Early STEM – Fuel for Learning

October 6, 2015

José, a preschooler in Mrs. Hardy’s classroom, had never talked in class. He was a dual language learner (DLL), and it was already December. His teacher was participating in our SciMath-DLL professional development project where she had been learning about how to incorporate moScreen Shot 2015-10-06 at 9.41.23 AMre science, technology, engineering, and mathematics (STEM) into her classroom and how to engage DLLs in these activities. One day, she set out ramps and cars and let the kids play with them. Then she asked the children if they knew how they might make the cars go down the ramps more quickly? “Blocks!” said José, as he ran to the block center to get blocks to prop up his ramp. His classmate, Molly, looked shocked and said, ‘He talked!” This child’s teacher was amazed at how rich (although relatively simple) STEM materials provided the fodder needed to encourage José to express himself out loud.

Children are natural scientists and are curious about their world. Even infants have an innate sense of quantity that is the foundation for more complex mathematics, such as counting and geometry (e.g., Hespos et al., 2012). Young children–including my 19-month-old–love to throw or drop objects down the stairs to observe what will happen . . . over and over again. Although not fully verbalized, they are conducting trials to test out a hypothesis about gravity and the physics of movement based on prior experience!

SciMath-DLL is a professional development model that aims to embrace these natural predispositions, to help teachers find the STEM in what children are already doing, and to design their own intentional learning experiences for their children. SciMath-DLL seeks to improve the quality of early STEM teaching and learning for all children, including DLLs. This is important. Recent research that has found that how children do in math and science by the end of preschool predicts how well they will do in these subjects later–even into adolescence (Duncan et al., 2007; Watts et al., 2014; Grissmer et al, 2010)! And early math skills predict later reading skills too–even better than early reading skills predict later reading. Unfortunately, many children and especially children who live in low-resource communities or who are DLLs, start preschool behind their peers in key domains and stay behind without intervention (Barnett, 2008; Denton & West, 2002).Screen Shot 2015-10-06 at 9.41.50 AM

The challenge is that many early childhood educators do not have the confidence or background knowledge to teach STEM effectively (Greenfield et al., 2009) or to work with DLLs (Freedson, 2010). Many educators did not participate in many–or any–STEM courses in their pre-service preparation programs (Zaslow et al., 2010). Our model aims to address this issue by using key STEM concepts as focal points at in-service interactive workshops, Professional Learning Communities (PLCs), and individual Reflective Coaching Cycles (RCCs). We weave throughout all components our approach to teaching STEM to young children. For example, we encourage educators to look for the STEM in every day activities (e.g., figuring out how many orange slices are needed at snack time so every child gets one), to thoughtfully expand the language strategies they use with children (e.g., “Emmanuel said he thinks the metal ball will sink in water. Emmanuel, why do you think that?”), to incorporate literature into STEM activities (fiction and nonfiction), and to “think outside the kit” when gathering materials to explore (e.g., using found or recycled materials to explore sorting).

Screen Shot 2015-10-06 at 9.41.30 AMOne teacher who was working with us–Ms. Anabela–who had done a length measurement lesson with her kids using worksheets and different types of units, reflected on her lesson: “My first lesson was a complete disaster because I had too much going on . . . After we talked about it, and I was like duh. The objective was there; the idea was there; the whole mapping it out, though, was not.” Ms. Anabela, in a later class, asked her kids how they might measure themselves using blocks on the rug. The teacher’s and children’s ideas of what measurement could look like expanded. The students were so excited to find out who was taller, that they asked Ms. Anabela and then the assistant teacher to be measured as well. The kids found additional ways to do measurement around the classroom to solve real problems (e.g., keeping track of the height of the water in the water table).

Just as José and Ms. Anabela found concepts that fueled their interests and promoted learning across STEM and language, we hope that other children and teachers will find the joy in STEM that encourages and motivates them to push their own learning and teaching boundaries. SciMath-DLL works with teachers to reflect on their practice, build their STEM knowledge base, and enrich their teaching using an innovative approach to professional development. We view our model as collaborative, with all of us bringing our own expertise to the table in a common goal to improve STEM learning for all young children.

Screen Shot 2015-10-06 at 9.41.41 AMTo learn more about SciMath-DLL, please visit scimathdll.com, or email us! Dr. Alissa Lange, Principal Investigator (alange@nieer.org) Hebbah El-Moslimany, Project Coordinator (he-lmoslimany@nieer.org).

Work presented here is made possible by grants from the National Science Foundation (DRL-1019576 & DRL-1417040). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

–Alissa A. Lange, Assistant Research Professor, NIEER


Lessons learned from Vanderbilt’s study of Tennessee Pre-K

October 2, 2015

Newly released findings from Vanderbilt’s rigorous study of Tennessee’s state-funded pre-K program are a needed tonic for overly optimistic views. No study stands alone, but in the context of the larger literature the Tennessee study is a clear warning against complacency, wishful thinking, and easy promises. Much hard work is required if high quality preschool programs are to be the norm rather than the exception, and substantive long-term gains will not be produced if programs are not overwhelmingly good to excellent. However, the Vanderbilt study also leaves researchers with a number of puzzles and a similar warning that researchers must not become complacent and have some hard work ahead.

Let’s review the study’s findings regarding child outcomes. Moderate advantages in literacy and math achievement were found for the pre-K group at the end of the pre-K year and on teacher ratings of behavior at the beginning of kindergarten. However, by the end of kindergarten these were no longer evident and on one measure the no-pre-K group had already surpassed those who had attended pre-K. The pre-K children were less likely to have been retained in kindergarten (4% v. 6%) but were much more likely to receive special education services in kindergarten than the no-pre-K group (12% v. 6%). The pre-K group’s advantage in grade repetition did not continue, but it did continue to have a higher rate of special education services (14% v. 9%) in first grade.

By the end of second grade, the no-pre-K group was significantly ahead of the pre-K group in literacy and math achievement. The most recent report shows essentially the same results, though fewer are statistically significant. Teacher ratings of behavior essentially show no differences between groups in grades 2 and 3. Oddly, special education is not even mentioned in the third grade report. This is puzzling since prior reports emphasized that it would be important to determine whether the higher rate of special education services for the pre-K group persisted. It is also odd that no results are reported for grade retention.

If we are to really understand the Tennessee results, we need to know more than simply what the outcomes were. We need information on the quality of the pre-K program, subsequent educational experiences, and the study itself. It has been widely noted that Tennessee’s program met 9 of 10 benchmarks for quality standards in our annual State of Preschool report, but this should not be taken as evidence that Tennessee had a high quality program. Anyone who has read the State of Preschool knows better. It (p.10) specifies that the benchmarks “are not, in themselves, guarantees of quality. Arguably some of them are quite low (e.g., hours of professional development), even though many states do not meet them. Moreover, they are primarily indicators of the resources available to programs, not whether these resources are used well. In addition to high standards, effective pre-K programs require adequate funding and the continuous improvement of strong practices.

The State of Preschool reported that Tennessee’s state funding was nearly $2300 per child short of the per child amount needed to implement the benchmarks. More importantly, the Vanderbilt researchers found that only 15% of the classrooms rated good or better on the ECERS-R. They also found that only 9% of time was spent in small groups; the vast majority was spent in transitions, meals, and whole group. This contrasts sharply with the high quality and focus on intentional teaching in small groups and one-on-one for programs found to have long-term gains (Camilli et al and Barnett 2011). The Tennessee program was evaluated just after a major expansion, and it is possible that quality was lowered as a result.

Less seems to be known about subsequent educational experiences. Tennessee is among the lowest ranking states for K-12 expenditures (cite Quality Counts), which is suggestive but far from definitive regarding experiences in K-3. We can speculate that kindergarten and first grade catch up those who don’t go to pre-K, perhaps at the expense of those who did, and to fail to build on early advantages. However, these are hypotheses that need rigorous investigation. Vanderbilt did find that the pre-K group was more likely to receive special education. Perhaps this lowered expectations for achievement and the level of the instruction for enough of the pre-K group to tilt results in favor of the no-pre-K group. Such an iatrogenic effect of pre-K would be unprecedented, but it is not impossible. There are, however, other potential explanations.

Much has been made of this study being a randomized trial, but that point is not as important as might be thought. One reason is that across the whole literature, randomized trials do not yield findings that are particularly different from strong quasi-experimental studies. The Head Start National Impact Study and rigorous evaluations of Head Start nationally using ECLS-K yield nearly identical estimates of impacts in the first years of school. Another reason is that the new Vanderbilt study has more in common with rigorous quasi-experimental studies than “gold standard” randomized trials. Two waves were randomly assigned. In the first wave, just 46% of families assigned to pre-K and 32% assigned to the control group agreed to be in the study. In the second wave, the researchers were able to increase these figures to 74% and 68%, respectively. These low rates of participation that differ between pre-K and no-pre-K groups raise the same selection bias threat faced by quasi-experimental studies. And, uncorrected selection bias is the simplest explanation for both the higher special education rate for the pre-K group and the very small later achievement advantage of the no-pre-K group. I don’t think the bias could be nearly strong enough to have overturned large persistent gains for the pre-K group.

Even a “perfect” randomized trial has weaknesses. Compensatory rivalry has long been recognized as a threat to the validity of randomized trials. In Tennessee one group got pre-K; the other sought it but was refused. It appears that some went away angry. Families who agreed to stay in the study could have worked very hard to help their children catch up and eventually surpass their peers who had the advantage of pre-K. Alternatively, families who received the advantage of pre-K could have relaxed their efforts to support their children’s learning. Similar behavior has been suggested by other studies, including a preschool randomized trial I conducted years ago for children with language delays. Such behaviors also could occur even without a randomized trial, but it seems less likely.

Randomized trials of individual children also create artificial situations for subsequent schooling. If only some eligible children receive the program, do kindergarten teachers spend more time to help those who did not attend catch and “neglect” those who had preschool? Would kindergarten teachers change their practices to build on pre-K if the vast majority of their children had attended pre-K and not just some; perhaps they would only change with support and professional development?

Clearly, the Vanderbilt study has given the early childhood field much to think about. I am reminded of Don Campbell’s admonition not to evaluate a program until it is proud. However, programs may also be in the habit of becoming proud a bit too easily. We have a great deal of hard work in front of us to produce more programs that might be expected to produce long-term results and are therefore worth evaluating. Researchers also would do well to design studies that would illuminate the features of subsequent education that best build upon gains from preschool.

What we should not do is despair of progress. The media tend to focus on just the latest study, especially if it seems to give bad news. They present a distorted view of the world. Early childhood has a large evidence base that is on balance more positive than negative. There is a consensus that programs can be effective and that high quality is a key to success. Research does help us move forward. Head Start responded to the National Impact study with reforms that produced major improvements. Some states and cities have developed even stronger programs. Tennessee can learn much from those that could turn its program around. If it integrates change with evaluation in a continuous improvement system, Tennessee’s program could in turn become a model for others over the next 5 to 10 years.

–Steve Barnett, Director, NIEER

Buried treasure: Discovering gold in the NIEER State of Preschool Yearbook

September 9, 2015

Similar to birds migrating north every year, a wealth of information on early education flies annually into the National Institute for Early Education Research (NIEER), as specialists from state education agencies provide data for the Annual State of Preschool Yearbook.

Entering its 13th year, the Yearbook reports valuable information on access to, quality of, and resources for state pre-K programs, allowing administrators and policymakers to keep pace with current developments and trends over time. The Yearbook has served as a useful, perhaps indispensable, resource as state-supported pre-K has expanded over the decade, rightfully cited as the “go to” resource on state policies and practices. Still, a wealth of information within the Yearbook remains untapped.

While the Yearbook may not rival To Kill a Mockingbird for popularity or reading enjoyment, anyone who has taken time to explore the annual report understands the abundance of practical information contained within its pages. From the Executive Summary highlighting major developments and trends, to individual state profiles with rankings, readers soon realize that the Yearbook, now published online, has “everything you wanted to know about pre-K but didn’t know to ask.”

The most informative section of the Yearbook is, perhaps, the most underutilized. Appendix A contains more than 60 pages of topical state information organized for at-a-glance review and comparison, supplemented by 27 pages of detailed state program notes, a veritable goldmine. For example, have you ever wondered:

  • How many English language learners are enrolled in state-funded pre-K? (Only 19 of 53 programs in 40 states and DC are able to provide an accurate count)
  • How many children are served in programs operating under the auspices of public schools versus private organizations?


Enrollment By Auspice (1)

  • Which states require pre-K programs to operate a full school day throughout the school year? (15 states and DC)?
  • What criteria do states use to determine eligibility, other than income?
  • Is a sliding fee scale based on income permitted? (13 states have some provision)
  • Which state programs require lead teachers to have a BA with specialization?


Minimum Lead Teacher Degree Requirement

  • Can faith-based programs receive funding for state pre-K? (17 programs directly, 35 programs indirectly; however, they may stipulate that religious content is not permitted)


Faith-Based Funding Eligibility (1)

  • What instruments do states use to monitor program quality?
  • Which states mandate an evaluation of the pre-K program? (21 of 40 states; some states operating multiple programs do not require evaluations for all programs)

States Requiring Formal Program EvaluationThese are but a few examples of data readily available to those wanting to explore policies and practices related to pre-K. While not every question imaginable can be answered using the Yearbook, it remains the best single compendium resource available with the click of a mouse. All you need to do is dig a little to satisfy your pre-K curiosity and discover gold.

–Jim Squires, NIEER Research Fellow



Common Core and DAP: Seeking clarity

April 20, 2015

April 20, 2015

Kyle Snow, Ph.D, Director, Center for Applied Research, National Association for the Education of Young Children, discusses Common Core State Standards and Developmentally Appropriate Practice.

The numerous, and diverse, entries in this series related to the Common Core State Standards is testimony to the complexity they present to early childhood education. The Common Core directly applies to young children (and teachers) in kindergarten and later, with implications for children (and their teachers) prior to kindergarten as well. In fall 2012, the National Association for the Education of Young Children released a brief outlining what were considered opportunities and concerns for early childhood education within the Common Core. Since then, we have heard far more about the concerns than the opportunities presented by the Common Core. The most typical of these is that the Common Core is not developmentally appropriate for young children, or some variation of this. Such a statement is indeed alarming, and may or may not turn out to be true. What is intriguing about it, however, is that it lacks specificity–what exactly is the concern being stated? If we can articulate the concern (or concerns) precisely, we can better formulate approaches to address it (or them).

Photo credit: Casey R. Brown

Photo credit: Casey R. Brown

Having talked about the Common Core with teachers, researchers, and policy makers, there seem to be three central issues buried within the “Common Core is not developmentally appropriate” concern:

Is the content of the Common Core appropriate for young children?

  1. Will the Common Core affect teaching?
  2. Will the Common Core lead to inappropriate use of assessment?

Variations of these have been raised in this blog series. These are also discussed in a new brief on this page from NAEYC.

As this dialogue unfolds, it is important to consider how much the concerns noted above are the result of the Common Core, and how much they are driven by other or additional forces. In other words, where is the pressure coming from? It is critical to understand the origins of what have been ongoing trends in early childhood education to formulate effective responses to them.

It is also critical to distinguish between what may be considered real threats and what are perceived threats to early childhood education ideals. A critical starting point in doing so is to ensure that we are well versed in the complexities of implementing developmentally appropriate practice (DAP) as well as the details of what the Common Core standards say (and do not say). As has been noted in previous blogs, the Common Core standards describe the learning goals and expectations at each grade (the “what”) not the processes of supporting children to reach towards these goals (the “how”). It is important to explore the reasonableness of all children reaching these goals (that is, validate the “what”), as well as ensuring that we not narrow our educational focus.

At the same time, we must ensure that early educators are prepared and supported to bring DAP into their classrooms (that is, nurture the “how”).

This page was edited April 21 to include a link to the new brief from NAEYC.

We are all teachers and learners

April 17, 2015

This response on literacy standards, conversation, and the Common Core State Standards is from Sharon Ritchie, Ed.D., Senior Scientist, FPG Child Development Institute-UNC CH.

I am a strong supporter of the Common Core. From the outset let me qualify that by saying that it is by no means perfect, and that people have perfectly good reasons to question the Standards and to look for revision and improvement. There is no single thing that should not bear up under scrutiny and inquiry.

Photo credit: Casey R. Brown

Photo credit: Casey R. Brown

The following quote from the Common Core: “Children are deep thinkers and it is the role of the teacher to capably guide and support them,” succinctly summarizes why I support and advocate for the Common Core Standards. The quote demonstrates real respect for both children and teachers, something that has been sadly lacking in an environment that has, for more than a decade, focused on isolated skill building, right answers, and prescribed curriculum. That environment has been even more strongly enforced for children of color and those who come from less advantaged homes, and put vulnerable children at an even greater disadvantage by depriving them of the use of their voice and their minds. Children need to know that what they care about, what they have to say, and how they feel is important. They need to move beyond basic knowledge to the application of their knowledge to problem solving, analysis, and creative development. They need to have multiple opportunities starting at a very young age to not only talk, but to listen, to participate in a community where everyone’s ideas are important and valued.

Two decades of data examining the minute-by-minute experiences of children indicate that on average there is about 28 minutes of meaningful conversation per day between the teacher and all the children in the classroom. There is about 24 minutes of meaningful collaboration between students. That is not enough. If children are getting less than an hour to express themselves, then teachers are using up more than their share of the space. If we are not hearing from children, how do we know what they understand, what confuses them, what they think? Part of children’s success depends upon their ability to engage in collaborative work. Regular opportunities to collaborate help children develop executive functions that support their ability to solve problems in multiple ways and to work with others to plan and organize. Children who are simply sitting and getting are not having adequate opportunities to develop executive functions.

In its best form, the Common Core advocates for classroom environments  where children feel safe to take risks and experiment with their thinking and have opportunities to communicate their ideas frequently and regularly. Specifically, the English Language Arts Standard requires that students have ample opportunities to take part in a variety of rich, structured conversations—as part of a whole class, in small groups, and with a partner and the Standard for Math across K-3rd grade similarly  stipulates that children should be able to make sense of problems and persevere in solving them and construct viable arguments and critique the reasoning of others.

A talented kindergarten teacher describes her practice of letting her students know right from the beginning of the year that:

  • There are lots of different points of view and they are all important
  • Right answers are not as important to her as the students being able to figure out how to solve a problem
  • Everyone makes mistakes–they are natural and we can learn from them
  • Doing your best is the most important thing
  • We are all teachers and learners.

The Common Core supports that teacher. Don’t you wish all children had teachers like that? I do.

Why CCSS-M Grades K-3 is developmentally appropriate and internationally competitive

April 13, 2015

In this post, Jere Confrey, Joseph D. Moore Distinguished University Professor, Science, Technology,  Engineering and Mathematics (STEM) Department, College of Education, North Carolina State University, discusses why the Common Core State Standards for Math can be considered developmentally appropriate. A more detailed version of this analysis, including this chart and others, is available here.

1. The CCSS-M development process drew on teachers and experts in early childhood math education. 

 According to Jason Zimba, a lead CCSS-M author, feedback was obtained from state directors, elementary teachers, and national experts (Fact Sheet, Student Achievement Partners. The NCR’s 2009 report, Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity was used. The National Association for the Education of Young Children in conjunction with the National Association of Early Childhood Specialists in States issued a joint statement publicly expressing their support for the Standards.

Photo credit: Casey R. Brown

Photo credit: Casey R. Brown

2. Standards are not meant to be read to children.

They represent professional knowledge in the field for teachers–just as in the case of medical knowledge, the Standards are not expected to be communicated verbatim to patients by doctors.

3. Standards typically state a clear target in the first sentence that describes the expectation, followed by research-based strategies for student success.

 After that, the Standards include suggestions for research-backed strategies for learning, to ensure that the students’ learning is made as conceptually rich and efficient as possible. Math is a language of connections.

Here is first grade example: “Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8+6 = 8+2+4 = 10+4 = 14); decomposing a number leading to a ten (e.g., 13-4 = 13-3-1 = 9)…and creating equivalent but easier or known sums (e.g., adding 6+7 by creating the known equivalent 6+6+1 = 12+1 = 13).”  These strategies, from the NRC’s Adding It Up, are a toolbox for a teacher to build on children’s ideas to reach towards the development eventually applying standard algorithms.

4. The Standards are consistent with international standards.

In Informing Grades 1-6 Mathematics Standards Development, AIR took the standards from Singapore, Korea, and Hong Kong, and created a composite set. The major topics in the numbers strand for all three countries follow a similar pattern, across grades, dictated by the logic of mathematics learning. In the chart below on understanding and reading whole numbers, CCSS-M is compared to this composite chart. If we claim our standards are not developmentally appropriate, then how is it that other countries achieve these outcomes? Note, these countries do not offer Kindergarten.

Table 1. Composite Standards for Hong Kong, Singapore, and South Korea, with the Addition of the CCSS-M. Composite Standards: Numbers—Whole Numbers for Hong Kong, Singapore, South Korea (AIR, p. 8)

Screen Shot 2015-04-10 at 10.06.20 AM


The Common Core State Standards are not a curriculum

April 10, 2015

Dorothy Strickland, NIEER Distinguished Research Fellow, responds to specific issues raised in various venues by questioners, considering whether literacy standards and related assessments can be developmentally appropriate.

Concern: Kindergarten standards are not appropriate for children that age. Assessment related to reaching standards will not be developmentally appropriate, and results may be misused.

Much of the concern about CCSS relates to two areas–curriculum and assessment–and not to the standards themselves. Please note: The Common Core State Standards are NOT a curriculum. The curriculum must be developed by those responsible for instruction. This might include collaborative efforts by State Departments of Education and school district personnel.


Regarding issues related to the absence of play: Developmental appropriateness has long been a part of our early childhood agenda. Fortunately, there is NOTHING in the CCSS to encourage concerns that there is no room for developmentally appropriate practice. Playful and experiential learning have always been essential elements of an early childhood curriculum and instruction and remain so.

Key Design Considerations are included in the introduction (p.4) of the CCSS: An integrated model of literacy is recommended. That is, the language arts (listening, speaking, reading, and writing) will be integrated with each other and with content of interest and importance to young children. Research and media skills will be blended into the Standards as a whole.

story time 3Educators familiar with EC know that the integration of process (ELA) and content (how plants grow, the weather, etc.) is fundamental to theme-based or project-based curriculum and instruction. This has been a basic tenet of early childhood literacy and it remains alive and well. Children explore/research questions related to topics of importance and interest to them. Books, objects, hands-on activities, and media of various types are used to explore topics/themes with children. Teachers engage children as they read aloud to them and discuss what is read. Children are also involved in shared /interactive reading. They are encouraged to follow-up independently as they explore the topics on their own through reading/pretend reading and drawing/writing about topics under investigation.

None of this is new to the field. However, the CCSS promote attention to specific goals, such as: With prompting and support, ask and answer questions about key details in a text. At the kindergarten level, the text is likely read/shared with the children by the teacher. This Standard encourages listening, responding, sharing ideas. Equally important, children are learning about a topic of interest to them. This will include new information and concepts and often includes new vocabulary or “known” vocabulary used in a new way.

A focus on thinking with text, and problem solving is encouraged. Again, this is meant to be done in a developmentally appropriate way with an emphasis on gradually increasing expectations throughout the grades. The CCSS are intended to promote skills/strategies that go beyond memorization and foster the application of what is learned in new situations.

The use of technology to support curriculum and instruction is encouraged. Indeed, texts may be traditional print or digital. And, we must not forget oral texts–these relate to listening.


Much of the concern expressed about CCSS relates to assessment. Excessive assessment is, indeed, an issue in some states. However, like curriculum, it is not a function of the CCSS. An increased reliance on Summative Assessments, in particular, has caused concern among many educators. Purposes and uses include to:

  • inform educators, students, parents, and the public about the status of student achievement
  • hold schools accountable for meeting achievement goals
  • inform relevant education policies re: areas in need of attention and resource allocation
  • adjust/differentiate instruction according to student needs
  • gauge performance of teachers and principals.

While these purposes/uses have always existed, they have taken on new emphasis in recent years (especially their use as tools in educator evaluation) and are often linked to the CCSS. For those whose states have adopted the PARCC assessment and others, I encourage a look at the Model Content Frameworks developed to bridge the Standards with the PARCC Assessments. They can be found online at www.parcconline.

  • Professional Development should make extensive use of the Model Content Frameworks that accompany the PARCC assessment. The Model Content Frameworks are:
    • a voluntary resource not a curriculum
    • designed to help teachers better understand the standards and how key elements of the assessment design interact with the standards within a grade and across grade levels.

Research Support

Appendix A: Common Core Standards for ELA/Literacy: Supporting Research and GlossarySimilar materials may be found in other appendices.

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