Paradigm shifts in current national standards, efforts to broaden participation, innovations in instructional technologies, and the increasing availability of digital and open education resources have transformed the landscape of STEM instructional materials. These changes call for new kinds of curricula, and while many DRK-12 projects engage practitioners as critical partners in developing these new materials, others are researching approaches and resources that support them in choosing, adapting, or developing their own.
In this Spotlight...
- Coherence Across the Mathematics Curriculum | Community Voice Blog by Corey Drake, Jill Newton, Amy Olson, & Marcy Wood
- Positioning Students’ Perspectives at the Center in Developing and Teaching with Science Curriculum Materials | Community Voice Blog by Brian Reiser
- Featured Projects
- Co-Developing a Curriculum Coherence Toolkit with Teachers (PIs: Corey Drake, Jill Newton, Amy Olson, Marcy Wood)
- CAREER: The Designing Mathematically Captivating Lesson Experiences (MCLE) Project (PI: Leslie Dietiker)
- CAREER: Expanding Latinxs' Opportunities to Develop Complex Thinking in Secondary Science Classrooms through a Research-Practice Partnership (PI: Hosun Kang)
- CAREER: Supporting Elementary Science Teaching and Learning by Integrating Uncertainty into Classroom Science Investigations (PI: Eve Manz)
Coherence Across the Mathematics Curriculum
Corey Drake (Professor & Director of Teacher Preparation Programs, Michigan State University), Jill Newton (Associate Professor of Mathematics Education, Purdue University), Amy Olson (Associate Professor, Duquesne University), Marcy Wood (Associate Professor of Mathematics Education & Department Head for Teaching, Learning, and Sociocultural Studies, University of Arizona)
One important aspect of any mathematics curriculum is its coherence, or connections, across lessons. This coherence links lessons and activities so that mathematical ideas, representations, practices, skills, instructional strategies, and ways of thinking build upon each other to help students construct mathematical meaning. When teachers rely predominantly on published curriculum materials, curricular coherence is implied or made explicit by the curriculum authors. However, many of today's teachers are no longer given a foundational textbook or single set of resources. Further, teachers have unprecedented access via the internet and social media to lessons and activities produced by many different curriculum developers (including other teachers). As a result, the important task of building curricular coherence becomes the responsibility of the classroom teacher. And yet, we know very little about how teachers think about curricular coherence or how their decisions about lessons and activities reflect the coherent mathematical story they hope students will learn in their classrooms.
When writing our grant proposal, we realized that curricular coherence could mean many different things. For example, the National Council of Teachers of Mathematics (NCTM, 2016) described a coherent curriculum as one in which “connections are made from one year to the next, from one idea to another, from one representation to another…There is coherence pedagogically, logically, conceptually, in terms of learning science and with the real world” (p. 1). This suggested that coherence meant connections not only across mathematical topics, but also across mathematical practices, representations, and strategies.
Coherence also seems to be tightly tied to Mathematical Knowledge for Teaching (MKT; Ball, Thames, & Phelps, 2008); in particular, the Horizon Content Knowledge domain (subject matter knowledge) described as “an awareness of how mathematical topics are related over the span of mathematics included in the curriculum” (p. 403) and the Knowledge of Content and Curriculum domain (pedagogical content knowledge) that highlights horizontal and vertical curriculum knowledge (Shulman, 1986). Horizontal knowledge relates knowledge of the curriculum being taught to the curriculum that students are learning in other classes (in other subject areas) and vertical knowledge includes “familiarity with the topics and issues that have been and will be taught in the same subject area during the preceding and later years in school, and the materials that embody them” (p. 10).
Finally, the Danielson Framework for Teaching Evaluation Instrument (Danielson Group, 2013) describes coherence in a couple of different ways. It is seen as alignment of instructional activities and assessment opportunities to learning goals. Thus, teachers demonstrate coherence through meaningful sequencing of lesson and unit and through alignment to academic standards and goals. Coherence is also developed coherence intra- and interdisciplinary content relationships, with special attention paid to awareness of potential student misconceptions and pedagogy that will address those misconceptions.
As a result of this investigation, we developed a preliminary list of aspects of curriculum which we are considering as we explore “curricular coherence” with teachers: (1) mathematical content, including horizontal and vertical coherence among mathematical topics, and between mathematics and other disciplines and real world contexts; (2) mathematical representations; (3) mathematical processes, including what it means to do mathematics; (4) pedagogical strategies, including instructional routines and philosophies; and (5) assessment, including the typical types of formative and summative assessments and the role of testing.
Positioning Students’ Perspectives at the Center in Developing and Teaching with Science Curriculum Materials
Brian Reiser (Professor of Learning Sciences, Northwestern University)
These are exciting times for science education. Decades of research has led to the innovations reflected in the National Research Council’s (2012) Framework for K-12 Science and the Next Generation Science Standards (NGSS 2013). These documents call for students to engage in science and engineering practices to build and use science ideas, rather than solely learning about the science others have done (Schwarz, Passmore, & Reiser, 2017). These reforms are taking hold. To date, 44 states (71% of U.S. students) have adopted NGSS or standards guided by the Framework.
But what does it mean to support students in figuring out the science through science and engineering practices? We view one shift as central —teaching approaches and instructional materials need to support coherence from the students’ perspective. If students are engaged in science as a practice then their science work should be meaningful to them. A classroom visitor should be able to walk over to a group of students and ask them What are you working on? and Why? Students should see how their science work addresses questions or problems their class has chosen to pursue, rather than answering “because that’s what it says to do on the worksheet” or “our teacher said we would need this for high school.”
However, most curriculum materials are organized with coherence from a disciplinary or expert perspective. The reason the class moves from one topic to another may be apparent to curriculum designers and teachers, yet this logic may not be apparent, convincing, or compelling for students. The teacher knows how learning about cells can address important biological questions; but for students, they are learning about cells because that’s the topic of the chapter in their textbook.
In contrast, teachers can present phenomena and problems designed to raise questions for students, work to cultivate those questions, and help the class figure out how to investigate them, building important science ideas in the process. This is a science storyline, where coherence is from the students’ perspective. Questions and problems motivate students’ science work. At each step, students make progress on their questions, adding to a developing explanation or designed solution. A storyline provides a coherent path toward building science ideas, piece by piece, anchored in students’ own questions.
Consider a middle school unit on sound developed to be coherent from a disciplinary perspective. It begins by introducing sound as a wave that travels through a medium, and then poses investigations to explore sound properties such as frequency and amplitude. The teacher could put a ringing timer in a bell jar, remove the air, and students discover that they can’t hear the ringing without the air. The experiment is clearly motivated for someone who already knows how sound works. But consider the lesson from the students’ perspective. Why are we putting a ringing object inside a jar with no air? Nothing in the prior conversation motivated students to explain this phenomenon. The teacher is essentially saying “trust me, this will be helpful, you’ll see why later.”
Suppose instead we start with an anchoring phenomenon in which students observe loud sounds making a window rattle (OpenSciEd 2019). While the result is not surprising to most students, they struggle to explain how this could work. The teacher pushes on students’ initial ideas — What is sound made of that could be strong enough to make the window rattle? How is it traveling? Her questions spark more questions from students. The teacher leads a question building activity, and students develop questions about what creates sound, how it travels, and what happens when sound reaches something that can detect it. Through a series of investigations students begin to see sound as occurring when vibrating matter pushes air, and wonder what would happen if there were no air when the sound is created. Then the teacher suggests she has a way to remove the air from a container, leading to the experiment with a ringing timer in a vacuum.
Teams of learning scientists and classroom teachers are developing, piloting, and investigating storylines like these in classrooms. Storylines have been successful in developing student questions that lead them to figure out the target important science ideas, where students feel like their learning is addressing their own questions. Studies are now underway to explore student learning and agency storyline curriculum contexts, and the teaching strategies that support this approach to sensemaking (e.g., Penuel & Reiser, 2018; Severance et al., 2016; Zivic et al., 2018).
Find out more about storyline materials, and download free storyline curriculum units:
- NextGen Science Storylines: (a) A collection of storyline curriculum units for elementary, middle school, and high school biology and chemistry; and (b) and storyline tools for curriculum developers and teachers
- Inquiry Hub Biology: A High School biology curriculum developed using a storyline approach
- OpenSciEd: research-based storyline curriculum materials for middle school
Co-Developing a Curriculum Coherence Toolkit with Teachers (C3T2) (NSF #s 1907650, 1907808, 1907831, 1908165)
PIs: Corey Drake, Jill Newton, Amy Olson, Marcy Wood
STEM Domain: Mathematics
Description: Many teachers today are responsible for selecting and modifying curriculum materials. Yet, we know very little about how teachers think about curricular coherence or how their decisions about curriculum lead to coherence for students. This project seeks to understand how teachers in Grades 3-5 make decisions about their mathematics curriculum.
Practitioners' Role in Curriculum Decisions and/or Design: Our project has two phases. Phase One is designed to examine educators’ curriculum selection and adaptation. Teacher education programs prepare novice teachers to adapt an existing curriculum to support their specific students. However, today’s teachers may be asked to source their curriculum from both traditional text and online sources. They may not be fully prepared to build bridges across different resources while still adapting their planning to support specific students. In this phase, we will be surveying teachers to understand the range of curriculum contexts in which teachers are working and the kinds of decisions teachers make when they select and adapt curricular resources. In addition, the preliminary survey data seeks to explore the strategies and skills teachers bring to supporting curricular coherence.
In Phase Two, we will use our survey findings to identify case study sites where we will seek to understand teachers’ curricular approaches in greater depth and then co-construct tools for supporting coherence and responsiveness in teachers’ curriculum use. In particular, we will select cases to achieve a range in both curricular autonomy (i.e., agency to select and adapt resources) and curriculum complexity, including the number and types of available resources.
Strategies to Ensure Quality and Coherence: This is the central question of our project. In Phase Two of the project, we will be working closely with Grades 3-5 teachers in a range of curriculum contexts to co-develop “toolkits” of conceptual and practice-based tools for selecting and using curriculum resources in coherent and responsive ways. These toolkits will focus on connections across topics, activities, lessons, units, and grades and will be intended to help teachers build a curriculum storyline for their students. The toolkits will be iteratively developed, piloted, and refined as part of the Phase Two work.
CAREER: The Designing Mathematically Captivating Lesson Experiences (MCLE) Project (NSF #1652513)
PI: Leslie Dietiker
STEM Domain: Mathematics
Description: This study explores how secondary mathematics teachers can design lessons that spur student curiosity, captivate students with complex mathematical content, and compel students to engage and persevere. MCLEs were designed using mathematical story framework where the mathematical concept unfolds in different plots and captures students’ aesthetic experiences along these plots.
Practitioners' Role in Curriculum Decisions and/or Design: Using content selected from the teachers’ existing courses, the teacher and researcher design team collaborates to identify potential aesthetic opportunities for students (e.g., what the property of logarithms can surprise students?). To design a mathematical story, they build a sequence of mathematical events (activities, such as tasks, discussions, presentations) so that the way in which the content emerges and develops across the sequence can enable particular desirable aesthetic student reactions (e.g., surprise, wonder, suspense, and conflict). The team uses the sequence of mathematical events to create or modify student-facing lesson materials that are then used in the classroom to facilitate learning and provide opportunities to produce student aesthetic reactions. Finally, we analyze surveys in which students describe their experiences throughout the lesson to inform later iterations of the mathematical stories. This cyclic design-based research approach to designing and testing lessons as mathematical stories will inform the broader educational community on how teachers can be supported to design and teach lessons that captivate their students with mathematical content.
Strategies to Ensure Quality and Coherence: The project will generate principles for lesson design usable by teachers in other settings and exemplar lessons that can be shared. The framework, the mathematical story framework, utilized in these exemplar lessons foregrounds both the coherence (does the story make sense?) and aesthetic (does it stimulate anticipation for what is to come, and if so, how?) dimensions of mathematics lessons. We also will report on teachers’ insights for MCLEs which did not turn out as expected and what adjustments were made to make the lesson more captivating.
Theoretical Framework: Similar to a literary story, a mathematical story is the ordered sequence of mathematical events (such as tasks or discussions) experienced by the reader (in the case of a text) or the students (in the case of an enacted lesson) connecting the beginning with its end (Dietiker, 2013, 2015). With this reframing of curriculum, the mathematical characters are interpreted as the mathematical objects brought into existence (objectified) through reference in the story, such as a number. Mathematical action describes the work of an actor (such as a student or teacher) in changing the mathematical objects of study, such as adding two numbers. Mathematical characters and actions are brought into being in a constructed “space” such as symbols on a piece of paper or a coordinate plane, referred to as the mathematical setting.
In addition to these story elements, an important aspect of a mathematical story is its mathematical plot; that is, the way it captivates and holds the interest of its audience. When a mathematical story hints of a future revelation, it may spur the formulation and pursuit of questions (“How many points do I need to plot the parabola?”) similar to how a reader of a literary story might wonder how the story will progress (i.e., “Will Romeo and Juliet live happily ever after?”). Thus, the mathematical plot describes the dynamically changing tension between what is already known and desired to be known by the participants as the story progresses (Dietiker, 2015). It enables the description of how a mathematical sequence can generate suspense (by setting up anticipation for a result) and surprise (by revealing a different result than the one anticipated).
The metaphor story brings with it new descriptive language for what happens along the way (i.e., action), environment (i.e., its setting), objects of focus (i.e., its characters), as well as the interrelationships between parts of the sequence (e.g., foreshadowing) that offers teachers potential conceptual resources in their curricular work (Dietiker, 2015). Framing mathematics curriculum as a story integrates both sense-making and aesthetic and is consistent with the pedagogic nature of stories. Egan (1988) argues that stories are a “powerful form” that sparks our imagination and help us “make sense of the world” (p. 2). Stories are not solely a form of narrative; stories entertain and communicate messages (e.g., the moral of a story). When stories do not make sense, readers do not gain understanding, or worse, may quit reading. Yet the aesthetic dimension of stories can compel a reader to keep reading and work at making sense of the story (Nodelman & Reimer, 2003).
Methodology: In order to understand whether lessons successfully engage students aesthetically, we turn to the students themselves. We have designed brief interviews and surveys for students to take at the end of every lesson observed in the project. The development and use of the survey has been described in more detail, which can be read here (Riling, Dietiker, Gates, 2019).
Products: Project Website | Mathematical Story Design Template | Sample Mathematical Story | Sample Teacher Storyboard | Lesson Experience Survey
CAREER: Expanding Latinxs' Opportunities to Develop Complex Thinking in Secondary Science Classrooms through a Research-Practice Partnership (NSF #1846227)
PI: Hosun Kang
STEM Domain: Integrated Science (Biology, Chemistry, Physics, Earth science)
Description: This project aims to reduce youths’ opportunity gaps in learning science in secondary science classrooms by building a sustainable research–practice partnership. We explore how deliberately coordinated activities that facilitate the collaboration between researchers and practitioners can reduce opportunity gaps at schools, promote complex thinking in youth, and build on student ideas to promote responsible citizenship.
Practitioners' Role in Curriculum Decisions and/or Design: We engage our K-12 partners in the process of: (a) co-designing curricula during professional development, (b) experiment with the curriculum with high school students in classrooms, and (c) revise the curricula based on the analysis of student participation and performance. The teacher participants are guided through this professional learning cycle repeatedly, developing their capacity to design and enact curriculum in a principled way. The ultimate goal is promoting equity and social justice through the learning of science. The project also supports teachers to address the core vision of Next Generation Science Standards, which is supporting students in making sense of the world as producers of knowledge. Therefore, the design or modification of curriculum focuses on creating inclusive, engaging and empowering science learning experiences in secondary science classrooms. Specifically, the principles that guide the design and enactment of curriculum are initially proposed by the university researchers, and iteratively revised through the collaboration between the researchers and practitioners over the five year project timeline.
Strategies to Ensure Quality and Coherence: In order to ensure the quality and coherence, we are engaging in three activities. First, we develop a shared understanding of our design principles and generate tools (e.g., checklist or rubric) that guides the design and assessment. Second, we routinely engage in a professional practice--critique curriculum--with multiple people who have diverse expertise. Finally, we collaborate with UCI scientists who have expertise in the relevant content area for each co-designed unit. The scientist reviews the curriculum and provides feedback. We revise the curriculum based on both the feedback from the scientists, teachers’ input, and students’ responses.
Theoretical Framework: Grounded in a sociocultural and situated perspective (Greeno & Gresalfi, 2008; Lave & Wenger, 1991), opportunity to learn (OTL) was conceptualized as a setting’s affordances for students to engage in science meaningfully and advance their thinking. With a sociocultural perspective, OTL are not just provided by the teachers, but rather are dynamically and interactively shaped by the features of the setting (e.g., classroom discussion, lab, etc.) and by the students themselves. When OTL are only considered from the curriculum planning perspective, the effectiveness of the curriculum cannot be guaranteed. Students’ perspectives of the educational setting, along with their prior experiences and opinions about science in school, out of school, and at home must be considered to have effective high quality learning opportunities for all students.
Methodology: We conduct qualitative analysis including observational/video analysis, analyze thematic patterns from participants' interviews. We also conduct quantitative analysis including analyzing student surveys and assessment data. We video-record classroom sessions with a focus on the teacher, video record professional development sessions, interview teachers throughout the year, and collect surveys from students about their experiences in class. To study student learning, we video-record classrooms with a focus on following specific students, conduct interviews with focus students, conduct identity surveys (“Is Science Me?”, an empirically validated questionnaire used to measure high schoolers’ science identity), and collect student work and initial and final assessments. To study the research-practice partnership, we consider video recordings of the professional development sessions, district partner interviews and meeting notes.
Products: Project Website | November 2019 Presentation
CAREER: Supporting Elementary Science Teaching and Learning by Integrating Uncertainty into Classroom Science Investigations (NSF #1749324)
PI: Eve Manz
STEM Domain: Science
Description: This project explores how to redesign the elementary science investigation to engage young students in grappling with the forms of uncertainty that drive scientific activity, for example, getting a grip on phenomena, determining what to count as evidence, and developing measures.
Practitioners' Role in Curriculum Decisions and/or Design: Our work is guided by a commitment to co-design – both to support professional learning and to ensure that designed materials will be responsive to teachers’ needs and constraints. Co-design teams of researchers, teachers, and district leaders adapt and implement investigations, examine opportunities for sense-making about uncertainty, and refine lessons and student supports. In the later stages of the work, teams will develop assessment materials and tools to support other teachers to implement designed investigations and adapt new investigations. This work is supported by a suite of tools we have developed to (1) define what we mean by productive uncertainty, (2) identify sources of uncertainty in a particular investigation, (3) consider which sources of uncertainty are likely to be most productive for students to grapple with, and (4) examine video to reflect on supports for students and teachers to grapple with uncertainty in investigations.
Strategies to Ensure Quality and Coherence: The project is located within, and supported by, a multi-year partnership with the school district. Working with the district director for K-8 curriculum, team members have supported the district’s review and adaption of NGSS-aligned curriculum units, provided ongoing support for a group of teacher-leaders who pilot and adapt materials, and co-designed a model for professional development for K-5 teachers implementing units. We have centered four tools in this work: anchoring phenomena, coherent conceptual builds, student sense-making conversations, and practices for making student thinking visible. The project’s focus on investigations will support investigation-focused curriculum adaptation and professional development that are coherent with, and further enhance, the district’s work.
Theoretical Framework: We draw from socio-cultural and emergent approaches that treat practices as constituted and adapted in communities to solve shared problems. From this point of view, if we want students to engage in practices such as argumentation, explanation, and investigation, they must experience some of the uncertainty inherent in scientific activity and participate in developing a classroom epistemic culture. Socio-cultural and situated lenses further guide our approach to working with teachers. We value the ways groups (e.g., teachers and researchers) work together using and shaping joint artifacts, where individuals might have different meanings and uses for the shared artifacts, and where surfacing different ideas, contradictions, and problems can surface new questions for the group to take up together.
Products: STEM Teaching Tools Brief on Productive Uncertainty | NGSNavigators Podcast
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Zivic, A., Reiser, B. J., Edwards, K. E., Novak, M., & McGill, T. A. W. (2018). Negotiating epistemic agency and target learning goals: Supporting coherence from the students’ perspective. In J. Kay & R. Lukin (Eds.), Rethinking learning in the digital age, 13th International Conference of the Learning Sciences (Vol. 1, pp. 25-32). London, UK: ISLS.