Tag Archives: T3

John Mighton and his JUMP Program

also posted on my bportfolio


I’ve been doing some research lately on John Mighton and his JUMP Math program.

David Ornstein wrote an article on JUMP in the New York Times. Mighton, the founder of the program, has written a curriculum for grades 1-8 in which he has broken down key mathematics algorithms into steps that ensure more mastery and learning.

Mighton states "Before children can read, they must acquire an extraordinary number of visual, auditory and cognitive skills. But children can master a great deal of mathematics simply by counting on their fingers (something we have evolved to excel at)." For example, the JUMP method teaches multiplication by repeated addition on fingers. As students get proficient with this, they can learn division and are soon passing standardardized tests on fractions with ease.

Mighton argues that all children can succeed. This has been supported by some preliminary studies and by the success of the program in some schools that have been early adopters of JUMP. The results have shocked some teachers who are not used to giving out all A’s to their *whole* class. This has been observed in classes with children of diverse abilities and SES. Mighton makes particulary strong claims that his curriculum can help even those who have long given up on mathematics, i.e. adults.

The part that I thought particularly relevant to our EDU6132 discussions was the cognitive justification that Mighton makes for his methods. By using micro-steps to teach algorithms and processes and by not moving on until everyone in the class has successfully achieved competency, he argues that the cognitive overload is decreased which fosters more learning. This intense scaffolding of the procedures to be learned ensures student success, which increases confidence. By building upon a chain of successes, all students are able to achieve at higher levels.

For more information, i.e. free download of teacher workbooks, see http://www.jumpmath.org


Mighton, J. (2004). The myth of ability: Nurturing mathematical talent in every child. Walker & Company.

Ornstein, D. (2011, April 11). A Better Way to Teach Math. The New York Times. Retrieved online April 30, 2011 from


What Works Clearinghouse Has Issued A Quick Review

The U.S. Department of Education, Institute of Education Sciens has issued a Quick Review entitled “Achievement Effects of Elementary School Math Curricula on First and Second Graders.  Check it out here:



Some Final Items for EDU6133

Here are links to my Sample Lesson Plan Packet, and the Powerpoint for my Presentation in fulfillment of classroom requirements for EDU6133.

Showcase Lesson Packet (Lesson Justification, Lesson Plan, Unit Plan, Classroom and Student Characteristics)

Class Presentation (120 MB PowerPoint, has the movie in it)

What I have Learned from Banks so Far

The biggest lesson I have learned from Banks so far is that there is really no down-side to being a culturally diverse teacher and striving to build a more multicultural education. Especially in math and science, there is an incredibly diverse body of contributors to past and current understanding in both fields. And yet, studies continue to indicate that race, gender, SES all contribute to a student’s prospects for success in STEM (science, technology, engineering, and mathematics). By not seeking transformative multicultural education, I believe we are impoverishing these fields, that is, we are limiting the progress of ideas in these areas of knowledge by not questioning the cause of limited aspirations of historically marginalized groups. The key to changing this, according to Banks, is to work actively to transform education, to forge equity pedagogy in classrooms across America.

The transformation starts small with building a corps of teachers that value cultural competence, that practice regular and deep content integration in their daily lesson plans. These teachers will not be blind to the diversity in the classroom, but will engage it, and will celebrate it in each individual. They will work to reduce prejudice by interrogating their own assumptions, their students’ assumptions and the assumptions in their texts and sources. The transformation continues as more teachers revise their curricula, differentiating their instruction to recognize and celebrate the backgrounds of the students in their charge. These teachers will encourage others to do the same. They will assume their role as facilitators of knowledge construction to create environments where all students identify that their own implicit cultural assumptions, frames of reference and biases are real and yet they still have a role to play, a contribution to make to form a more just community, a more fair society and a more hospitable world. Finally, progress is assured if the entire school culture is transformed to empower students. We as teachers must strive to increase proportionality in student achievement; to end grouping and labeling practices; to foster healthy interaction of students across ethnic, racial and SES lines. It rests on teachers to start this process of transformation and to see it through.

I am convinced that it is only up-side benefit and positive potential to help inspire students from different race, ethnicity, gender, sexual orientation, socio-economic status, age, physical abilities, spiritual practices, political beliefs and other ideologies. By enfranchising these students, we build a stronger country, a stronger future.


Banks, J.A., & Banks, C. A. M. (2010) Multicultural Education Issues and Perspectives (7th ed.). Hoboken, NJ: Wiley. p. 22.

OK, if you haven’t checked out Vi Hart, you really should.

[Thanks Elizabeth Alford for the tip!]

Elizabeth sent me the NPR article containing the below video.  Here’s how Robert Krulwich (NPR Science Blogger) introduces Vi Hart.

Vi Hart calls herself "a recreational mathemusician currently living on Long Island." She talks faster than a machine gun, loves math, and draws like a dream. Her newest video: "Doodling in Math Class: Snakes + Graphs" is eye-popping.

Vi Hart’s web site is here [permalink]

Week9 Reflection: Authentic Applications

While reading about Authentic Applications, a reflective assessment strategy, I was reminded of a science fair in which I participated as a grade school student.  The topic of my report was Solar Eclipses, and the event made such an impact on me at the time that I can remember clearly many minute details around the science fair and other exhibits that were there besides my own.  My own exhibit was comprised of a bright light, a globe, and a small foam ball mounted on a bent coat hanger.  I can remember the written report which I had made as well detailing all the notable total eclipses prior to that date.  In particular,  the 1974 total eclipse for Madagascar stands out in my mind (see table below).


Thus, I believe I am proof that this assessment strategy, in my case a science fair, caused serious learnings and impressions that lasted far beyond the event.

Now to bring this assessment strategy forward and apply it to some of our readings this week, I can’t imagine a more powerful way to teach landmark Supreme Court cases then to re-enact them, in public, in a moot court style.  Students could be selected to portray the sides of the case as well as the justices.  They could be asked to review oral arguments for the case and to present or read them (in an interpretive/dramatic fashion if appropriate).

For instance, this week we were asked to read a couple of historic Supreme Court decisions:

Plessy v. Ferguson (1896) and
Brown v. Board of Education (1954)

One could imagine that a systematic analysis of the Decision and Dissent in Plessy v. Ferguson (1896) would be catalyst to a whole host of interesting conversations.  Not the least of which would be germane to current understanding of race relations in this country.  In choosing which parts of the decision to read or set forward in a public portrayal of the trial, a discussion of the merits of the argument would naturally come forth, and a lesson on how to read/write legal decisions would be in order.  This would have immense educational value.  Consider this from Justice Harlan in Dissent (Plessy v. Ferguson, 1896)

The white race deems itself to be the dominant race in this country. And so it is in prestige, in achievements, in education, in wealth and in power. So, I doubt not, it will continue to be for all time if it remains true to its great heritage and holds fast to the principles of constitutional liberty. But in view of the Constitution, in the eye of the law, there is in this country no superior, dominant, ruling class of citizens. There is no caste here. Our Constitution is color-blind, and neither knows nor tolerates classes among citizens. In respect of civil rights, all citizens are equal before the law. The humblest is the peer of the most powerful. The law regards man as man, and takes no account of his surroundings or of his color when his civil rights as guaranteed by the supreme law of the land are involved. It is therefore to be regretted that this high tribunal, the final expositor of the fundamental law of the land, has reached the conclusion that it is competent for a State to regulate the enjoyment by citizens of their civil rights solely upon the basis of race.

What student would not find their hearts stirred upon reading this document, if not to read it publicly and with a fuller understanding and emotion?

Now consider Brown v. Board (1954), reading the court’s opinion written by Chief Justice Warren, where he comments on the extension of Plessy v. Ferguson which involved railroad conveyance to Brown v. Board which handled education thus:

Today, education is perhaps the most important function of state and local governments. Compulsory school attendance laws and the great expenditures for education both demonstrate our recognition of the importance of education to our democratic society. It is required in the performance of our most basic public responsibilities, even service in the armed forces. It is the very foundation of good citizenship. Today it is a principal instrument in awakening the child to cultural values, in preparing him for later professional training, and in helping him to adjust normally to his environment. In these days, it is doubtful that any child may reasonably be expected to succeed in life if he is denied the opportunity of an education. Such an opportunity, where the state has undertaken to provide it, is a right which must be made available to all on equal terms.

Suddenly I could imagine the students in a classroom would realize that their very education is a right and a duty upon which the whole of free society rests.  Equality in that venture is of utmost importance.


Plessy v. Ferguson.  163 U.S. 537. (1896).  CornellLaw

Brown v. Board of Education of Topeka.  347 U.S. 483 (1954). CornellLaw

Defined: “Authentic Applications”, A Reflective Assessment Strategy

Ellis & Denton (2010, p. 47) maintain that “when ideas are not applied they seem to start nowhere and go nowhere.”  This reflective strategy is powerful in its ability to ground the theoretical in the practical, to bring the lofty down to the pedestrian, to get the latex out of the laboratory to where the rubber meets the road.  In the words of the authors

The purpose of the Authentic Applications strategy is to challenge you and your students to become involved in ways that transform the curriculum from one of potential energy to one of applied, functioning energy.  And the key to doing this is to find as many outlets for student work as possible.  (Ellis & Denton, 2010, p. 48)

The procedure is simple, and involves getting student work out into the public square, where it on display for critique, engagement, explanation.  For the mathematics or science curriculum, Ellis & Denton (2010) cite Gainsburg (2006) that modeling or the application of principles to daily problem-solving “was found to be central to and ubiquitous in the engineers’ work, giving rise to some of their greatest intellectual challenges.”  Facilitating the contact between students and real practitioners of the arts that they are learning is key to this strategy.

Outcomes for this strategy are profound throughout the exercise.  Again Ellis & Denton (2010, p. 49)

Knowing that your work will be displayed in some way changes the stage of preparation…. This foreknowledge enables the learner to … focus the work.  The stage in which the event takes place (e.g., science fair, athletic contents, play, concert) offers further opportunity for reflection, judgment, review, and analysis.  And when the performance is over, this final stage represents a time to reflect, to think about meaning, truthfulness, beauty, and effort, and to take the measure of what went right or wrong toward improvement in the future.

Finally this strategy holds much promise for both engaging the student with the content, and engaging the student in the processes that are involved in real world application of that content.


Ellis A.K., & Denton, D.W. (2010) Teaching, learning, and assessment together:  Reflective assessments for middle and high school mathematics and science.  Larchmont, NY:  Eye on Education.  Amazon. Google Books.

Gainsburg, J. (2006). The mathematical modeling of structural engineers.  Mathematical Thinking & Learning. 8(1). 3-36. PDF

Defined: “All Things Considered”, A Reflective Assessment Strategy

Arthur Ellis (2001) views effective education as having three parts, teaching learning and assessment.  By assessment he means a technique of self-assessment whereby both student and teacher find meaning.  Through a process of reflective thinking, mere teaching becomes great teaching, since what we are learning must impact who we are becoming.  He describes that pursuit of meaning as being the central idea sometimes missed in all the activity that is modern education:

This is the essence of reflective thinking, a search for meaning.  Reflection involves stepping back from what you’re doing in order to achieve some measure of perspective. It means thinking, talking, and otherwise expressing your feelings, the things you’ve learned, the growth you’ve achieved, and the sense you have of accomplishing something. I am convinced that this is one of the greatest problems we face in classroom life.  The problem is, a failure to reflect.  The remedy is to take the time to do it in spite of the fact that you and your students won’t be able to “cover” as much. No amount of “fun” activities can make up for the loss that accompanies a failure to search for meaning.  (Ellis, 2001, p. 5)

In the intervening years since Teaching, learning and assessment, Ellis has been refining strategies that can help build more effective teachers and students through reflective thinking, what he calls the reflective classroom.  In particular, he has been tailoring the reflective assessment strategies for different grade levels and subject matter.  For example, in Ellis & Denton (2010) he describes 16 strategies for “Middle and High School Mathematics and Science.”

  1. I Learned
  2. Think Aloud
  3. The Week In Review
  4. Post It Up
  5. Jigsaw
  6. Key Area Identification
  7. Authentic Applications
  8. Parents on Board
  9. Search for Meaning
  10. I Can Teach
  11. Write It Down
  12. Learning Illustrated
  13. Clear and Unclear Windows
  14. Letting Questions Percolate
  15. Record Keeping
  16. Pyramid Discussion

As I get to apply some of these strategies in pursuit of the MAT, I would like to post a short description of each technique separately from the application of that technique to some coursework.  I will tag each post that intends to illustrate a given technique with the name of that technique; thus for this post “AllThingsConsidered” is the tag.  In particular, here is how Ellis (2001, pp. 115-117) describes that strategy.

The All Things Considered strategy asks students and teachers to take a few minutes at the end of the day, when the time comes in the afternoon that the day is a history that began that morning, to think back over the things that happened, and to see whether some of them might in some ways be related or connected, and if so, how they might be connected. This search for connections should cause students to focus on the essence of the activities and lessons in which they were engaged. It should bring about some sort of inquiry into what  the day at school was "all about.”

Initially, I am prone to think that there are a lot of similarities between the strategies, but that may be simply because they all have a metacognitive aspect, namely “what are you thinking about what you are thinking about”.  I am looking forward to trying out many of these techniques in the course of my study.


Ellis, A.K. (2001) Teaching learning and assessment together:  the reflective classroom.  Larchmont, NY:  Eye on Education.  Amazon. Google Books.

Ellis A.K., & Denton, D.W. (2010) Teaching, learning, and assessment together:  Reflective assessments for middle and high school mathematics and science.  Larchmont, NY:  Eye on Education.  Amazon. Google Books.

Garrett Keizer, No Place But Here, last paragraph from the chapter “Souls in Prison”

Dr Samuel Johnson 1709 - 84, John Opie RA




Opie’s portrait of Dr Johnson shows the brooding intensity and uncompromising directness of the celebrated lexicographer. His original compositions are seldom read these days, but his observations on life, his contemporaries and English literary have become gnomic and he occupies a central a position in the development of English literary criticism. He was also, of course, a superb conversationalist, and the members of his Club included some of the foremost figures of the mid-georgian intellegentsia, men such a Sir Joshua Reynolds and David Garrick.


Dr Samuel Johnson
1709 –84 

John Opie RA 
1761 – 1807


Keizer, G. (1988). No Place But Here. Hanover, NH: University Press of New England. 159

Rosie, the Dutch Belt, of Brownington Vermont.

well not really, but at least a reasonable facsimile

A good read, left me wishing for more, or more of me left wishing for time to read it all again and be struck as I was the first time.

Ravitch, D. (2010) The Myth of Charter Schools. The New York Review of Books


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