UBD in math: What next?
(Last of three parts)
Various public high schools started implementing Understanding by Design (UBD) last year. In the last two weeks, we discussed problems arising from faulty implementation in mathematics.
Pure and applied math
Teachers think that “transfer” in UBD means applications to real life. They often “force” activities that are contrived.
“Sometimes applications are beyond students’ experiences,” says Carmela Oracion, managing director of the Ateneo Center for Educational Development, who also teaches math at the Ateneo High School. “Other activities are impractical for huge classes.”
Since math is too abstract, people think it is hard to understand. But math always has to be applied to the real world to be understood.
National Scientist and mathematician Fr. Bienvenido Nebres, S.J., has discussed the dangers of focusing on understanding alone to the detriment of other skills (see “Eureka,” Sept. 19, 2011).
Ateneo math professor Ian Garces agrees, “People want knowing to come after understanding. But much of the time, understanding comes after knowing…this is just the way math behaves…. The Hungarian mathematician John von Neumann said, ‘In math, you don’t understand things. You just get used to them.’”
In the article “The Problem of So-called Problems in Mathematics,” creator Grant Wiggins says, “I am not suggesting that only ‘real-world’ problems that are immediately relevant to kids’ experiences count as ‘real problems’…. There is a limitless number of purely theoretical problems that math students should encounter as part of a good K-12 education, [like those] found in competitions.”
Killing UBD from the start
In the paper “Now What? Possible Next Steps,” Wiggins lists ways to “kill UBD from the start.”
These include: “Mandate that every teacher must use UBD for all of their planning immediately (without sufficient training, ongoing support or structured planning time). Provide one introductory presentation on UBD and assume that teachers now have the ability to implement UBD well.”
Many public school teachers said that after attending a session or two, they were left to do UBD in their classes. Others were not directly trained but were told to just follow the guides. Some did not get any guides, so they had to do “UBD-sounding” lesson plans on their own.
Wiggins says another way to kill UBD is to introduce it as the year’s focus, implying that it can be fully implemented in a year, and the previous year’s initiative bears no relation to it.
Many schools say they do not know what textbooks to use since current books are not “UBDized.” But good existing texts likely already have hallmarks of UBD. They should not be thrown away just because they do not follow a certain format.
“Through the years, in the Philippines, we typically bring in a new approach, usually theory-derived and usually from the US,” says Nebres. “Then we develop materials and, if funding is available, implement on a national scale.
“Then we train through a cascade, from national to regional to division to district and, lastly, to school levels. By the time we get to the actual implementers, the classroom teachers, there is only a short time left. The new approach and books wipe out the past, but since training gives no time for actual classroom teachers to absorb them, they are not really learned.”
If and when the K-12 curriculum comes into play, this will be the next UBD killer: “Attempt to implement too many initiatives simultaneously.”
Garces says teachers are still debating whether or not to use UBD. “If this is combined with classroom implementation of K-12 math, the result will be a huge hullabaloo,” he says.
The way ahead
If UBD is deemed appropriate for schools, then groundwork has to be done. In some private schools, like Xavier School, UBD works. Since 2004, as part of the Ignatian Pedagogical Paradigm, faculty, administrators and students have continued to fine-tune the UBD process, consonant with their context, needs and goals.
“Think big, but start smart,” say Wiggins and McTighe. “Ask all teachers to plan ONE unit per semester, for starters. Encourage them to work (together), and begin with a familiar unit topic. Develop a multi-year plan that links long-term goals to UBD strengths, and show how UBD will be slowly implemented as part of a strategic plan. Build a year composed of workshops, study groups, action research groups, in which staff go through many cycles of learn/try/feedback/revise.
“Train so that designers have tried out a few unit strands through all stages at least twice, then a full-blown unit, by year’s end.”
One unit after one year, not one year’s worth of units by the end of one or two sessions.
In the 1960s, educational reformers in Hungary made the mistakes we are making now. Nebres quotes reformer Tamas Varga who says, “Attempts to speed up a natural, organic growth rarely give satisfactory results.”
“The development of school math, especially in a developing country, has to follow the laws of organic growth,” says Nebres. “It is foolish to try to speed things up too much as it will simply lead to a withering or distortion of the growth.” Hungary has learned its lesson, and is now one of the top countries in the world in math.
“In Japan, another model of reform, a cycle takes around 12 years,” says Nebres. “Immediately, on implementing a new reform, a process begins of feedback on books and materials from teachers and classrooms. Feedback is processed through reports and conferences at different school system levels. Then policies and decisions are made on the main lines of the next cycle of reform and carried out in guidelines for new materials, which are tested before the new cycle begins.
“Reform begins from the classroom and the implemented curriculum, and the key players are the classroom teachers and school leaders. It is a more evolutionary, not revolutionary, approach, bottom up rather than top down. We begin with what we have and improve on it, rather than wipe it out and totally replace it.”
UBD was done in our public schools with good intentions, and teachers are trying to make it work.
But if Wiggins and McTighe’s recommendations are not followed, they warn that “UBD will be killed from the start.”
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