An Unorthodox but Pragmatic Approach to National Math and Science Literacy

Liz Gewirtzman
School of Public Affairs, Baruch College, CUNY
2008

Prepared for the Carnegie-IAS Commission on Mathematics and Science Education

Dear Commissioners:

I have chosen the form of a letter so that this paper is in no way mistaken for an academic scholarly work. It is instead the result of an un-systematic reading of research and literature in the field of education, and a considerable amount of my own professional and personal experience as well as that of others who I have come to respect. In particular it draws heavily on what we have learned in the development of SAM.

The Scaffolded Apprenticeship Model (SAM) is an approach to comprehensive school reform that integrates the work of school improvement into the work of building leadership capacity and succession planning.

Developed in 2003 through a grant by the Carnegie Corporation of New York, it was initially designed to respond to instructional leadership concerns at the high school level; its core principles and structure have since been incorporated into the New York City Department of Education’s Children First Initiative inquiry team process grades K-12.

Based upon research on effective instruction and organizational development, SAM applies a systematic evidence based approach to making sustainable changes in the core decision-making processes that drive student outcomes:

• Curriculum (what we teach, when and how often);
• Human Resource Distribution (who teaches it and to whom)
• Pedagogy (how we teach it); and
• Quality of Instruction (how well we teach it)

SAM approaches the identification of the systemic changes in core processes through the lens of a small group of students for whom the instructional practices in use are not working well enough. The strategy is designed to address both the presenting “problem” and its root causes. The procedure is in many ways similar to that used to identify and treat disease in the human biological system.

The process is perhaps best described by an example:

A team of teachers, aspiring to be instructional leaders in one of the SAM schools, selects a group of 15 “target” students struggling to pass 9th grade mathematics.

Through an investigation of standardized assessment results they identify misconceptions around fractions as interfering with the target student’s mastery of the 9th grade curriculum.

A deeper analysis using teacher generated assessments (often test items lifted from standardized assessments to which teachers have added more instructionally sensitive districtors) surfaces, for example, confusion around denominators and in particular the relationship between the size of the number and the size of the part.

An investigation of the curriculum in use confirms the team’s hypotheses that this particular content is not being explicitly taught in the school. It is assumed that students enter 9th grade with the prerequisite understandings.

The SAM team develops and implements (either directly or with the cooperation of fellow teachers) teaching strategies to address the misconceptions and identifies assessments to evaluate their effectiveness.

If the issue seems to be presenting among non-“target” students they often elect to expend class time on the new strategy – explicit teaching of the identified content. Some SAM teams, experiment with instructional adjustments within the context of a pull out or tutorial program. In these cases, SAM team members analyze what was effective about the tutorial or pull out teaching and move to incorporate the strategies into classroom practice.

Once SAM teams have been successful in moving a “target” group of students, they analyze the decision-making system(s) that produced the conditions under which students were supposed to learn what they needed to know. This sequence is based upon our experience that success with a group of students with whom the school has previously been unsuccessful profoundly shifts the beliefs and expectations of the SAM team about what is possible and effectively transforms them into agents of and advocates for change among their colleagues.

The SAM team might, for example, examine the curriculum decision-making process and find that: information about in-coming student’s level of mathematical understanding is not communicated by the guidance department to 9th grade teachers; in general the mathematics department’s decisions about what parts of the publisher’s curriculum and state pacing calendar to emphasize are made based upon an analysis of the prior year’s test results and focuses on what the average student has or has not mastered; no curriculum adjustments are being made to the 9th grade curriculum. An examination of classroom transcriptions and homework assignments might also reveal that there is wide variability in individual teacher implementation of department-wide decisions and that formal and informal supervisory conversations with teachers do not address how teachers actually make day-to-day curriculum decisions.

The SAM team then moves to affect the decision-making system itself by identifying and making a small change (over which they have control) that will make the biggest difference to student outcomes over time. In selecting their change strategy careful consideration is given to the particular players and the context in which they operate. For example a team might choose to administer a short mathematics diagnostic assessment during 9th grade orientation, analyze the results quickly and be prepared to adjust the curriculum for the fall semester to address knowledge gaps and misconceptions that could interfere with mastery of the prescribed 9th grade curriculum. They may have selected this approach based upon an analysis of the structures already in place and the level of receptivity of the players involved, and may have come to the conclusion that the introduction of new, more finely grained information at the beginning of the curriculum decision-making process will, over time, have the effect of bringing the curriculum into greater alignment with what struggling students need to learn to be successful.

The Scaffolded Apprenticeship Model (SAM) is an approach to comprehensive school reform that integrates the work of school improvement into the work of building leadership capacity and succession planning.

The SAM team is expected to monitor the impact of their change strategy on student outcomes to ensure that it is having the desired effect and make adjustments accordingly. Their objective is to accelerate and deepen the impact on student outcomes by acting strategically to remove obstacles to the strategy’s capacity to develop and sustain momentum.

As a result of this process SAM has amassed a lot of “close-to-the-ground” information about schools and how they operate. What has emerged is a deeper understanding of the “design flaws” built into school organizations that severally limit their capacity to respond to individual student learning needs, and that make them resistant to the influence of external accountability pressures.

What is promising about the SAM experiment is that we are also amassing a body of evidence that by carefully studying students for whom current practices are not working and strategically changing the conditions under which they are expected to learn, it is possible to systematically improve student outcomes for growing numbers of students.

The question we face, however, is to what end? What will we have achieved if we are successful? That is, if every student meets the criteria for success in their local school will we in fact have a math and science literate workforce? Are we teaching the right stuff, at the right time and place and in the right way to achieve the Commission’s goals?

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An Experiment:

I am assuming that you would not have been asked to serve on this Commission if you did not have enough knowledge of math and science to be productive in your professional and social life. That is, if every citizen (legal or otherwise) were as literate as you are, we would not need this commission today.

So to develop a set of baseline data, please indulge me in a very un-scientific experiment.

Please take out two pieces of paper and fold them vertically down the middle.

Mathematics

Write “Math Literacy” across the top of the first piece of paper. On the left side of the paper list all of the math that you use in your job. On the right side of the paper list the math you wish you knew that would be of benefit to you in your personal life.

• Example – Left Side: At one point in my career I was responsible for the oversight of about $2 billion in public funds allotted to the New York City Board of Education’s centralized instructional programs, including the Division of High Schools, the Division of Special Education and the Office of Curriculum and Instruction. The technology I used to track revenue and expenditures was a calculator and green spread sheets. Although the relationship between the rules governing the revenue streams and those driving the expenditures were complex, the math I employed consisted of adding, subtracting, multiplying and dividing whole numbers and factions and a fundamental understanding of the algebraic concept of variables and their effect on the equilibrium of the whole. Knowledge of these skills enabled me to figure out how to assess the current fiscal condition and make projections about the future – without formal knowledge of projection methods and models.
• Example – Right Side: In my private life I have always wished I knew more about how stocks, bonds and markets worked. It would be of great benefit to me as I get older and look forward to some sort of retirement.

Science

Now, write “Science Literacy” across the top of the second piece of paper. On the left side of the paper list five mechanical objects that you use every day.

Example – Left Side:

• Elevator
• Car
• Cell phone
• Flush toilet
• Computer

Now draw a circle around the one(s) for which you can explain exactly how they work to someone unfamiliar with them – there will be a test!

On the right hand side write down the science you have had to learn in the course of your life, why you needed to learn it, where you learned it, and how long it took you to learn it.

Example – Right Side: In 2004 my son was diagnosed with MS. Within six weeks (the time we were given to make decisions about treatment) I had acquired a sophisticated understanding of the biology of the human nervous system, enough chemistry to make sense of the treatment options and a whole new vocabulary. Although I’m relatively certain that my high school biology course covered some of the content, the only knowledge I could actually recall at the time were images from a book I read in elementary school called “How Our Bodies Work.” It could be argued that my K-12 education prepared me to make sense of the information which I subsequently needed to, and did, acquire—largely through the internet. As a result of this self imposed technology-based crash course, I am fluent enough in the language and ideas of this disease to make informed (if imperfect) decisions about it.

States typically post their standards and curriculum guides on their websites. Take a look at the Science and Math standards for your state. How well do your lists individually and collectively map on to the curriculum that is supposed to be taught in your local school. My guess is that an investigation would result in a Venn diagram – with some over lap between what you actually need or want to know and what students are being taught in school. It would not be a tight fit.

Are we teaching the right stuff?

Without real information on which math and science skills students will need in their futures? Schools rely on a “laundry list” of standards that provide no real guidance.

Who determines what is supposed to be taught? Well, there are two groups who have primarily influenced the curriculum. The first group is professional educators—groups of teachers in professional associations that have agreed through a rigorous and thoughtful process on what students should know and be able to do at various points in their educational careers – an example of this would be the National Council of Teachers of Mathematics (NCTM). We could say that this group represents the past. That is, their choices are primarily based upon what they know and ideas about best teaching practices associated with that knowledge base.

The second group is professional mathematicians and scientists. They seem to be less organized in their influence on K-12 curriculum but are often very vocal in response to positions held by the first group. Their primary concern is about the future – both of their individual disciplines and the problems that those disciplines face on behalf of us all.

These ingredients are then pureed in a political process that results in a set of state and local “standards” that are palatable to the public at large and baked in the everyday reality of what schools and school systems have the capacity to accomplish given time and resource limitations.

In New York City it looks something like this for science at the high school level:

• Students need 44 credits to graduate from high school. They are required to take 6 of those in Science. Each semester course is typically worth 1 credit and consists of 54 contact hours. Students must select at least 1 physical and 1 life science.
• In addition students need to pass 5 Regents examinations with a score of 65 or better in one of the following sciences: Living Environment, Earth Science, Chemistry or Physics. All students in a Regents science course must complete 1200 minutes of hands-on laboratory time prior to taking the Regents exam.
• For each of the Sciences New York State provides an online Core Curriculum guide along with a Laboratory Checklist. The Core Curriculum guide for Living Environment, under which Biology falls, has 2 standards; 10 key ideas, 34 performance indicators and 110 major understandings. In addition the lab checklist contains 17 items.

Missing entirely from the equation is reliable information on what students are likely to need to know and be able to do to be productive members of a workforce, informed members of an electorate and responsible decision-makers in their private lives in the future. The system by which state and local Math and Science standards and requirements are determined is simply not designed to access this information (where and when it exists), and make decisions affecting prescribed curriculum based upon it.

The result is our current condition – a growing laundry list of content and skills to be mastered, a shrinking capacity of schools to meet the demand, and a growing gap between what people like you actually need to know and be able to do to successfully navigate your professional and personal worlds and what we teach in school.

So what’s the problem? Well, it feels to schools more like a dilemma to be managed than a problem to be solved. The amount of time for math and science education within the current construct of schooling is limited. Schools therefore make choices about how to allocate time, space, and financial and human resources. Since they don’t have formal access to information about what their students are likely to need professionally and personally, both individually and collectively, a decade or more in the future, and a great deal of information on what various constituencies (including oversight agencies) think is important to teach and learn and hold them accountable for in the present, they end up in the unenviable position of having to make those choices in a very un-scientific way – and, we end up with a curriculum with which no one is satisfied.

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Are we teaching it at the right time?

Schools are not well designed to be responsive to the interests or processing idiosyncrasies of individual learners.

Typically this question is approached developmentally. That is, if we agree that a math- and science-literate person should know a particular thing, what do they need to learn first, second, third, etc. and how important is the order in which they learn it?

School systems are linear in how they distribute knowledge acquisition. One unit of study is more or less expected to build on another in the systematic construction of knowledge. It is, as Peter Senge points out, a factory model with assumptions built in about time needed for and sequencing of learning, opportunity for teaching, quality control of outcomes, and mechanisms for addressing those who do not conform to the model of our learning norm.

The problem of course is that people don’t actually learn most things that way, at least not according to cognitive science researchers and probably your own experience. It is particularly and perhaps perversely true about math and science. For example I mastered pre-algebra long before I was able to conquer long division. And there is no particular logic to learning about how a mechanical object works before or after learning how your body works or why the sky is blue. However, we do know that if you are interested in the subject either because you are naturally curious or because you are compelled to do something with that information, you are more apt to learn it faster, more easily and more deeply.

Schools are not typically designed to be responsive to the interests or processing idiosyncrasies of individual learners. They follow their own logic based upon ideas about sequencing to be sure, but also based upon the pragmatics of complex scheduling factors and resource limitations. As a result, all things being equal, they are much more likely than not to try to teach a student about the human nervous system at a time when s/he has no need for or interest in the subject matter.

Educators have valiantly struggled against this design flaw and the corresponding learner resistance by trying to invent “real world” problems for students to solve. This strategy has had limited success. The problem with these problems is that they do not feel “real” to students. And students therefore have no real stake in the outcome other than pleasing the teacher, getting a good grade, graduating on time and being successful at something some time in the future. By all accounts a relatively weak set of incentives for learning.

As students move through the school system, cognitive differences amplify. This is especially problematic in a standards-based environment.

Another problem with the logic of when schools teach what they teach is that they are not typically well designed, particularly at the secondary level, to respond to students who didn’t learn it when they were supposed to learn it. We live in a very mobile society and students may begin their education in one place and complete it in another. And we do not have a national curriculum. So it is more than likely that students who move from school to school will have gaps in their knowledge base.

Mobility is of course not the only reason students might experience such gaps. The curriculum discussed above may or may not be implemented as intended, creating wide variability in the opportunities students have to learn specific content.

Most of the work we do in the SAM program is in secondary schools. It is a truism of systems, including school systems, that differences amplify as you move through them. So, it is not surprising that we are finding groups of students in the schools we work with who enter high school with gaps in their foundational understanding of the subject matter—gaps that interfere with their capacity to make sense of the prescribed high school curriculum. That is, the curriculum being taught is not well aligned with what these students need to learn next.

Furthermore, high schools are not well designed to (a) identify these gaps before students fail at the course work, thereby further contributing to the motivational issues described above or (b) respond instructionally to foundational gaps. This is particularly true in a standards-based environment.

Here is one theory of how it works. As students move through the school system cognitive differences between them amplify. High school is at the end of the K-12 system. So, small differences between learners at the elementary and middle school levels have become big differences by the time they get to high school. This will be true to some degree no matter how well we prepare students at the lower levels. And, it has always been true. The way comprehensive high schools typically managed the variability problem prior to the standards movement was to distribute students among a range of graduation options associated with a range of curriculum from purely academic to vocational.

This is no longer the case. In a standards-based environment, while students vary in their learning needs entering high school, high schools are required to ensure that all students meet minimum exit criteria. And, they are trying to accomplish this within the context of an organization not designed at the classroom or school level to manage the range of differences.

Take for example the design of the typical math class. We begin with the teacher doing a mini-lesson introducing students to a concept. The teacher talks about the concept and then models its application. Students are then asked to apply the concept to a problem individually or in groups. The teacher circulates while the students work. After a while the teacher invites a student or group of students to share their work publicly. The class discusses it under the facilitation of the teacher and the students who have not shared their work self-correct based upon this discussion. End of lesson.

By design, this lesson assumes that all of the students in the class are starting with roughly the same prerequisite background knowledge – as we have learned, a poor assumption. And, by design, at the end of the lesson the teacher can be sure of what only those students who actively participated in the discussion learned from the lesson. As a result, s/he has very little information to guide them on what they need to teach next, and to whom. In the absence of accurate information on what students know, teachers rely on a one-size fits all prescribed curriculum or their gut to make instructional choices.

Most teachers are hard working and well meaning. However, they are working within a system that was not designed to do what they are being asked to do.

Most teachers are hard working and well meaning. However, they are working within a system that was not designed to do what they are being asked to do. If this were a machine in a factory (back to Senge’s analogy), we would say there was too much friction in the system – the work is taking too much effort and is producing too little progress. We would say that we need to go back to the drawing board and look at how the machine was designed.

We have found that organizing to correct for these design flaws and address the learning needs of students with foundational gaps in their understanding at the high school level often requires practitioners and administrators to be willing to be out of compliance with state and city requirements and incentives and/or confront strongly held beliefs about how coursework should be organized and students should be grouped. The path of least resistance is the one most often taken.

So how do we explain the outliers – the successful schools and classrooms? Here are two possible explanations. The first is the artful teacher. Some teachers are able to overcome the design flaws one way or another. And, that’s great for the students in their classrooms. The problem is that we have no evidence that our teacher preparation programs can reliably produce teachers with this artistry and/or that our human resource distribution systems can ensure that they end up in the classrooms that need them.

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The second explanation is that the students in the “successful” classrooms would be successful no matter how un-artful the teaching. Their learning is not primarily dependent upon what goes on in school.

This leads us to our next question:

Are we teaching it in the right place?

Where students have the opportunity to learn profoundly affects what they have the opportunity to learn.

Where do we actually learn what we need to know? Where did you learn it? If you go back to the beginning of this paper and look at the math you use on your job, where and when did you acquire these skills? How much did you learn in school? How much outside of school? How much on the job? Where would it make sense to learn it?

Now let’s look at schooling. We live in a diverse nation, in so many ways. One of those ways is how learners, of every size and shape, are geographically distributed from physically remote areas with sparse populations to dense urban communities. What a student in New York City has access to within the context of schooling and what a student in a rural community in Wyoming has access to are significantly different. A matter of place has a profound affect on the nature and quality of what students are exposed to.

No less diverse is the distribution of human capital. But here the data suggest a pattern. In general the most qualified teachers are serving the least challenging students. So, to the extent that the quality of teaching matters – and the data suggests it does – where you go to school matters.

Although each state and most localities have adopted content and/or academic performance standards they differ widely. The data comparing performance on state assessments of learning and the National Assessment of Educational Progress (NAEP) – the only national assessment of student knowledge – reveal wide discrepancies in what is considered proficient, where and by whom.

Another contributing factor is diversity of financial support for schools and local differences in the cost of education. Our school finance system is designed to place the financial burden for education primarily on states and localities. The processes by which levels of support are determined are political in nature. Furthermore, the buying power of the educational dollar differs dramatically from place to place based upon local bargaining agreements, land values and cost of living factors.

Where we have the opportunity to learn makes a profound difference in what we have the opportunity to learn. And yet we live in a world in which you can withdraw money on just about every corner. Although banks exist with more or less regular “banking hours,” we are no longer dependent upon either the location of a bank building or the length of the work day for tellers to access our money. To what extent should this dynamic function for math and science literacy? To what extent is it already functioning?

If there were robust multiple access points to an agreed upon national math and science literacy curriculum how would it effect the role and design of schools—particularly at the high school level?

If there were robust multiple access points to an agreed upon national math and science literacy curriculum how would it effect the role and design of schools—particularly at the high school level?

Are we teaching it the right way?

Many teachers are teaching in ways that aren’t compatible with the ways in which most students learn.

Please indulge me in another little experiment in the form of a field trip to your local high school.

Before you begin, describe briefly how you learn best. Do you like to read about it first or do it first and read about it later? Do you like to understand the gestalt first or put the pieces together one at a time? Is it easier for you to remember things if you hear them or if you see them? Now, find a high school student to shadow for an entire day. Yes, the whole day.

Before the day begins, ask the student you are shadowing to describe how s/he learns best. If they don’t know, ask them how they learned something recently. If your student is typical of this generation of high school students, they are far more likely (according to the research) to be parallel processors than linear processors, decode graphics first and text second, and be an active rather than passive learner.

As you move through your day in school, record what you are thinking and what you are feeling as if you were a student in the class – note when you were frustrated, bored, amused, etc. and the extent to which you are learning in spite of (rather than because of) instruction.

To what extent was how the classes were taught compatible with how you learn? How the student you shadowed learns? To what extent did it make a difference in your receptivity to learning – what you thought and felt during the lesson? How similar was the teaching to the teaching when you were in high school? In what way was it different?

Not only do different students need to learn different things next, they will learn them best in different ways. Again, this was always true. However, today in a standards-based environment we are requiring everyone to meet the same minimum level of proficiency.

Schools, particularly high schools, are not designed to adjust to students’ learning styles or the differing levels of scaffolding needed to support their learning. In fact it is usually at this point in the discussion that teachers and administrators throw up their hands and declare that it is simply not possible to individualize instruction for each and every student!

And I think they are right, if by instruction they mean what we have come to understand constitutes teaching and learning in a classroom. Again, we have a problem in design. And most attempts to improve schooling do not fundamentally alter the design.

Does the picture above explain the current condition of math and science literacy?

This analysis of the conditions under which schools and school systems have labored to achieve national math and science literacy is by no means exhaustive. Its purpose is to create a common understanding of some of the factors that have contributed to the present circumstances, provoke an appreciation for the complexity of the problem and promote a respect for the fact that (a) if this were an easy problem to solve we would have done so, (b) most of the obvious solutions have been tried and have met with only limited success and© it’s time to try something different, but something that we have reason to believe will address the limitations of previous efforts.

Problem Identification:

At the core of SAM is the idea that the key to the solution is in the problem. So, what problem are we trying to solve? Are we trying to achieve national math and science literacy (assuming we could define it and identify how we would know if we had achieved it) or is our goal to fix our national system of schools or is it both? If both, how will we determine what makes sense to “teach” in school and what makes sense to teach outside of school? What role should schools play in national math and science literacy?

While there are many limitations to the ways schools operate, education to a point is required of every American. As leverage points go this is a powerful one, perhaps necessary but not sufficient to achieve the Commission’s goals.

And the answer is?

As a learning environment, technology is responsive to a learner’s individual needs while scaffolding what is learned toward a common goal. It provides timely and accurate feedback on the learner’s progress both to the learner and anyone else who needs it—a feature that cognitive scientists suggest accelerates learning.

To recap, we need an approach with some or all of the following characteristics:

• It addresses the right stuff. It doesn’t impose a floor or a ceiling on what will be learned and thereby addresses past, present and future learning needs in subject matter of interest to learners as diverse as doctors, lawyers, plumbers and supermarket clerks.
• It can be accessed at any point in the learning process, and adjusts to the learner’s skill level as well as learning preferences. This feature ensures that if content is missed or forgotten it is not lost to the learner.
• It is available on demand wherever and whenever it makes sense for learning to take place.
• It provides the learner, as well as teachers and oversight agencies, with an accurate assessment of learning outcomes across diverse contexts.
• It is intrinsically and extrinsically motivating for the learner.
• It is not solely dependent on the availability of high quality human resources.
• It is relatively inexpensive to produce, distribute and maintain.

An approach that meets the above criteria:

There is a growing body of literature that suggests that game-based computer simulation technology is ideally suited to meet these criteria.

As a learning environment, technology is responsive to a learner’s individual needs while scaffolding what is learned toward a common goal. It provides timely and accurate feedback on the learner’s progress both to the learner and anyone else who needs it—a feature that cognitive scientists suggest accelerates learning. It is action-oriented with clear objectives, which the game industry has found to be so motivating that young and old alike are willing to persist in the process over time, until successful.

It is not context dependent, and could be accessed both in and outside of schools, anywhere and at any time. It is relatively inexpensive to produce, and could therefore be made available to anyone with internet access independent of financial means – a truly public educational system!

Furthermore, there is reason to believe that game-based computer simulations among other things improve problem-solving skills, enhance rule “discovery” and hypothesis testing, require the active use of prior knowledge, build specialized vocabulary and encourage reflection.

So, what’s the problem? Why hasn’t it happened? On this I can only speculate, and you no doubt can as well. Some of the issues that come to mind are:

• Communication: Those with the knowledge of the subject matter, those with the knowledge of how people learn and those with the knowledge of the technology don’t speak the same language and are rarely to be found at the same time in the same place.
• Constructs: We tend to think of schools as the only place where education takes place. We tend to think about technology as ancillary, not central, to the instruction in schools. We have a bias against video games as we once had a bias against comic books – now called graphic novels.
• Commerce: Our business models are too narrowly focused, not designed to appeal to or address a wide-spread public need. School systems themselves do not have the know-how or the resources for production.
• Custom: Where attempts have been made to use technology for K-12 teaching and learning, more often than not the designers have attempted to transfer the classroom experience to a virtual environment rather than explore what a virtual environment can offer the learner that a classroom cannot.

Promising practices: That said, there are some sectors that know more about how this can and should work than others. The military has had a long history of success with the use of simulations (with and without computer technology) as a learning tool; corporations are beginning to develop and invest in the use of game technology to develop the skills of their employees; the medical profession is using it more and more for training practitioners; and there is growing literature on the critical design principles successful products have employed.

Conclusion and recommendations: Above we have discussed some of what we know or think we know about the problem the Commission is charged with addressing. SAM is based upon the idea that the reason why previous solutions have not had the desired effect is that they have not sufficiently considered the dynamics of the problem that are hidden under the surface.

SAM’s approach is to study the problem more deeply by selecting a sample – a small group of students who are outside of the school’s sphere of success in a particular skill–and studying the conditions under which students are expected to learn it and the decision-making systems that produced those conditions.

What we have found in so doing is that schooling is a relatively closed system. The advantage of it being a closed system is that it is possible to align the parts so that there is more rather than less internal inconsistency. And it is possible for this to result in systematic improvements in outcomes on standardized accountability measures. It’s hard work but it’s entirely possible. The disadvantage of it being a closed system is that it is too isolated from the larger economic and social environment in which it operates to be adequately responsive to the demand for education where, when and how it presents itself in the world at large.

Furthermore, if the financial pages are to be believed we are about to enter an economic recession. Inevitably that will mean fewer resources for schooling. To the extent that education is the lever for literacy in the absence of a different approach, one that is not exclusively focused on schooling, we can expect less math and science literacy not more of it in the near future.

It is therefore my recommendation that the Commission invest in:

• Defining what is meant by math and science literacy and how we would know if we have achieved it, including a process for identifying what we expect the workforce of the future to need to know and be able to do to increase the quality of what they produce; a mechanism for transmitting this information to all the relevant social organizations including but not limited to school systems; and indicators for determining if, when and in what way we have as a nation met our math and science literacy goals.
• Seeding multiple points of public access to learning the requisite knowledge and skills, filling gaps in understanding and correcting misconceptions that take advantage of existing structures and substantially reduce the cost of delivering education – as opposed to schooling.
• Supporting the development of game-based computer simulations that simultaneously teach and assess learning, automatically adjust to the learner’s proficiency level, can be offered to the public free of charge and can be accessed both inside and outside of the classroom.

I hope this discussion has been helpful.

Yours sincerely,

Liz Gewirtzman
Distinguished Lecturer
School of Public Affairs, Baruch College CUNY
Project Director
Scaffolded Apprenticeship Model (SAM)