Central Bucks Schools Teaching Authentic Mathematics in the 21st Century


Topic 2.1.3: How Do I Teach Authentically and Still Meet Academic Standards?



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Topic 2.1.3: How Do I Teach Authentically and Still Meet Academic Standards?

Authentic Intellectual Work and Standardized Tests: Conflict or Coexistence – A Summary Report

 

There has been a long-standing debate between urban educators and teachers of disadvantaged students about the need for back-to-basics instruction versus the need for rigor and relevance in students' classroom experiences. The back-to-basics proponents claim that students need to become proficient in basic skills in order to perform well on standardized tests and before being able to tackle more meaningful tasks in school. The pedagogy associated with this thinking tends toward rote memorization and practicing discrete skills in isolation. In this model, teachers are the experts imparting knowledge to their students; therefore, they are responsible for deciding on the right answer and students are responsible for reproducing the knowledge in the same format in which it was received. Tasks often include multiple-choice questions and short-answer responses designed so students regurgitate dates, rules, and lists.



However, there is another school of thought that takes exception to this wisdom. These educators believe that providing all students with rigorous and relevant experiences each and every day in school will indeed improve standardized test scores, and create an environment in which students will develop the basic skills being tested by these instruments. A study conducted by Dr. Fred Newmann and associates in the Chicago Public School system illustrates the positive relationship between meaningful classroom learning experiences and standardized test results. This article will summarize the findings of this study and examine the implications for practice for educators who serve urban populations and disadvantaged students in other settings.

The Study

This three-year study took place in between 12 and 19 of Chicago's public elementary schools each year, representing a total of 349 teacher participants. It was funded by the Chicago Annenberg Challenge, whose mission is to "improve student learning by supporting intensive efforts to reconnect schools to their communities, restructure education, and improve classroom teaching" (Newmann F.M., Bryk, A.S., Nagaoka, J. 2001, p. 5).

The researchers collected samples of teacher assignments in writing and mathematics. They asked the participating teachers to submit four samples of daily assignments and two samples of long-term, more challenging assignments. These assignments were judged by a team of educators recruited by the project. Readers can access the complete study report at (http://ccsr.uchicago.edu/publications/p0a02.pdf) to see samples of assignments these researchers found to be exemplars of intellectually authentic tasks.

All assignments were scored using a four-point rubric that measured three quality standards in each content area:



Writing

  • Construction of Knowledge: The assignment asks the student to interpret, analyze, synthesize, or evaluate information in writing about a topic, rather than merely to reproduce information.

  • Disciplined Inquiry: Elaborated Written Communication: The assignment asks students to draw conclusions or make generalizations or arguments and support them through extended writing.

  • Value Beyond School: Connection to Students' Lives: The assignment asks students to connect the topic to experiences, observations, feelings, or situations significant to their lives.

Mathematics

  • Construction of Knowledge: The assignment asks students to organize and interpret information in addressing a mathematical concept, problem, or issue.

  • Disciplined Inquiry: Written Mathematical Communication: The assignment asks students to elaborate on their understanding, explanations, or conclusions through extended writing; for example, by explaining a solution path through prose, tables, equations, or diagrams.

  • Value Beyond School: Connection to Students' Lives: The assignment asks students to address a concept, problem, or issue that is similar to one that they have encountered or are likely to encounter in their lives outside of school (Newmann F.M., Bryk, A.S., Nagaoka, J. 2001, p. 22).

The researchers reported that 1785 third-grade students, 1686-sixth grade students, and 1425 eighth-grade students participated in the writing assignment study; and that 1794 third-grade students, 1522 sixth-grade students, and 1278 eighth-grade students participated in the mathematics assignment study. The authors note that some of these students may be replicated if the teachers taught in a self-contained classroom and taught both language arts and mathematics. There was no mention of whether the same students may have participated during all three years of the study. Data were reported as growth from one year to the next, not longitudinally over the course of the study.

Student progress was monitored by comparing standardized test results and whether the students received rigorous instruction and authentic intellectual work in their classrooms. The researchers compared the performance on two standardized tests typically used in Chicago Public Schools: the Iowa Test of Basic Skills (ITBS) and the Illinois Goal Assessment Program (IGAP). Their hypothesis was that students completing intellectually authentic assignments with basic skill instruction embedded in those assignments would perform as well or better on standard measures than students in classrooms that stressed basic skills and rote learning strategies.



The Results

The results show that students learn more in classrooms with high-quality, rigorous assignments (Newmann, 2001). Both standard measures showed significant gains in the test scores of students in classrooms with regular, intellectually authentic and relevant assignments. On both the IGAP and the ITBS, students in high-quality assignment classrooms surpassed their counterparts in low-quality assignment classroom settings. These students also surpassed the national average score gains on these standard measures.

The researchers wondered how this intellectual work was distributed in Chicago's public schools. They wanted to be sure that already high-achieving students were not the only recipients of intellectual authenticity. In fact they found that the most important variable in determining whether students would be in an intellectually authentic learning environment was the teacher and that teacher's instructional style. Students' ability level had an insignificant correlation to success in this study. The data indicate that all students benefit from high-quality assignments and the opportunity to read, write, think, and speak about relevant learning experiences on a daily basis. One can only assume that the quality of their assignments positively affected their acquisition of basic skills as evidenced by the improved scores on measures of these skills.

(See Addenda for the graphed data charts.) (Figure 3, 4, 5)



Implications

This study illustrates that focus on high-quality learning experiences for all students is warranted, especially if our schools' success continues to be measured by standardized test scores on measures of basic skills. High-quality assignments and intellectually authentic learning in the classroom help build students' knowledge of basic skills by giving them the opportunity to practice these skills in meaningful ways. They are using these skills to make meaning of the content under consideration.

Although this study was conducted in elementary schools, it has implications for teaching and learning at all levels. As a nation, our high school drop-out rate in many settings is alarming. Dropping out is the ultimate expression of disengagement. The data presented in this study indicate that if students can make connections between their work at school and their lives outside of school, they will be more invested in their work in school. It suggests that when students have an opportunity to participate in learning environments that have high expectations they will perform better on standard assessments. Finally, the study also illustrates how quickly districts can see gains in test scores when they focus on student learning, high-quality instruction, and authentic assignments.

The authors of this study did not indicate that such practices were prevalent in Chicago Public Schools. They also did not advocate for a particular menu of teaching strategies; rather they endorsed a balance of instructional strategies, keeping the focus on authentic intellectual assignments in all content areas.

"Our key point is that it is the intellectual demands embedded in classroom tasks, not the mere occurrence of a particular teaching strategy or technique that influences the degree of student engagement and learning" (Newmann et al, 2001, p. 31.)

These researchers also recognized the need for professional learning opportunities for teachers to "advance their expertise with a diverse mix of teaching strategies" (Newmann et al., 2001, p. 31). Since this study was completed and reported we have seen the rise of site-based staff development initiatives to support teachers on the job. We have embedded teacher learning in the school day and focused more attention on deliberate instruction and learning. Study groups, Critical Friends groups, peer coaching, and walk-throughs are all examples of site-based staff development designs that focus teachers and school leaders on high-quality teaching and learning. When implemented effectively, they can provide the focus schools need to implement high-quality, intellectually authentic assignments for all students. According to this study, this focus on learning will also yield improved standardized test scores, without compromising an intellectually stimulating environment.

The results of this study provide compelling evidence of the need to focus in schools on learning, and gathering evidence of that learning, to provide instruction and authentic experiences that engage both students and their teachers in the enterprise of schooling. If we are to move students to more authentic, intellectual endeavors. we must also prepare their teachers to create the learning contexts that will allow those students to succeed in school and beyond the schoolhouse walls.

 

 



Reference

Newmann, F.M.; Bryk, A.S.; & Nagaoka, J.K. (2001). Authentic intellectual work and standardized tests: Conflict or coexistence? Chicago: Consortium on Chicago School Research.

 

 

Addenda



Figure 3

http://www.learningaccount.net/managed_files/ta001_320.jpg

Figure 3 shows the ITBS (Iowa Test of Basic Skills) standardized test score gains in classrooms with high-quality assignments. It shows these scores in relation to the national average gain in scores. In both reading and mathematics, students in high-quality assignment classrooms made significant gains when compared with classmates in classrooms with low-quality assignments. They also scored better than the national average in both subjects.

Figure 4

http://www.learningaccount.net/managed_files/ta001_321.jpg

Figure 4 graphs the data from the IGAP (Illinois Goal Assessment Program) standardized tests in reading, mathematics, and writing. These data echo the data reported in Figure 3. Students in classrooms with high-quality assignments outscored their classmates on every test. The gains on this measure were seen most dramatically in mathematics.

Figure 5

http://www.learningaccount.net/managed_files/ta001_322.jpg

Figure 5 describes the one-year learning gain trends found in students with both low and high prior achievement. The results show that both sets of students benefit from the regular use of high-quality assignments. There were, however, differences in who responded to what. High prior achieving students responded better in Reading, while low prior achieving students responded better in mathematics. These data led Newmann and his colleagues to conclude that high-quality assignments benefit all students.

 

© Copyright 2007 Learning Sciences International.


All Rights Reserved.

Prediscussion Activity: Meeting the Standards

In this activity you will consider the relationship between authentic instruction and the academic standards.



  1. Using the questions provided, reflect on teaching authentically and meeting the academic standards.

    • How do you create a balance between meeting academic standards and teaching authentically?

    • What concerns did you have about teaching authentically and student achievement prior to reading the article?

    • Which concerns were alleviated?

    • Which concerns have not clearly been addressed?

    • How will you find additional information or whom would you ask for assistance?



  1. For the purpose of the online discussion, summarize your responses in the space provided.

 

 


  1. Fill in the "L" and "D" columns of your "Authentic Teaching K-L-D Chart."

  2. Return to the course and advance to the next screen in order to receive further instructions to share your summary online.

Personal Notes for Implementation:
 

 

 



 
Topic 2.1.4: What Is the Student Experience?

Balancing Real World Problems with Real World Results

By Rick Gordon, Co-Director, Critical Skills-Education By Design Program,


Antioch New England, Keene, NH 03431

"Mankind likes to think in terms of extreme opposites. It is given to formulating its beliefs in terms of Either-Ors, between which it recognizes no intermediate possibilities" (Dewey, 1938, p. 17).

How Realistic is Real? Authentic learning, real world problems, constructivist classrooms, performance assessment... Engaging students in "authentic" performance situations seems the latest wave to wash over schools. On the surface, this is a most appealing contrast to the decontextualized, rote learning typified by "traditional" education. As Brooks and Brooks (1993) proclaim, in describing the benefits of constructivist classrooms, "they free students from the dreariness of fact-driven curriculum and allow them to focus on large ideas; they place in students' hands the exhilarating power to follow trails of interests, to make connections, to reformulate ideas, and to reach unique conclusions" (p. 22). Without doubt, the possibilities are great and the language lofty when addressing this latest wave. Speaking as one who comes to this movement with long experience engaging students in real world problems, it is important to warn against the all too familiar tendency in education to be enamored with new ideas while losing sight of the grounded perspective needed to make things work in real classrooms with real kids.

The program I work with, Critical Skills-Education by Design (CS-EBD), pioneered "Learning by Real Problems" in the early 1980's. Directed to conceive educational practices that allow children to develop the knowledge and skills needed for success in school and beyond, CS-EBD originally involved only real-life problems. In six-week summer institutes, teachers were engaged in real-world problems to directly experience the power of this mode of learning. The response to this experience was consistent—participants found this among the most compelling learning experiences of their life; they felt engaged, challenged, energized, and overwhelmed. It was this last factor that proved most problematic.

Real world problems, by their nature, are messy- involving uncertainty, complexity, and nuanced judgment (Lauren Resnick in Wiggins (1993, p. 215). These characteristics tend to confront norms prevalent in most schools. Real world problems often don't mesh well with mandated curricula, textbooks, standardized tests, state standards, and the seven period day. Teachers who actually tried real world problems with their students tended to be those renegades who thrive on change and risk taking. Unfortunately, this is too small a segment of the teaching population.

A more typical response for institute participants was that while they found the summer experience invigorating, managing this in their class seemed daunting. For others, identifying and managing real life problems simply seemed too much work (where would they find resources, how do you assess student work, what will parents/administrators say....?). Finally, there was the omnipresent concern with "covering" the curriculum and assuring student exposure to the content at the heart of a teacher's subject area. For many teachers, real life problems, despite their promise, seemed incompatible with the realities of their classrooms.

Stepping back to step forward as a program, we have stepped back from this solitary focus on real world problems to consider what are the essential elements engendered by "authentic" learning. What is it about real life problems that make them powerful and engaging and how can this be recreated in environments, such as the classroom itself, that often has relatively loose ties to the "real world?" Here is what we have found:



  1. Authentic learning demands students actively solve problems. Life involves an on-going series of problems to solve, decisions to make, concepts to understand, and products to produce. Whether it's a relatively simple problem of what to eat for breakfast or a more complex one such as how to reduce pollution in your area, in life we do things that have concrete results (parenthetically, in real life very few of us do "worksheets").

  2. In authentic learning situations, people work together. There are not the artificial boundaries of what some call the "graveyard model of teaching" (everyone in rows and dead). Students move about, talk to each other, and are active in both a physical and mental sense. They access resources to help solve problems- whether it be fellow students, books, or the internet. The focus is not just on what you have stored inside your head but what you can actually do to solve a problem using the resources around you.

  3. Authentic learning situations simultaneously involves one's knowledge, skills, and attitudes. In real life situations, you use your organizational skills to manage resources to make decisions about how to solve problems using the knowledge you have to produce a result that meets your internalized sense of quality. Rather than being individual elements taught to students, knowledge, skills, and attitudes develop in the context of actual work.

  4. Authentic learning is driven by "essential knowledge" meaningful to students. Not every element of student work must be "real," but meaning for students entails seeing connections to the real world on some level. This is best ensured by tying student work to the "big" questions, what Ernest Boyer (1993) characterizes as the "human commonalities." These questions get to the heart of our culture, history, and future as they relate to the human life cycle, command of symbols, understanding of the social web, connection to science, technology and the natural world, and the interdependence of community and the individual. Likewise, attention to real life skills, such as decision making and problem solving, can link students' work to real life experience.

  5. In authentic learning environments, activities are connected. Knowledge, skills, and attitudes learned and employed in one context carry over into another. The curriculum looks less like a compilation of discrete building blocks and more like a continuous ascending spiral where each experience builds on previous ones as students increase their understandings and improve their skills.

  6. In authentic learning situations, students publicly exhibit their learning and there are often real life standards of quality. Authentic problems don't generate scores on a test. Rather, there usually is some authentic benchmark to which students are accountable. For example, if students make a proposal to the town council, the feedback comes from its reception and approval by the council. If students are making a product such as a poster, play, or mural, there are models of excellence against which the product can be compared. Exhibiting one's work publicly places student work up against these real world standards of quality.

The purpose in listing these features of authentic learning experiences is to make clear that they are achievable in regular classroom settings. While it may be true that the most authentic context may be the real world beyond the schoolyard fence, there are reasonable approximations that can be created in the classroom to enjoy the same level of engagement, meaning, and learning on a consistent basis in the classroom.

Making Learning Authentic

While real life problems may continue to be the ultimate authentic learning experience, they can be out of reach (at least initially) to many teachers and students. Both may lack the skills and attitudes to wade into the muddy waters of messy real life problems. Still, there are ways to design problems that retain many of the elements of authentic learning while easing teachers and students and schools into more real life experiences.

The framework which guides the creation of authentic learning in all settings is the experiential learning cycle (ELC). This model offers a framework to make "smaller" learning activities more authentic and to make more grandiose real life problems more focused (see Figure 1).

At the heart of the ELC are what we call challenges, or problems to solve, that are driven by desired outcomes for what we want students to know, do, and be like (knowledge, skills, and attitudes). To help make challenges accessible to teachers and students, we categorize them on three levels of generally increasing authenticity, complexity, uncertainty, and student self-direction.

Academic challenges are an entry point into authentic, problem-based learning. An academic challenge is student work structured as a problem arising directly from an area of study (see insert 1). It is pursued primarily to promote greater understanding of selected subject matter. The academic challenge is crafted by transforming existing curricular material into a problem format. Academic challenges tend to look relatively more familiar to teachers and students accustomed to traditional educational environments. They serve as a useful access point for developing capacity for actively constructing learning, working collaboratively, targeting specific outcomes, focusing on standards of quality, and grappling with essential questions.

Scenario challenges increase the authentic nature of the pursuit of the area of study by casting students in a real-life role (current, historic, or futuristic) and asking them to perform that role in the context of a scenario (reality based or fictional) (see insert 2). The scenario challenge simulates many of the elements of the real world to work with existing curricular material. Students begin to see themselves in real-life roles as they develop knowledge and skills needed for success in school and beyond.

A real life problem is an actual problem in need of a real solution by a real person or organization (see insert 3). It has the potential for actual implementation at the class, school, community, regional, national, or global levels. It involves students directly and deeply in the exploration of an area of study. Through a real-life problem, students move outside the classroom, take action on issues and have a tangible impact in their communities. These can be powerful learning experiences, but pulling off more than one or two of these a year seems beyond the resources (energy, time, and money) of most teachers.

Moreover, to succeed with real-life problems, it helps if students have experience working as a collaborative problem solving team. The skills and attitudes of collaborative problem solving are best developed through coordinated work on problems of increasing complexity and uncertainty (such as provided by academic and scenario challenges.)

Regardless of the scope of the challenge, authentic learning results from the "wholeness" of the learning experience. The ELC, articulated with both student and teacher dimensions, is the blueprint for the design of problem-based events that engage students to exhibit their learning on which they then reflect in order to connect their learning to future experiences. Preceding and following a learning experience is a housekeeping phase during which teachers and students can wrap up the previous experience and prepare for the coming learning experience.

As students work through each of a series of interconnected problem-based challenges, they are guided through the student phases of the cycle - engagement, exhibition, reflection. First, they are engaged in a problem crafted by the teacher to target specific areas of knowledge, skills, and attitudes. This challenge, as does many real-life problems, usually requires some concrete product as evidence of student learning. During the engagement phase, students and teachers spend time articulating standards, based on real world models, for the quality of the product. In the course of engagement, and in the exhibition of this product, students demonstrate their learning. After completion and exhibition of their products, the students are not "done" with their learning. Students participate in the reflection phase where they examine their work and reflect on what they have learned (reinforcing and constructing knowledge and considering their personal and interpersonal behaviors). Students then may join the teacher in assessment of their work based on their preestablished quality standards.

The teacher phases of the cycle are design, coaching, and feedback. Once the students have begun work on the problem that has been carefully designed by the teacher to put the students in a substantive problem that targets knowledge, skills and attitudes, he or she assumes the role of coach. As coach, the teacher helps students to develop their skills and knowledge, shape their strategies, and access resources. Like a coach, however, the teacher remains on the sidelines at times, allowing students to own their successes and failures. Here, the students truly are the workers and the quality of their work reflects their efforts. In the feedback phase, teachers create structures within which students can reflect on and assess their products, process, and level of understanding.

Finally, this learning experience is connected to subsequent experiences as students move into the housekeeping phase where they consider what they learned and what they need to proceed ahead. They articulate what they might do better next time, and address skills and knowledge they need to further develop as they move into other challenges. Notably, they also give consideration to the status and needs of their learning community. They address issues that arose during their work and develop strategies for future work to further improve the learning of their community.

In short, the classroom is structured so that students are given a meaningful context for interdependent work throughout the learning cycle. Purposes and processes are made explicit and students understand what they are doing, why they are doing it, and how it relates to work in school and outside. Experiences are organized to build on each other, so that like in the real world, we can learn from our successes and failures and carry these lessons to our future work. Most importantly, the work of the classroom consistently demands students authentically exhibit their knowledge, skills, and attitudes throughout the learning cycle instead of only for a scheduled performance.

Authentic learning is a laudable goal and should be promoted and pursued vigorously. Students not only should see their work in school related to the real world, but must if they are to be able to apply their learning in real life contexts. As we pursue this goal, however, our experience warns us to remain grounded in the realities of teachers' and students' school lives. Working with real life problems is a sophisticated process which demands refined skills and a tolerance for ambiguity and complexity. While only some teachers and students have an innate capacity for such undertakings, almost all teachers and students can develop such capacity. Designing to develop the understandings, skills, and beliefs to be successful with real life problems involves a commitment to authentic learning experiences of increasing sophistication. The experiential learning cycle and the combination of academic, scenario, and real life challenges provides a blueprint to bridge the vision of real world learning to the realization of authentic student results.




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