principles buried in a PDF document in some archive of government documents.  I agreed to work with the group focused professional learning for higher education instructors (the second bullet in the above list).  Our work is just getting organized, but at least one of the groups is already quite far along in their work; Teresa Foulger’s group working on technology competencies will report their work at the March 2017 SITE Conference.

Locally, I am curious about the implementation of educational technology experiences for pre-service teachers that are program-deep and program-wide, rather than one-off courses (bullet three in the above list).  I have already had some information conversations with my Dean about how this could be done in my College and I hope the conversation continues. The program-deep and program-wide goal is admirable, but many of us work in environments where student credit hours are the coin of the realm and having designated courses for educational technology makes those hours easy to count. Similarly, those of us who are faculty members in Educational Technology or Instructional Technology programs do not want to become support personnel to others implementing technology in their classes.  Implementing program-wide and program-deep experiences for pre-service teachers will take some creative thinking to ensure it works within systems that have been built for decades around the concepts of classes and semesters.

Dr. South and his staff from the Office of Educational Technology did a great job organizing and facilitating the summit.  I hope that the work of his office and the work growing out of the summit is able to continue through the transition to the next President’s administration.



Is technology pushing college-level Math Courses up Bloom’s Taxonomy?

prof lecturing about math

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Many college or university-level math courses are delivered with the following general structure. A course meets 3 days per week for the length of the semester.  In each class meeting there is a one-to-many lecture delivered by the instructor, and possibly some questions answered about the lecture or the homework assigned during the previous class period.  There are variations on this structure; a quiz might be involved for example, or graded homework might be collected or returned.  Periodically there will be an assessment of some type, often a closed-book, written exam.  Calculators may or may not be allowed on the exam.  Of course there are exceptions to this type of structure, but my experience as a college math teacher and my work at universities gives me this gut feeling that this is the most common course structure.

Homework is a staple of most college-level math courses.  Instructors often will assign students the even-numbered exercises in the text book to be turned in as part of a homework grade.  The beauty of the even-numbered exercises are that their answers are not provided in the back of the book.  If you work the odd-numbered problems, many books include at least the correct final answer so that you can check your work.  In some cases there are hints for how the solution can be found there too.  Expanded solutions manuals are sometimes available, at an extra cost to the student that show you in a step-by-step fashion how to work those odd-numbered exercises.  You see the importance of assigning the even-numbered exercises; the ones with no solution available.  The students can use the resources available to them with the odd-numbered exercises to learn and self-evaluate their learning, but when it comes time to do some grading, you need to see how they do with no such resources.  Enter some modern technologies…

Technology in math courses has long been a source of debate.  Many of us have had math courses where the instructor commanded “no calculators allowed”.  Others may have been able to use them sometimes, and others yet perhaps all the time.  A strategy I have often seen enacted is for the math instructor to construct exercises and/or quiz and test questions where the use of a calculator was really no help.  Two freely available online resources are changing a lot of how this might be working: Wolfram|Alpha and YouTube.

wolfram|alpha logo           

The combination of these two technologies creates the largest solution manual ever created and renders the even-numbered math exercise strategy pretty much useless. Wolfram|Alpha has tagged itself a “computational knowledge engine for computing answers and providing knowledge“.  The stated long-term goal for Wolfram|Alpha is to “make all systematic knowledge computable and broadly accessible“. Since a lot of the exercises assigned for math homework fall into the category of being solved by the use of various algorithms, it seems like Wolfram|Alpha will have it done.  Actually, it already does quite a lot. You can enter standard calculus problems of calculating derivatives and integrals and Wolfram|Alpha will produce the final answer, produce graphs, and here’s the kicker — show you the step-by-step work from the statement of the problem through to the final answer.  You can get up to three step-by-step solutions per day for free, but a very modest fee eliminates that limit.  If you have not tried Wolfram|Alpha, do it.  I taught university-level calculus and differential equations for several years and I am impressed with the information Wolfram|Alpha provides, and it does it all quickly on just about any Internet connected device.

Some of you reading may be thinking that Wolfram|Alpha is impressive, but it cannot do “real” math.  It cannot do a mathematical proof.  Enter YouTube.  Do you need to prove that a subgroup of a cyclic group is cyclic? Click here.  Do you need to prove that a scalar multiple of a continuous function is continuous?  Click here. Will there be incorrect proofs posted online?  Sure.  However, the comments and “likes” available will allow users to find the best versions available.  What does all of this mean for college and university-level math teaching?

Some math students who choose to rely on these resources for homework solutions will be discovered when their test scores show that they cannot solve the problems.  Some math students will regulate their learning using these resources and perform well on tests.  But should an instructor wait until the tests to see which students are really engaged with the course material in a meaningful way?

What about flipping your classroom? Make use of the online resources like lectures and examples of proofs and then utilize class time for collaboration and problem solving.

Many of you have heard of Bloom’s Taxonomy for learning objectives.  Where do you think “traditional” math homework falls in this taxonomy? Do tools like Wolfram|Alpha and YouTube push assignments up the taxonomy to make them worthwhile? The fact is that Wolfram|Alpha and YouTube are becoming ubiquitous thanks to mobile devices and increasing access to wi-fi and cellular networks.

bloom taxonomy pyramid

Bloom’s Taxonomy from:

Acknowledge that these tools exist.  Design your courses to make use of them.  Leverage their power to help you create courses that require students to function higher on the Bloom pyramid.   Will you do it?

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