## Tuesday, May 20, 2008

### What Does Everyone Need to Learn?

The characteristics of the family in which children are raised have an enormous effect on the kinds of formative experiences they enjoy, which, in turn, direct the trajectory of the remainder of their lives in dramatic ways. Children born into wealthy families have access to rich formative experiences, which lead to a greater variety of opportunities during adult life than children born into poorer families. But this hardly seems fair: Why should opportunity for success in adult life depend so much on the luck of birth, irrespective of natural ability or personal motivation? In recent decades, the international community has pushed for universal schooling as a means of equalizing, in part, the formative experiences of children in richer and poorer families. Unfortunately, many states find themselves in the unhappy position of having too few resources to provide every child with the lavish education they might desire. As a result, it has become increasingly important for states and other educational providers to seek out ways of maximizing educational benefit given limited resources, while still achieving the opportunity-equalizing function we assign to schooling.

This suggests the question: Is there some guideline curriculum planners can use to reduce the cost incurred by a given curriculum without jeopardizing the power of their schools to reduce the opportunity gap between rich and poor? Is there some minimal set of content to which everyone ought to have educational access? The international community has yet to establish a detailed answer to this question. International discussions about education have certainly underscored the great importance of educational and curricular quality, but descriptions of what counts as quality content have remained rather vague. Moreover, the common indicators used in international monitoring reports are unrelated to the quality of curricular content. Since access to schooling is nearly irrelevant if the quality of what students learn in school is insufficient, the international community needs to begin monitoring curricular content, in addition to the current indicators. This can be facilitated by an analytical device---a schema for basic education curricula---used in the evaluation and comparison of curricula in diverse contexts.

Read more in my Ed.M. thesis! I also have audio for a 10 minute overview and a 1 hour presentation with discussion under "Talks and Posters" in the Repository.

## Monday, May 12, 2008

### Narrowing the Curriculum

From oldandrew at Scenes from the Battleground:

We don’t need to consider whether French is more important than Latin, or whether biology is better for children than history for it to be possible to identify a failure in education where large number of those leaving the system are unable to read, write or behave like civilised human beings.

Recent national education reform efforts here in the United States that require school accountability for student outcomes in reading and mathematics have received a considerable amount of push-back, some of which has taken the form of complaints about a narrowing of the curriculum, saying that students need well-rounded educational experiences and that testing only in reading and math forces schools to myopically hammer these skills to the exclusion of other important lessons. I've never found the complaint convincing: Schools that successfully get students to learn to read and do math should have no problems with their students' passing mandatory external assessments, and can go on their merry way teaching as many other subjects as they like; schools that can't even get their students to read have major problems that need to be addressed before we can even begin to consider what kind of well-rounded curriculum students should learn (since they aren't really learning anything at all at this point, after all).

What's really going on behind the outcry against trying to teach students to read and do math? I have a sinking suspicion that much of it has to do with (a) incompetent administrators who respond to national and state reforms by imposing inane requirements on teachers who are otherwise doing a fairly good job and (b) teachers and administrators in failing schools who don't particularly like the fact that there are now consequences for that failure. As for the latter, we've known for half a century that our schools are failing far too many low-income and minority students, and yet have failed to make much progress in correcting the problem. It's about time to expect that students leave school able to read, write, and behave like civilized human beings---if achieving that means teaching fewer subjects in certain schools for the time being, so be it.

## Sunday, May 4, 2008

### A Few Notes from the History of the Massachusetts Department of Education

In 1837, the Massachusetts General Court established the nation's first state Board of Education, whose statutory mandate was to

collect information of the actual conditions and efficiency of the common schools and other means of popular education; and diffuse as widely as possible throughout every part of the Commonwealth, information of the most approved and successful methods of arranging the studies and conducting the education of the young, to the end that all children in this Commonwealth, who depend upon common schools for instruction, may have the best education which those schools can be made to impart.[1]
In its first eighty years, the Board established ten teacher-training institutions, improved the leadership and organization of schools, pushed for the first compulsory school attendance law in the nation (1852), pushed for the first free textbook law in the nation (1884), and established schools for children with disabilities.[2] Thus, from its inception, the Massachusetts Board of Education acted in accordance with its mission as an educational development agency.

In the early Twentieth Century, Massachusetts executed a series of administrative reorganizations. These included merging the Board of Education with the Commission on Industrial Education in 1909 and placing them under the direction of a commissioner of education, who replaced the original office of the secretary of the Board of Education.[2] In 1919, the state again enacted a widespread consolidation of boards and commissions, which dissolved the Board of Education and replaced it with an advisory board for the new Department of Education (DOE) with divisions for elementary and secondary education, vocational education, teacher training, immigration, public libraries, and post-secondary colleges.[3] Despite the many administrative changes, the Department of Education has retained its developmental character with the mission to
provide a public education system of sufficient quality to extend to all children including a limited English proficient student ... , and also, including a school age child with a disability ... the opportunity to reach their full potential and to lead lives as participants in the political and social life of the commonwealth and as contributors to its economy.[4]

The DOE's Student Assessment Services (SAS) unit developed in response to the Public School Improvement Act of 1985, the purpose of which was to
ensure educational excellence and equity for all students in elementary and secondary schools of cities and towns, regional school districts and independent vocational schools of the commonwealth [and] increase accountability of teachers and students, provide resources for creative educational improvements at the local level and provide resources to equalize educational opportunity.[5]
SAS therefore continues in the Board of Education's original mission to "collect information of the actual conditions and efficiency of the common schools" and supports the developmental goal of improving equity of educational opportunity through increased accountability. Specifically, the Act of 1985 called for "a statewide testing program to improve curriculum and instruction and to identify those students needing assistance in mastering basic skills."[6] This testing program consisted of two parts. The first, the Massachusetts Educational Assessment Program (MEAP), provided information about the progress of educational achievement in schools and districts by means of reading, math, and science tests administered biennially in grades 3, 7, and 11. After the initial cycle, the assessment added a social studies component and shifted to grades 4, 8, and 12 in alignment with the National Assessment of Educational Progress (NAEP). MAEP also included test items from NAEP to provide a basis for national comparisons.[7] The second, the Massachusetts Basic Skills Testing Program, provided information about individual students' achievement in reading, writing, and mathematics in grades 3, 6, and 9 to identify students for additional assistance in mastering basic skills.[8]

In the wake of the federal Goals 2000: Educate America Act (P.L. 103-227), the Massachusetts General Court passed the Education Reform Act of 1993, which included provisions for the establishment of statewide curricular frameworks and an accompanying Massachusetts Comprehensive Assessment System for
evaluating on an annual basis the performance of both public school districts and individual public schools [with respect to] the extent to which schools and districts succeed in improving or fail to improve student performance, as defined by student acquisition of the skills, competencies and knowledge called for by the academic standards ... in the areas of mathematics, science and technology, history and social science, English, foreign languages and arts, as well as by other gauges of student learning judged by the board to be relevant and meaningful to students, parents, teachers, administrators, and taxpayers.[9]
MCAS expanded the state testing program to include standards for academic achievement, a competency determination requirement for graduation, and state-wide comparisons of the performance of schools and districts.[10]

Today, SAS manages the development, administration, and analysis of MCAS tests in English/Language Arts (grades 3-8, 10), math (grades 3-8, 10), science and technology/engineering (grades 5, 8), and history/social science (grades 5, 7) in order to provide the data necessary for tracking the improvement of school performance and student achievement in partial fulfillment of the requirements of the 2001 reauthorization of the federal Elementary and Secondary Education Act of 1965 (ESEA, No Child Left Behind,'' P.L. 107-110) and in support of the DOE's primary mission to provide high-quality and equitable educational opportunities to all children.

[1] Chapter 241 of the Acts of 1837, section 2.
[2] Payson Smith, Eighty-third Annual Report of the Department of Education, Boston, 1920, at 15.
[3] Ibid. at 13.
[4] Massachusetts General Laws, chapter 69, section 1.
[5] Chapter 188 of the Acts of 1985, section 1.
[6] Ibid., section 6.
[7] Massachusetts Department of Education, The Massachusetts Educational Assessment Program: 1990 Statewide Summary, 1990, p 1.
[8] \footnote{Massachusetts Department of Education, \emph{Massachusetts Basic Skills Tests: Summary of State Results, 1989 Update.}}
[9] Chapter 71 of the Acts of 1993, section 29; Massachusetts General Laws, chapter 69, section 1I.
[10] Massachusetts Department of Education, "Education Fact Sheet," August 1997, at 20.

## Friday, April 25, 2008

### The Speed of School Reform

There is a public evil of great magnitude in the multiplicity and diversity of elementary books. They crowd the market and infest the schools. One would suppose there might be uniformity in rudiments at least; yet the greatest variety prevails. Some books claim superiority because they make learning easy, and others, because they make it difficult. All decry their predecessors, or profess to have discovered new and better modes of teaching. By a change of books a child is often obliged to unlearn what he had laboriously acquired before. ... It would seem, beforehand, that no duty of school committees should be more acceptable to parents, than that of enforcing a uniformity of books in all the schools of a town.
Horace Mann in the First Annual Report of the [Massachusetts] Board of Education in 1838.
At the present time educational standards in Massachusetts lack definition. The schools of the various cities and towns are organized without particular reference to any general or State educational program. To say, for example, that a child is rated in the fourth grade of any school system does not at all imply that he would receive the same classification in any other school system in the State, or that he would be pursuing the same subjects or the same courses if he were attending school in another town. In a State, a large part of whose population is so constantly shifting, this lack of reasonable co-ordination brings loss to thousands of our youth, to say nothing of the confusion it creates in the minds of parents and of citizens with reference to the educational accomplishments of their children as measured by teachers and school officers. No one would argue for an absolute uniformity of education throughout the State, and no one would desire any system which would eliminate individual or local initiative. These can unquestionably be preserved at the same time that general standards can be better defined and secured.
Payson Smith in the Eighty-second Annual Report of the Board of Education, 1919.
The board shall establish a set of statewide educational goals for all public elementary and secondary schools in the commonwealth. The board shall direct the commissioner to institute a process to develop academic standards for the core subjects of mathematics, science and technology, history and social science, English, foreign languages and the arts. The standards shall cover grades kindergarten through twelve and shall clearly set forth the skills, competencies and knowledge expected to be possessed by all students at the conclusion of individual grades or clusters of grades.
Massachusetts Education Reform Act of 1993.

## Friday, January 25, 2008

### Decomposing Word-Problem Solving

A couple of years ago, I was tutoring a sixth-grade boy in mathematics. I noticed that although my student was fairly adept at arithmetic, he had difficulty in knowing which operations to perform in sequence for multi-step computations, which was especially evident in solving word problems. One manifestation of this divide between knowing how to perform a computation and knowing what the computation signifies or how it functions in a larger context came in his stubborn refusal (conscious or otherwise) to retain terms associated with operations. For example, when multiplying mixed numbers, I attempted to remind him several times first to "convert the mixed number to an improper fraction." Each time he would look at me or the page for a moment and then say something like, "Oh, you mean 2 times 3 plus 1?" (if the mixed number was 3 1/2), frequently pointing to the numbers with his pencil as he spoke. "Blank times blank plus blank"---that is, the concrete sequence of operations contextualized in the specific problem at hand---seemed to be the extent of his understanding of what he was doing, and the rejection of proper terminology seemed to suggest that the concepts of improper fractions and converting between different representations of the same number were irrelevant to him. Now, although I love words and expressing ideas succinctly, precisely, and elegantly, I don't intend to suggest an unnecessary proliferation of terminology. However, discipline-specific terms, in moderation, facilitate communication in the discipline, particularly at a level of abstraction necessary for understanding how the various component concepts of the discipline function with respect to one another, which is vital in constructing multi-step solutions to non-trivial problems.

When teaching complex skills---that is, skills that require more than one action, simultaneously or in sequence---it's frequently necessary to break the complex task down into simpler skills, teach the simple skills independently first, and then have the student blend the simple skills together to complete the complex task. Let me refer to this intentional, metacognitive pedagogical sequence as decomposition of the complex skill, and to instruction that does not involve decomposition as holistic. Decomposition is frequently latent in math instruction sequencing: One teaches whole number addition, then multiplication, then least common multiples, before blending these component skills into addition of fractions. Unfortunately, in other areas, traditional instruction has not always achieved sufficient decomposition; and, while bright students can figure out the component skills for themselves in the process of being taught the complex skill holistically, students who struggle with complex skills could potentially benefit greatly from training first in simple skills and then (metacognitively) in blending the simple skills together to achieve a complex task. (For an example outside of mathematics, consider Why Our Children Can't Read, where Diane McGuinness claims that instruction based on phonemic awareness---a decomposition of reading---is necessary for the 30% of students that whole language and traditional phonics, both more holistic with respect to reading as a complex skill, will inevitably fail.)

Now, word problems have long been used in math classes to connect pure operations with real-life applications, develop reasoning skills, and increase student interest. Unfortunately, when many people recall their school days, they remember word problems as the bane of their math class. This, I imagine, is due in part to the fact that solving word problems is a complex skill and that traditional instruction has not sufficiently decomposed word-problem solving. Although students may master simple skills such as arithmetic operations, they may not figure out on their own how to select and blend them in the context of a word problem. From my limited exposure to recent elementary-school math textbooks, I have the impression that textbook authors are beginning to move toward decomposing word problems with periodic special pages with metacognitive tips, such as identifying unnecessary information and selecting a problem solving strategy; but, I believe more work can be done toward this end, and indeed must be done to raise achievement levels in mathematics.

I envision a sequence of graded exercises that would train students in the skills of (1) selecting the operation required for a computation, (2) identifying the information required for a computation, (3) identifying what is being asked, (4) identifying what information is given, (5) identifying extraneous information, (6) identifying missing information, (7) constructing a "knowledge chain" to fill in missing information, and (8) constructing a sequence of operations to arrive at the desired result. Each exercise would focus only on one of these skills. For example, the exercise for (2) would consist of problems of the form "You would like to purchase some oranges. What do you need to know to find out how much to pay?" (the number of oranges and the unit cost) or "You would like to put a fence around your yard. What do you need to know to find out how long the fence will be?" (the length and the width of the yard) but not "You would like to put a fence around your yard. What do you need to know to find out how much it will cost?" which is a compound problem (the unit cost and the perimeter, which comes from the length and the width) and fits under (7). The exact wording of each problem could, of course, be varied or stay the same according to the learning styles and needs of the students. As the students progress through the sequence of exercises, the teacher would also provide explicit (metacognitive) instruction in how to combine the simple skills. For example, "When you read a word problem, first determine the question, then ask yourself what information you need to know in order to answer the question like we practiced last week." To emphasize the metacognition, students should explain verbally the steps as they perform them (something akin to "I read the problem, and now I have to identify the question. In the problem, John wants to find out how much to pay. Next, I have to figure out what information is necessary for figuring out how much to pay. To figure out how much to pay, I have to know the number of hot dogs and the price of each hot dog. The problem tells me that here. Next, I have to decide what operation to use. I have to multiply the number of hot dogs and the price. Now, I can calculate the answer.")

Of course, the trick comes in finding developmentally appropriate ways of expressing and teaching each component skill, since the ability to understand abstractions comes only over time; but, I suspect that there are exercises that can facilitate even handling abstractions in the decomposition of learning about problem solving (as a skill distinct from problem solving itself). Nevertheless, the guiding principle of decomposition remains: break complex skills into component parts, practice the component parts, train students to think explicitly about how the component parts fit together, practice blending the pieces into complex skills. With this kind of simple, explicit, step-by-step, cumulative method, the most daunting of complex skills can come within students' grasp.