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Tools for Critique: Chapter 5
The Subject Matters: Constructing Knowledge Across the Content Areas


Chapter 5, “The Subject Matters: Constructing Knowledge Across the Content Areas,” introduces readers to the content areas of mathematics, language arts, social studies, and science, and reviews current professional and political debates concerning these subjects. The chapter also describes how the “standards movement” and current emphasis on test-based, high-stakes “accountability” have shaped teaching and learning in each of these four major academic subjects.

Chapter Headings

  • Mathematics
    • The Math Crisis
    • Traditional Mathematics: Skills-Based and Sequential
    • Progressive Mathematics: Meaningful Knowledge in Context
    • The Math Standards: The Politics of Mathematics Continues
  • English Language Arts
    • Traditional Language Arts: Mastering Skills, Rules, and Forms
    • Progressive Approaches to Language Arts: Developing Literacies
    • National Standards in the Language Arts
  • Social Studies
    • Traditional Social Studies: Facts and Figures Framed by the Dominant Culture
    • Progressive Social Studies: Critical and Multicultural Approaches
    • The National History Standards: Seeking a Middle Ground
  • Science
    • Traditional Science: Sequences of Topics, Subtopics, and Facts
    • Progressive Science: Inquiry and Investigation
    • National Science Standards: Deep, Integrated, Socially Relevant Science for All
    • Access to High-Quality Science Instruction
  • The Struggle for the Subject Matter

Generative Questions and Activities

    The Subject Matters: Making School Knowledge Meaningful

  1. As background for this chapter and for the questions that follow, take a look at a few “curriculum guides” used by different grade levels, for different subjects, in different schools.  When you can, interview teachers or administrators to get a sense of whether and how these guides reflect what these educators think is their most important work.  Look for evidence in the guides—particular items and language or terms used to express them—showing whether sociocultural perspectives are thought to be important in the school or district.  To what extent is the curricular content in these guides explicitly connected to contexts and activities that are relevant to the students’ and their families’ backgrounds, histories, and standings in their communities?


  2. The authors discuss how the mathematics curriculum “diverges for different students” beginning in middle school, with more successful students promoted to advanced math classes and less successful students relegated to “dead-end remedial courses.”  Briefly sketch the history of your own mathematics coursework.  Would you identify yourself as highly competent, not very competent, or somewhere in between?  Did you take calculus in high school?  Why or why not?  What was the highest level math course you took?  How do you make sense of your own successes and/or struggles in math?  If you did take “advanced” math courses, what was the racial and gender composition of those classes?  How do you explain that?  Once you graduated from high school, was a college major in mathematics, the sciences, or engineering a realistic choice for you (assuming that you at some point had an interest in these career areas)?  In your estimation, does it take special talents to acquire skill in mathematics?  Recount instances when someone skilled in mathematics lavished encouragement on you to study math.  Describe the circumstances of your meeting—perhaps a guest speaker in a mathematics class, or a woman engineer, mathematician, or scientist.  Did you ever have an African American mathematics teacher?  Share and analyze these questions and answers, along with others that may arise.

  3. Is the discussion of progressive views of mathematics learning in this chapter consistent with your prior understanding of math learning?  Or have you always assumed that traditional approaches were the “only” way?  Do you think your math learning—both knowledge and appreciation of mathematics—might have been different if you had had progressive mathematics teachers in elementary and high school?  On the other hand, not all progressive approaches in mathematics education are necessarily carried out competently.  Describe your best and worst math class experiences—whether traditionally or progressively taught.

  4. First-year teacher Zeba Palomino describes her “critical” approach to teaching high school mathematics.  Many of her ideas reflect the constructivist and student-centered philosophy posited in Everybody Counts.  Discuss the degree to which Palomino’s account applies to younger students in elementary schoolWhich aspects of her approach would apply to teaching elementary school students?  What modifications might need to be made?

  5. As the authors note, the mathematics standards originally proposed by the NCTM in 1989 suggested that mathematical ideas should “be embedded in problems that are familiar and meaningful to students.”  In your opinion, why might this be important?  Is this how math is taught at your school?  How might you connect mathematical ideas to contexts and problems with which your students are familiar—even if you are not a mathematics instructor?  Think back to your own experiences learning math.  How, if at all, did your teachers embed mathematical ideas within familiar and meaningful problems?

  6. The authors mention Eric Gustein’s approach to connecting mathematics instruction with social justice goals, suggesting that it is one model for making math more accessible to African Americans, Latinos, girls, and other groups that have been underrepresented in mathematics.  Based on what you know of traditional and contemporary learning theories (see Chapter 6), what types of pedagogical approaches do you think Gustein would advocate?  Why do you think these approaches would be effective for African Americans, Latinos, and girls from all racial groups?

  7. Using your answer to number 6 as a guide, design a math lesson plan that employs a culturally relevant and gender-sensitive pedagogical approach for the grade you (would like to) teach.  How would you strategically go about teaching such a lesson, given the fact that current mathematical standards may focus on rote computation?  (Secondary teachers, do not “excuse” yourself from this question with the claim that you are not a math teacher.  Reflect critically on your own math classes and discuss instances of cultural and gender relevance and sensitivity.  Also, discuss how the teacher might have made a particular lesson more relevant and sensitive.)

  8. Has your state adopted the Common Core State Standards (CCSS) for mathematics? If so, analyze the math CCSS for your grade level. What do you think of them? Do they align more with traditional or progressive approaches? How so? How might you use the lesson you developed in question 7 to teach one of the CCSS?

    English Language Arts

  9. The authors contrast traditionalists’ narrow views of reading and writing (as discrete sets of skills) with progressives’ more expanded notions of literacy (as a meaningful cultural practice).  Which of these conceptions of literacy most closely matches your own views about what reading and writing are and how they should be taught?  Which most closely matches the way that you learned to read and write when you were in school?

  10. New media literacies, such as texting, blogging, and tweeting, are central practices in many young people’s lives. Have you incorporated – or observed another teacher incorporate – any of these mediums in the classroom? If not, how might you go about capitalizing on these forms of literacy to further students’ academic content and literacy learning?
  11. The authors discuss the importance of incorporating multicultural literature as a means of making the language arts curriculum more inclusive.  In your view, why is this important?  What implications are there with respect to student identity and motivation?  What implications are there with respect to improving inter-racial communication and understanding?  Has reading fiction broadened your cultural horizons? If so, how? List those novels that have opened your eyes and heart to peoples of different cultures, backgrounds, ethnicities, and so on.  In particular, list the novels you have read by African American, Latino, Asian, or non-American, nonwhite authors.  Select one or more to comment on specifically, and discuss your overall experience reading (or not reading) these works.  Were any of these works assigned in school?  If not, who, if anybody, suggested that you read them?

  12. The “Balanced Literacy Approach” described in this chapter refers to a literacy program that emphasizes teaching phonics (phonemic awareness) and other literacy skills within meaningful contexts (e.g., while reading quality children’s literature or engaging in purposeful activities).  One reason to implement such an approach is that a wealth of research demonstrates that teaching skills in a meaningful context is more effective than teaching them in isolation. Based on your own experience as a student and/or teacher, do you believe that such a “balanced” approach is more effective than emphasizing the mastery of isolated skills before engaging students with stories, themes, and more complex literacy skills?  Thinking back on your own teaching and/or learning, discuss examples of successes and/or difficulties that have resulted from using “balanced” and skills-based approaches to language arts instruction.

  13. NCLB’s Reading First program stipulates that federal funds can be spent only on programs and practices that have been proven effective with “scientifically based research.”  What does this policy suggest about programs and practices that teachers know to be effective based on their own (and their colleagues’) experiences in the classroom?  Since this valuable knowledge cannot be experimentally controlled (and therefore is often dismissed as not “scientifically based”), many teachers find ways to infuse their own knowledge and “best practices” into official and approved programs.  Talk to experienced teachers and observe in classrooms to find evidence that experienced teachers can find ways to infuse their professional expertise and social justice commitments into mandated programs. How do you imagine you might you go about modifying and/or supplementing mandated curricula? 

  14. One of the biggest complaints about “scientifically based” curricula is that they tend to “script” the teacher’s role.  Visit a classroom in which the teacher uses a scripted curriculum.  Observe the scripted lessons carefully, taking notes on the practices and interactions that you observe.  Next, visit a classroom in which the teacher does not use a scripted curriculum.  Observe the “unscripted” lessons carefully and take notes.  Afterwards, write a brief summary describing the differences that you noticed between the two classes.  What stood out to you?  What appear to be some of the advantages and disadvantages of each class?  How might you apply what you’ve learned to your own teaching?

  15. Under NCLB, most school districts with low-income students and students of color must choose from a handful of approved reading programs and then monitor whether teachers are fully implementing the adopted program.  Meanwhile, districts serving white students and wealthier students tend to have much more discretion to select the curricula and instruction that they deem most appropriate for their students.  What beliefs and attitudes underlie this tendency to give teachers of low-income students and students of color less flexibility to respond to individual needs and local conditions, while districts with white students and wealthier students have greater independence and flexibility?  Quickly brainstorm a fairly long list of possible reasons; then examine each for biases and inaccurate assumptions.

  16. As mentioned in question 14, there is an ever-growing trend to adopt “scripted” language arts programs, especially in “underperforming” districts that tend to serve low-income students of color and English learners.  Such programs tend not to support the balanced literacy model, favoring instead an approach that emphasizes skills over meaning.  What are the implications of this trend for teachers who must follow such top-down mandates and yet still want to expose their students to a rich and meaningful curriculum?

  17. First-grade teacher Benji Chang describes how he incorporated multicultural literature as a way of supplementing his school district’s scripted language arts curriculum.  How might you use similar resources to supplement the scripted language arts curriculum in your school/district?  What texts could you incorporate in order to emphasize meaning over isolated skill development?  Are there other ways to creatively resist the top-down imposition of scripted curricula?  Brainstorm a list of strategies, techniques, and resources that you might draw on in order to ensure that your students receive the instruction that they need and deserve.

  18. Consider the extent to which decisions about language arts curricula are influenced by political views and agendas rather than by an informed understanding of how children actually learn.  What do political and economic interests stand to gain when districts mandate certain curricular models and/or particular textbooks?  Who benefits, for example, when multi-million dollar contracts are signed between school districts and publishing companies?  To what extent do such decisions take into account students’ needs or research-based theories about student learning? 

  19. The authors continue to emphasize the political influences that determine what is taught in school.  Interview one or more teachers and ask how their curricular decisions are influenced by the political climate in their school district, community, or state.  Probe for specific short-term effects that result from recent legislation or school-board policy, as well as long-range influences that teachers notice taking place over many years.  Be sure to ask your interviewee to reflect on trends or events that he or she sees as positive.  Some teachers develop a perception that they are not affected by circumstances outside their schools or classrooms.  With this in mind, be sure to prepare for the interview by having specific knowledge of the political climate and recent events in the teachers’ communities or states. This knowledge will help you think of follow-up questions and prompt more complete answers. Be sure to ask about the Common Core State Standards and how your interviewee views their effects.

    Social Studies

  20. Judy Smith presents social studies to her high school students in ways that encourage them to make critical connections to their own experiences and practices.  What do you think about this approach to teaching social studies?  Is it appropriate and/or effective to ask students to reflect critically on how social practices, including their own, relate to broader social injustices?  What are the potential benefits of this approach?

  21. Conservative educators express concerns that critical multicultural approaches in school, especially as they relate to United States history, cause cultural divisiveness, pit races and ethnicities against each other, and deny students the factual building blocks necessary to ensure national unity.  In your opinion, how legitimate are these concerns?  Is it important and/or necessary to represent history from a critical perspective?  If so, is it possible to do so without undermining national unity?  Have you ever experienced such multicultural pedagogy?  If so, how did it contribute to your understanding of your own role as a citizen or resident of this country? 

  22. The authors note that one progressive approach to teaching social studies is to “challenge students to view history from the perspective of those at the bottom of the social ladder.”  Can you think of a time when you were encouraged to look at an historical event from the perspective of a non-dominant group?  Can you think of a time when you encouraged students to do so?  Brainstorm examples of how changing one’s perspective would afford a deeper understanding of a particular historical event or era.  Examine a current social studies textbook to determine whose perspectives are privileged and whose are marginalized or ignored.  Discuss why this is important.

  23. Review the history of traditionally marginalized peoples in your locale: Native Americans, African Americans, Asians, Latinos, and other people of color, immigrants, and/or religious groups.  How and how extensively are these histories represented to local schoolchildren?  What distinctions are made among the experiences of these groups according to their ethnicity and/or race?  What are the lasting or continuing effects of these histories on today’s populations?  Is there evidence that not all non-dominant groups experience similar social or educational effects due to their inclusion or omission—representation or misrepresentation—in texts and schools?

  24. The authors cite the social studies standards’ distinction between “historical thinking skills” and “historical understandings,” but they do not develop these with examples.  Select a contemporary “event” that is likely to have historical significance, and suggest how students in K-12 schools might find the relevance of this event by focusing both their historical thinking skills and their historical understandings on the event.

  25. The authors suggest that “teachers who want to press their students to think deeply and ask hard questions about the rhetoric and realities of social life” may have to find resources outside of school textbooks and state standards.  Why do you suppose this might be necessary?  What is missing from official standards and textbooks?  What other resources could you draw on in order to develop a more comprehensive and critical social studies curriculum?

  26. Refer to Christine Sleeter’s prompts from Un-standardizing the Curriculum, shown in Focal Point 5.2 to analyze a curricular document (e.g., textbook excerpt, suggested film, etc.), using the “questions to guide analysis.” Then, use the “curriculum planning guide” to develop a portion of a social studies unit, perhaps covering the same topic covered in the source you analyzed.


  27. Review your K-12 science experiences.  Were they largely based on project and laboratory experiences, or were they largely lecture/demonstration/ reading/memorizing?  Describe a course that gave you important scientific knowledge, interest, and/or background.  Do you recall any particular passionate science, social, or political interests of the teacher of this course?  How were these interests relevant or irrelevant to your own interests?  What concepts or ideas do you remember most clearly from this course?  Why?

  28. Often, middle and high schools use mathematics background or achievement as a “filter” to screen students they expect to be low achievers out of higher-level science classes.  Were your science opportunities influenced (either positively or negatively) by your proficiency in mathematics?  Explain/analyze the effects of linking math proficiency to science on your own course-taking and future science interest.  How could this linkage have social-justice implications?

  29. Given the current emphasis on “back-to-basics” literacy and math instruction in elementary and middle schools, there is little time for other academic subjects such as science.  How might you go about integrating content areas through thematic units?  What connections do you see between concepts, themes, and standards across language arts, math, social studies, and science?

  30. The authors identify the following four “new” conceptions of science content contained within the science standards, calling them “provocative and exciting”:
    * The content of science cannot be placed outside of science’s unifying concepts and processes.
    * Participation in inquiry is scientific content, not just process.
    * Scientific knowledge is not distinct from societal challenges.
    * The history of science is science content that underscores science as a human and social enterprise.
    These standards are far from what most people are used to thinking of as science content.  Select one of these standards and offer arguments that might be posed by someone who holds a traditional view of curriculum.  How would you respond to these arguments?

  31. Consider Angela Calabrese Barton’s “science and social justice” work discussed in Focal Point 5.3. Think about your own school and community. What are some ways you could “help children use science to make their lives better”? What issues do you anticipate students in your community might want to address? How might you use science – and rigorous scientific knowledge – to affect change? In what other ways can science be used to achieve social justice goals?
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