A systematic review of learning progressions for the concept of matter in science education

Abstract

This study evaluated recent advances in learning progressions for the concept of matter (LPCM) and explored trends by reviewing the literature on the topic published between 2005 and 2021. A total of 21 studies were reviewed. Fifteen studies were devoted to developing LPCM of varying spans and grain sizes. There were six follow-up studies based on LPCM, which were divided into two categories: curriculum research and items design. This study explored the value of the existing research on constructing learning progressions, which focused on the challenges in using LP research to specify the content of the curriculum. It analyzed the terms used to represent the big ideas, the upper anchor, progress variables, the expression of intermediate level, the characteristics of stepping stones and grades/school levels. There were some differences among individual studies on constructing LPCM in the above aspects, which makes combining LPCM difficult. These studies have also reached some consensus: the multidimensional structure of the matter concept has been empirically confirmed. These studies on the development and validation of LPCM had the following characteristics: (a) the construction intention for LPCM focuses on the development of knowledge; (b) the choice of progress variables depends on experience; and (c) the developed LPCMs are mostly linear. These constructed LPCM have not been widely applied in practice. In order for research in this field to better contribute to the curriculum and instruction, we also proposed some suggestions for future research.

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Introduction

A characteristic of science is that it produces a highly interlinked knowledge structure. Science educators expect that learners will come to appreciate this value through the science curriculum and to realize the development of coherent and integrated scientific knowledge (Taber, 2005; National Research Council [NRC], 2007). In order to achieve this goal, science educators have been trying to change the focus of the science curriculum from a broad range of concepts to a few core ideas (NRC, 2012). In reports submitted to the NRC, Catley et al. (2005) and Smith et al. (2004) were first commissioned to produce comprehensive descriptions of the learning progressions (LPs) of “evolution” and “the nature of matter” (Corcoran et al., 2009; Duncan and Hemlo-Silver, 2009). In a subsequent article, Smith et al. (2006, p. 2) proposed that LPs “should be organized around central concepts and principles of a discipline (i.e., its big ideas).” Since then, LPs have been developed gradually for many challenges.

In 2009, at a conference on LPs in science organized by the Center on Continuous Instructional Improvement (CCII) and the Consortium for Policy Research in Education (CPRE), the panel agreed on a description of LPs: “LPs are hypothesized descriptions of the successively more sophisticated ways student thinking about an important domain of knowledge or practice develops as children learn about and investigate that domain over an appropriate span of time” (Corcoran et al., 2009; p. 37). In other words, LPs are descriptions of knowledge, skills or abilities, focusing on a few foundational and generative big ideas and practices. In addition, the conference identified the need to develop an LP to include the five essential elements—target performances or learning goals, progress variables, levels of achievement, learning performances, and assessments—which provide theoretical support for the subsequent research on LPs (Alonzo and Gotwals, 2012). In the same year, the Journal of Research in Science Teaching set up a special sixth issue to solicit research in this field. A total of eight articles were presented, covering various aspects of LPs, including general approaches (Duncan and Hemlo-Silver, 2009; Lehrer and Schauble, 2009), measurement problems (Steedle and Shavelson, 2009; Wilson, 2009), hypothetical LP studies (Duncan et al., 2009; Schwarz et al., 2009), and empirical LP studies (Mohan et al., 2009; Songer et al., 2009). During this period, several studies on LPs emerged (Hammer and Sikorski, 2015). In 2015, the journal Science Education published a series of articles, identifying many different challenges that researchers have faced when constructing LPs. In 2018, Chemistry Education Research and Practice published a series of articles on “learning progression and teaching sequence in chemistry education” (Taber, 2017). This move further promoted the development of theoretical research on LPs in general and empirical research on LPs in the field of chemical education.

LPs have been adopted by the science education community as a possible way to achieve “big ideas-oriented learning” and construct a coherent science curriculum (NRC, 2005; 2007; 2012; NGSS Lead States, 2013). It promotes the development of these big ideas through top-down (scientist and science educator's perspective) and bottom-up (learner's perspective) approaches to achieve consistency in curriculum, instruction, and assessment (Alonzo and Gotwals, 2012; Jin et al., 2019). Although science education researchers have recognized the value of organizing the content system about big ideas based on LPs to develop students’ scientific literacy, there are always challenges in the process of using LP research to specify the construction of curriculum content. For example, there is a lack of consensus on what big ideas exist in physical science and current research is not sufficient to support the big ideas involved and the grade bands required for this (Foster and Wiser, 2012; Mohan and Plummer, 2012).

As Krajcik (2012) advocated, in science education, a few LPs of big ideas need to be developed. At present, the concept of “matter” has been put forward as a big idea in national science curriculum standards (NGSS Lead States, 2013). At the same time, “matter” is one of the most studied big ideas in the field of LPs (Jin et al., 2019). With the help of the standardized content in curricula and existing research on LPCM, how could curriculum developers encourage students to cultivate a deep understanding of matter? The LPCM research now appearing in academic publications differs in many fundamental dimensions (e.g., terms representing the same specific domain, progress variables, and grain sizes). Curriculum developers often struggle with differing terminology, progress variables, and grade bands. The fragmented and incomplete research on LPCM highlights the inability of research in this field to provide well-tested LPs for the larger core idea of matter in the standards. Thus, the obtained research results cannot provide illustrative examples and relevant suggestions for curriculum standard developers and curriculum designers. However, around the big idea of matter, systematic reviews have not been found concerning “how students develop their understanding of matter and how to foster students’ progression in understanding matter as a big idea” (Liu and Lesniak, 2005; Hadenfeldt et al., 2014). The purpose of this study, therefore, was to systematize the findings of previous studies of LPCM and to provide recommendations for the curriculum standards developers, curriculum materials designers and LPCM researchers. The following questions were addressed in this review:

(1) What advances have been made in research on LPCM?

(2) What are the main characteristics of existing studies of LPCM?

Method

This systematic review of LPCM was based on the preferred reporting items for systematic reviews and meta-analyses (PRISMA) statement, which includes a 27-item evidence-based checklist and a four-phase flow diagram (Moher et al., 2009). While the checklist proved unuseful as a quality assessment tool for a systematic review, the four-phase flow diagram provided general methodological guidance.

Search strategy

First, potentially relevant articles were identified in the web of science (WOS) database. We focused on journals with a focus on science education, which are widely regarded as high-quality sources, namely Journal of Research in Science Teaching, Science Education, Studies in Science Education, International Journal of Science Education, and Research in Science Education. In addition, considering that the concept of matter has always been regarded as a core idea in chemistry, we added two chemistry journals: Chemistry Education Research and Practice and Journal of Chemical Education. The term LPs first received attention in the report Systems for state science assessments in 2005 (Corcoran et al., 2009; NRC, 2005). Thus, we used the TS = (“learning progression*” AND “matter”) to search the selected journals for the period between 2005-01-01 and 2021-12-31. Asterisks (*) were used to allow declinations (progression*s). The search resulted in 44 unique articles. We screened those articles, using both inclusion and exclusion criteria to set the boundaries for the review.

In line with our research questions, the inclusion criteria were: (a) articles that addressed the concept of matter in science education, (b) theoretical or empirical studies of LPCM, and (c) studies of a longitudinal design that took place over at least a one-year period of time.

Exclusion criteria were as follows: (a) articles that cited the LP literature but were not focused on LPCM, (b) preliminary work of large-scale research (e.g., introducing the instrument design, Hadenfeldt et al., 2013), and (c) articles that addressed students’ understanding of matter rather than focusing on constructing LPCM.

The screening resulted in 12 articles on LPCM in science education. To search for further relevant publications, we used snowball sampling and scrutinized the reference lists of the 12 articles. Nine additional studies were identified, three from journals (one from Journal of Research in Science Teaching, one from Science Education, and one from Chemistry Education Research and Practice), four from conference papers, and two from the book Concepts of Matter in Science Education (Tsaparlis and Sevian, 2013). The journals from which these articles were retrieved are from the journals we initially specified. The authors of the retrieved conference papers are committed to LPCM and have published relevant journal articles in journals. The book Concepts of Matter in Science Education is highly relevant to this research topic. The quality and relevance of the studies obtained in our secondary search is thus evident. A total of 21 studies published between 2005 and 2021 were finally reviewed. These studies are marked with an asterisk (*) in the reference list. The search and selection process are summarized in Fig. 1.

Fig. 1 Flow diagram for study selection.

Data analysis

The 21 selected studies were analyzed to address the two research questions, and to explore future research trends. Two researchers reviewed the abstracts of all 21 articles to generate the initial categories. The studies were divided into two main axes: (1) research on constructing LPCM (theoretical and empirical research) and (2) follow-up research based on LPCM (curriculum research and items design). These analytical categories are shown in Fig. 2.

Fig. 2 Analytical categories.

LPs describe the learner's learning performance in the progress variables from the lower anchor to the upper anchor. Intermediate levels are set to reduce incommensurability between the upper anchor and the lower anchor (Wiser et al., 2012). According to the essential elements of LPs and the four challenges in using LP research to specify the content of curriculum standards proposed by Foster and Wiser (2012), we identified the initial coding scheme in the 15 articles on constructing LPCM.

Although there were 15 studies labeled as research on constructing LPCM, after reading the full text, the two researchers found that they were different in their ways of construction. The two coders identified test grades and school levels around Challenge 1—the limited scope of available LPs to inform PreK–12 standards. At the same time, to capture the consistency of big ideas across grades, we coded the progress variables that identify key dimensions of conceptual understanding or skill development (Wilson, 2009). Around Challenge 2—integrating the different concepts of what constitutes an LP—we identified the expression of intermediate level. When constructing the intermediate level, LPs rely on conceptual analyses of students’ misconceptions from the cognitive perspective (Mohan and Plummer, 2012). However, given how the curriculum standards would be designed to be scientifically accurate, we examined whether the misconceptions were included in the intermediate level of LPs. Drawing on the “stones across a river” analogy, a series of stepping stones that gradually approach the upper anchor is an important guide for standards developers. Stepping stones can help them in building standards around productive ideas. Considering the multi-faceted and complex nature of stepping stones (Wiser et al., 2012), we coded the characteristics of stepping stones. The establishing of the upper anchor in LPs is influenced by societal expectations that students in the upper anchor will make informed personal decisions about social issues (e.g., global warming), based on scientific ideas of learning. For Challenge 3—establishing what upper anchor students should achieve—we identified the expressions of the upper anchor to determine whether they included societal expectations. Different researchers hold different selection criteria for big ideas. Some believe that big ideas reflect the theory of the discipline, while others believe that big ideas embody the explanatory power of the theory. Different concepts (or terms) are used in research on LPCM. Around Challenge 4—defining big ideas—we coded the terms that represent big ideas. In addition, the number of participants, test instruments, and data analysis method were collected as basic information in the empirical LPCM studies (Table 1).

Table 1 The initial coding scheme

Categories (C) and sub-categories (S)
C1 Grades/school levels	C2 Big ideas terms	C3 Progress variables
C4 Upper anchor reflects societal expectations	C5 Intermediate level includes misconceptions	C6 Characteristics of stepping stones
S4.1 Yes	S5.1 Yes	S6.1 Promoting conception enrichment
S4.2 No	S5.2 No	S6.2 Promoting conception integration
		S6.3 Identifying misconceptions
C7 Participants	C8 Test instruments	C9 Data analysis methods
S7.1 Fewer than 100	S8.1 Multiple choice	S9.1 Rasch model
S7.2 100–500	S8.2 Open-ended questions	S9.2 Classical test theory
S7.3 500–1000	S8.3 Interviews	S9.3 Qualitative
S7.4 1000–5000	S8.4 Multiple choice + open-ended questions	S9.4 Others
S7.5 More than 5000	S8.5 Multiple choice + interviews
	S8.6 Open-ended questions + interviews
	S8.7 Others

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The two coders worked independently. When reading through the article, the coder jotted down information about the categories without sub-categories and coded sub-categories for the ones with sub-categories. After reading the full text of the study, coding was applied. The data analysis methods were not limited to one coding scheme. If other coding schemes were provided, the coder jotted down the method of the coding scheme. To ensure the reliability of the data, the two coders discussed all instances of disagreement to arrive at a consensus. For example, Talanquer (2009; 2018) did not explicitly mention the grades involved in the LPCM, but only emphasized the development path, from naïve through novice to expert. The two researchers unanimously decided to refer to the records of Hadenfeldt et al. (2014), and coded the grades category as K–12. Although Stevens et al. (2010) emphasized the establishment of connections among multiple progress variables to promote knowledge integration, the progress path described by Stevens et al. (2010) did not clearly reflect such connections. As Emden et al. (2018) wrote: “Development in both dimensions can be described to run parallel, while assumed relations between the dimensions are not spelled out (p. 1098)”. After discussion, the two coders agreed to identify the characteristics of stepping stones as promoting conception enrichment, based on the LPCM presented. The final inter-coder reliability was determined as the percentage agreement reached 100%.

Results

In this section, we provided an overview of LPCM research. We sorted 21 studies into four categories. Fifteen studies focused on the construction of LPCM; ten of them were empirical studies and five described theoretical LPCM. Among the empirical studies, only one was a longitudinal study; the others were cross-sectional studies. The six studies were follow-up studies based on the existing LPCM, among which five were curriculum studies. Only one article (Stains et al., 2011) concerned items design. In terms of time span, these were published in journals, books, and conference papers almost continuously from 2005 to 2018 (except 2012 and 2015).

Research on constructing LPCM

The basic coded information for the 15 studies on constructing LPCM is provided in Table 2. In general, although many researchers have put forward the theoretical ideas of constructing K–12 LPCM from the perspective of grade span from lower anchor to upper anchor development, there was no empirical study across four school levels (kindergarten, primary school, middle school, and high school). In the empirical studies on constructing LPCM, cross-sectional studies were the most common. Most of them spanned two to three school levels. Junior and senior high school students were the two most investigated participants.

Table 2 Coding results of the research on constructing LPCM

No.	Study	Big ideas	Progress variables	Upper anchor reflects societal expectations	Intermediate level includes misconceptions	The characteristics of stepping stones	Grade/school levels	Category
1	Liu and Lesniak (2005)	Matter	Matter	No	No	Promoting conception enrichment	3, 4, 7, 8, and 12	Empirical
2	Smith et al. (2006)	Matter and atomic-molecular theory	Knowledge variables: the properties of matter and material kinds, conservation, and transformation of matter; practice variables: measurement, modelling, and argumentation	No	No	Promoting conception enrichment	K-8	Theoretical
3	Stevens et al. (2007)	The structure of matter	Particle model of matter (solid) and atomic structure	No	No	Promoting conception integration	Junior high school – college	Empirical
4	Margel et al. (2008)	The structure of matter	The conceptual model and the context of application	No	No	Promoting conception enrichment	7–9	Empirical
5	Mohan et al. (2009)	Environmental science literacy	Matter and energy	Yes	No	Promoting conception enrichment	4, 6, 7–12	Empirical
6	Talanquer (2009)	The structure of matter	Structure, properties, dynamics, and interactions	No	Yes	Identifying misconceptions	K–12	Theoretical
7	Stevens et al. (2010)	The nature of matter	Atomic structure and electrical forces	No	Yes	Promoting conception enrichment	7–14	Empirical
8	Johnson and Tymms (2011)	Substance	Properties and substances, mixtures, chemical change, particle models and explanations, and mass changes	No	No	Promoting conception enrichment	7–10	Empirical
9	Rogat et al. (2011)	Structure, properties, and transformation of matter	The structure and properties of matter and the transformation of matter	No	No	Promoting conception enrichment	K–12	Theoretical
10	Johnson (2013)	Particle theory	The basic particle model	No	No	Promoting conception enrichment	7–10	Empirical
11	Hadenfeldt et al. (2014)	Matter	Structure and composition, physical properties and change, chemical reaction, and conservation	No	Yes	Identifying misconceptions	K–12	Theoretical
12	Hadenfeldt et al. (2016)	Matter	Structure and composition, physical properties and change, chemical reaction, and conservation	No	Yes	Identifying misconceptions	6–13	Empirical
13	Morell et al. (2017)	The structure of matter	Macro properties, physical changes and other changes of state, physical changes of particulate explanations, and chemical changes of particulate explanations	No	No	Promoting conception enrichment	6, 8, 10	Empirical
14	Emden et al. (2018)	Transformation of matter	The structure and properties of matter and the transformation of matter	No	No	Promoting conception integration	10	Empirical
15	Talanquer (2018)	Structure–property relationships	The intrinsic properties of materials and the explicit behaviors of materials	No	Yes	Identifying misconceptions	K–12	Theoretical

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The determination of the upper anchor in LPCM was mostly based on curriculum standards (e.g., Stevens et al., 2010). Only Mohan et al. (2009) constructed an environmental science literacy LP that considered societal expectations. Many researchers emphasized students’ misconceptions in the process of constructing LPCM but did not include the misconceptions in the description of LPCM intermediate level (e.g., Rogat et al., 2011). Overall, two-thirds of the 15 studies did not incorporate students’ misconceptions in their LPCM intermediate level.

“How does a student get to the next level” is about the reconceptualization process (Wiser and Smith, 2016). In this process, students are expected to maintain coherence about concepts and promote the development of their knowledge networks (Amin et al., 2014). Owing to differences in understanding coherence (curriculum coherence or cognitive coherence), in LP research, stepping stones that help in achieving upward anchor progression are used in a variety of ways to provide potentially productive pathways for students (Shavelson and Kurpius, 2012; Sikorski and Hammer, 2017). Stepping stones can represent the gap in curriculum knowledge. For example, students in lower grades master the weight concept of solids and liquids and those in higher grades master the mass concept of gases after learning related contents such as atoms and molecules. It may help to reconceptualize “matter has mass” in the process of providing higher students with conception enrichment stepping stones. When there are multiple progress variables, stepping stones can highlight the relationship between progress variables and help construct a knowledge network. They can also highlight the cognitive difficulties of students at different progression levels, that is, the concept that students at different stages have difficulties with. In general, stepping stones identify the change pattern of progress variables in the process of progression. No matter which types of stepping stones they are, they encourage students to realize the re-conceptualization in the path of progression and push them to gradually reach the upper anchor of LPs. Although many researchers are developing along “the cognition, curriculum, and instruction superhighway” mentioned by Krajcik (2012) when constructing LPs, the identified stepping stones that shorten the distance between upper and lower anchors have a different emphasis. We coded the characteristics of stepping stones presented in research on constructing LPCM: promoting conception enrichment, promoting conception integration, and identifying misconceptions (Table 2). There were also various situations about the expression of the big idea of matter and the selection of progress variables. These differences were described in detail in the following sections.

The research on constructing LPCM was divided into two categories: theoretical research and empirical research. The difference between them lies in whether the LPCM had been validated through assessment tasks. Basic information for the empirical LPCM studies is provided in Table 3. The number of students participating in the tests ranged from small scale (fewer than 100) to moderate scale (500) and then to large scale (more than 1000). Empirical studies of very large size (more than 5000) were involved in Liu and Lesniak (2005). They used the US national sample from the Third International Mathematics and Science Study (TIMSS). Single test instruments (multiple choice, interview, and open question) were mostly used. Studies that collected large-scale data used the item response theory (IRT) approach to analyze the collected data. Studies that collected small-scale data used qualitative methods.

Table 3 The basic information for empirical LPCM studies

Basic information	Descriptive information and number of studies
Participants	Fewer than 100	100–500	501–1000	1001–5000	More than 5000
	2	1	1	5	1
Test instruments	Multiple choice	Interview	Open-ended questions	Open-ended questions + multiple choice	Open-ended questions + interview
	4	2	1	2	1
Data analysis tools	Classical test theory	Rasch model	Bayesian networks	Qualitative
	2	6	1	3

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The term for representing matter as a big idea

In the process of developing LPCM, what are the big ideas chosen by researchers? This question is an important one to guide researchers to carry out related work. We found that different researchers use different terms to express the big idea of “matter” when constructing LPCM. In addition to the direct use of the concept of matter, researchers also used the structure of matter, the nature of matter, particle theory, atomic-molecular theory, and structure–property relationships. These different terms reflect different understandings of big ideas: whether big ideas are used to reflect major theoretical tenets in a discipline or to reflect the explanatory power of theories (Mohan and Plummer, 2012). In the 15 studies, most researchers tend to use major theoretical tenets to characterize the big idea of matter. Talanquer (2018) used the term “structure–property relationships” to emphasize how the structure of matter accounts for its properties and behaviors, which represents the idea that big ideas are represented by the explanatory power of theories. Comparatively speaking, relatively few researchers hold the latter view.

It is worth noting that there are differences in the terms used by researchers to represent the big idea of “matter.” Even if the same term is used, its connotations may be different, which may easily lead to a confusion between concepts. For example, Rogat et al. (2011) divided the matter concept into two dimensions: “structure and properties of matter” and “transformation of matter.” The term “transformation of matter” includes both physical transformations (i.e., phase changes) and chemical changes (i.e., chemical reactions). Different from Rogat et al.'s (2011) definition of the “transformation of matter,” Emden et al. (2018) emphasized that the contents related to this term include the particulate nature of matter, changes in the properties of matter, and the theories of chemical bonding. They are more inclined to use the term to refer to the concept of matter as a whole.

Although these 15 studies were all identified as those on constructing LPCM, further identification of their progress variables showed that the researchers focused on different aspects. Stevens et al. (2007), Margel et al. (2008), Talanquer (2009), and Morell et al. (2017) used the term “structure of matter” to construct LPCM. Margel et al. (2008) focused on content related to the particulate nature of matter, constructing a single dimension LPCM. Stevens et al. (2007) constructed LPCM around two progress variables, particle model of matter (solid) and atomic structure. Talanquer (2009) constructed a progress path for students to understand content related to the particulate nature of matter based on four dimensions (i.e., structure, properties, dynamics, and interactions). The LPCM for the structure of matter proposed by Morell et al. (2017) built a four-dimensional model around the atomic-molecular theory of matter, including the macro properties, physical and other changes of state, physical changes of particulate explanations, and chemical changes of particulate explanations. The difference in the selection of progress variables arose from researchers’ varied understandings of the big idea of matter. When “matter” is regarded as a core concept in chemistry, researchers directly take important topics as perceived by individuals as progress variables. For example, most researchers chose the particle nature of matter to construct LP (e.g., Margel et al., 2008; Talanquer, 2009). When the concept of matter was regarded as a crosscutting concept in science education, researchers focused on the inflow, outflow, and cycles of matter in a social-ecological environment (e.g., Jin et al., 2017).

The multidimensional nature of the concept of matter

There is a diversity of progress variables in LPCM research (Table 2). Of the 15 studies that focused on the construction of LPCM, one study constructed LPCM around five matter-related concepts: properties and substances, mixtures, chemical change, particle models and explanations, and mass changes (Johnson and Tymms, 2011). The rest of the studies divided the concept of matter into different dimensions (see Table 2).

Researchers determined the dimensions of the big idea of matter based on experience, which is one of the reasons for the existence of different progress variables. For example, Liu and Lesniak's (2005) summary of extant articles revealed that students’ misconceptions about the concept of matter had four aspects: composition and structure, physical properties and change, chemical properties and change, and conservation. Structure of matter, size-dependent properties, forces and interactions, and quantum effects are the four dimensions of the big idea of matter that reflect consensus in the field of nanoscience as reported by Stevens et al. (2006; 2007). This consensus was reached by 39 outstanding scientists and science educators through participation in a national workshop funded by the National Science Foundation (NSF).

Another reason for the diversity of progress variables is that researchers are constantly exploring the multidimensional nature of the big idea of matter. Whether this exists unidimensionally, or as several dimensions, has also been explored (e.g., Hadenfeldt et al., 2016; Emden et al., 2018). Although there is no consensus on “which dimensions constitute the big idea of matter,” existing data from empirical research have shown that matter as a big idea is multidimensional.

Using a multi-dimensional version of the Rasch model, Hadenfeldt et al. (2016) in their empirical study confirmed that the four-dimensional conceptual model (structure and composition, physical properties and change, chemical reaction, and conservation) was superior to the two-dimensional model (structure and composition and the transformation of matter) and the two-dimensional model was superior to the one-dimensional model (the concept of matter as a whole). By observing the degree of fit of the data on the one-dimensional and two-dimensional Rasch models, Emden et al. (2018) found that unidimensional data from “matter as a whole” had an inferior fit than data on two dimensions, “the structure of matter” and “chemical reaction.” Emden et al. (2018) and Rogat et al. (2011) emphasized that the concept of matter can be divided into two dimensions from the empirical and theoretical perspectives, respectively. Unfortunately, Emden et al. (2018) did not explain the difference between the two dimensions (“the structure of matter” and “chemical reaction” vs. “structure and properties” and “transformation”).

Compared to the above studies, Morell et al. (2017) divided the concept of matter into four different dimensions (macro properties, physical changes and other changes of state, physical changes of particulate explanations, and chemical changes of particulate explanations). Using multidimensional random coefficients, and a multinomial logit model, they also found that the four-dimensional model fits the data statistically better than the unidimensional model when exploring LPCM. In particular, they found that there were three sub-dimensions in the dimension of chemical changes of particulate explanations and each sub-dimension could be divided into three levels. For details, see Morell et al. (2017). Dividing the concept of matter into different dimensions does not mean that each dimension is not a completely independent construct. These dimensions represent different aspects of the same construct, and there is a certain latent correlation between each dimension (Hadenfeldt et al., 2016). So, relevant research between dimensions has been conducted (e.g., Talanquer, 2018).

Characteristics of stepping stones

Among the 15 studies that focused on constructing LPCM, nine provided promoting conception enrichment stepping stones, two provided promoting conception integration stepping stones, and four provided identifying misconceptions stepping stones as the characteristics (Table 2).

Promoting conception enrichment stepping stones. LPs that provide promoting conception enrichment stepping stones are mostly based on the order of the curriculum, focusing on the logical structure of knowledge and concepts that students learn at different grades. For example, the LPCM proposed by Rogat et al. (2011) was based on five models of matter, including the macroscopic component model (objects can be divided into smaller parts that still maintain their material identity), microscopic component model (objects are composed of very tiny pieces), particle model (matter is composed of tiny particles), atomic-molecular model (particles are collections of atoms and molecules), and subatomic model (atoms have a substructure composed of charged particles). Students can use different models to explain questions with different levels of complexity. Students can use an atomic-molecular model to explain “what makes one substance different from another” and can also use a subatomic model to explain “why some substances react to form new substances while others do not.” The learning performance of students at each level is consistent with the performance expectations mentioned in the National Curriculum Standards (NGSS, 2013). For example, junior high school students are required to develop models to describe the atomic composition of simple molecules and extended structures (NGSS, 2013, p. 56). In the LP constructed by Rogat et al. (2011), the corresponding learning performance of students at level 4 (grades 7–9) can be found, which involves explaining the difference between a substance and a mixture using atomic-molecular models. It is worth noting that cognition is not ignored in this process. In dividing performance expectations at each level, the misconceptions held by students were considered. This type of LP often spans a large number of grades. Students’ progression patterns are related to the curriculum content they learned.

Promoting conception integration stepping stones. In addition to helping students develop vertical coherence in concept understanding, stepping stones can also help in constructing horizontal coherence when there are multiple progress variables in LPCM. Promoting conception integration stepping stones will help students to develop from lower to higher cognitive stages. As the level increases, the links between different concepts in different topics or disciplines are gradually established. Students’ knowledge structure becomes more integrated, which is more conducive to explaining phenomena and solving problems in different situations (Lee et al., 2011). An example can be found in the earlier work of Stevens et al. (2007). The LP developed by Stevens et al. (2007) describes how students built their understanding of the nature of matter. In particular, they focused on how and when learners developed connections between ideas. They found that the understanding of the “particle model of matter (solid)” needed to be associated with the understanding that “particles are atoms” before they were able to establish an understanding of atomic structure at the next level. Therefore, the idea that “particles are atoms” was the critical point in the path of understanding the nature of matter.

Emden et al. (2018) also found some critical points when they investigated the LP in the two dimensions of composition and structure and chemical properties and changes. In the dimension of chemical properties and changes, students recognized that chemical reactions brought about “the formation of new substances with new properties,” which made it easier for them to understand the level of the composition and structural dimension of “describing chemical elements and compounds as pure substances and can differentiate them from each other” (p. 1107). In other words, they found that the understanding of an idea that exists in another progress variable helps in driving the understanding of concepts at the next level of the dimension. In general, “critical points” can be understood as the key stepping stones that promote the connection between concepts of different progress variables. This can help in achieving the knowledge integration of different dimensions and promote in-depth understanding.

Identifying misconceptions stepping stones. Providing identifying misconceptions stepping stones to construct LPs shows that researchers pay special attention to the coherence of students’ cognitive development, focusing on difficulties in learning more advanced and counter-intuitive concepts. LPs that provide such stepping stones tend to be diagnostic—focusing on the transformation of concept content and reasoning form—that is, developing unscientific concepts into scientific ones and developing intuitive reasoning into counter-intuitive scientific reasoning (Jin et al., 2019). To this end, researchers tend to present students’ possible misconceptions or the form of reasoning in learning performance at each level when constructing LPCM.

Talanquer (2018) argued that the LP about the structure–property relationship combined the two categories well. Based on the previous studies about misconceptions, Talanquer (2018) put forward a complex conceptual progression process in the transition from novice to expert and also pointed out the learning performances in causal reasoning. Specifically, he mentioned that students’ thinking about the properties of materials goes through five intermediate stages from the “inherent characteristics of substances” to the scientific understanding that “the properties of substances emerge from the dynamic interactions between structural components.” In the first five stages, students have an unscientific and incomplete understanding. For example, students at level 4 usually regard atoms as macroscopic objects with inherent characteristics. Students may think that hydrogen atoms are acidic, which will lead them to think that “substances with more hydrogen atoms in their chemical formula are more acidic.” When students explain some properties of substances, there are primarily five kinds of gradually complex causal reasoning diagrams from “macroscopic concentrated causality” to “structural interactions.” An understanding such as “oxygen gas is reactive because it is composed of highly electronegative atoms” reflects causal reasoning at the atomic level, which is the fourth achievement level.

Follow-up studies of LPCM

Science educators have advocated using the LPs approach to build coherence across the curriculum, instruction, and assessment (Lehrer and Schauble, 2015). Therefore, the LPCM can guide the subsequent work. The six studies in this category were divided into two subcategories: curriculum research and items design. Curriculum research is a practical study that uses the curriculum and instruction to promote the development of students’ conceptual understanding, assessing whether students’ performance is toward the upper anchor of the LPCM. Items design refers to the development of new testing instruments to facilitate assessment by researchers or teachers.

Curriculum research based on LPCM

Five studies described LP-based interventions, which were implemented in science classrooms. Their purpose was to validate the coherence between the LPs and curriculum or to prove the effectiveness of the LP-based interventions. Pre- and post-assessments or longitudinal assessments were used to measure student learning gained in the intervention. Jin et al. (2013) found that the original matter-and-energy LP did not provide a fine-grained depiction through practice and modified the LP in empirical studies. The revised LP showed that students had made significant learning gains, but there were certain difficulties in achieving the upper anchor. The Chemistry, Life, the Universe, and Everything (CLUE) curriculum developed by Cooper et al. (2012) includes an LP on molecular structure and properties. Over the course of a full year, CLUE students were significantly better at plotting Lewis structures and predicting the properties of matter than control students. Wiser et al. (2009) developed a curriculum based on the LP developed by Smith et al. (2006), which used concepts as the primary organizer.

The selected studies also paid attention to teaching strategies. Merritt and Krajcik (2013) examined how a unit (15 lessons) supported LPCM development to promote the development of students’ understanding about the particle model of matter. “How can I smell things from a distance?” was the driving question of the unit. Students needed to create models to explain how they could smell the object from a distance. Their work showed that a carefully sequenced curriculum that supported students in using the scientific practice of modeling helped them in developing an initial particle view of matter. Jin et al. (2017) developed a plant unit dedicated to the upward anchor (level 4) development of students at level 2 and level 3 about the matter-and-energy LP in social-ecological systems. By comparing students’ performance before and after the teaching intervention, they confirmed that the course promoted students’ performance and found that discourse strategies played an important role in it.

Item design based on LPCM

The development of LPs has gone hand-in-hand with the development of assessment tools that help in characterizing where students are located in the LP. After constructing a hypothetical LP, assessment tools need to be developed and the LP then needs to be revised based on the assessment results. This cyclical revision process sometimes does not end after one round of work (Corcoran et al., 2009). The LPs describe the change in learning performance over a period of time, which needs to involve different grades and even different school levels. For this reason, the development of the items design is sometimes a challenging task. A few researchers have developed tools that can be implemented easily by science teachers in their own classrooms.

In the ten empirical studies of the construction of LPCM, multiple choice was used most frequently, followed by interviews and open-ended questions. The interview method makes it impossible to carry out a large sample survey. Considering the knowledge base of students in different grades, the number of test items is often high. Johnson and Tymms (2011) developed 176 multiple choice questions for computer testing. Liu and Lesniak (2005) developed 62 test questions including multiple choice, short answer, and extended answer questions. These items are time-consuming to test and difficult for teachers to use directly in the classroom. From a teaching practice perspective, Stains et al. (2011) developed an assessment tool related to “the structure and motion of matter” based on the LP proposed by Talanquer (2009). It is a teacher-friendly tool with a test time of 15 minutes. We did not include a study that only introduced tool design and was later judged to be a follow-up large-scale empirical study about constructing and validating LPCM. Finally, we only reviewed one study that belonged to this category.

Discussion

The review found that there were limited studies on LPCM published in high-quality journals. LPCM developers focus on different aspects of the big idea of matter, each with its own focus, construction criteria, and unique progression path. The LPCM based on empirical verification lacks close links; hence, it is difficult to directly link these research results to guide the construction of the content system for the big idea of matter across K–12 grades. In addition, among the 15 studies that focused on constructing LPCM, four provided identifying misconceptions as stepping stones. Duschl et al. (2011) believed that although this type of LP has a certain value for testing the effectiveness of instructional intervention, such research does not give a real sense of LP. Curriculum standards developers and curriculum materials designers appreciate how students’ knowledge can be meaningfully constructed over time. The review found that fewer studies provided illustrative examples for this. According to the review's findings, we next discuss the characteristics of the research on constructing LPCM from three aspects: the intention for constructing LPCM, the basis for selecting progress variables, and the dimension of constructing LPCM. Through an in-depth discussion, we hope to find the direction for future research in this field.

The intention for constructing LPCM

At present, the teaching aim of school education has achieved a transformation from teaching knowledge to cultivating competency. For example, the “21st century skills” advocated by the Organization for Economic Cooperation and Development (Ananiadou and Claro, 2009) and the “key competences” proposed by the European Union (EU, 2008) both emphasize that school education should cultivate the essential key competences required for students’ lifelong and social development. Competency is a complex combination of knowledge, skills, and attitudes (Hoskins and Crick, 2010). People's competency determines how complex a task they can complete. An LP measures growth in competence in core concepts (knowledge) or scientific practice (skill). Considering that participation in practical activities is an important way to promote knowledge construction and transfer (NRC, 2012), the integration of core concepts and scientific practice should not be ignored when constructing LPs to promote students’ competency development. This is consistent with Duschl et al. (2011) who proposed that “considerations of knowledge use and coupling with science practices are criteria for LP research” (p. 174). However, of the 15 articles on constructing LPCM, only one integrated the concepts related to matter and scientific practices (Smith et al., 2006). Through the development and engagement in scientific practice, the development of the conceptual understanding was achieved.

In addition, it should be emphasized that understanding knowledge does not mean mastering the competency to solve problems. In other words, the mastery of scientific concepts does not mean the understanding of complex phenomena (McCain, 2015). We found that only Mohan et al. (2009) constructed an LP of environmental science literacy that considered societal expectations. The setting of the upper anchor focused on the important role of the scientific concepts, making students build a deep and interrelated understanding of the construction of natural phenomena (generate organic carbon, transform organic carbon, and oxidize organic carbon), and see this as “coherent” (NRC, 2012). Most researchers acquiesced in the assumption that the content that students should learn is a subset of expert knowledge (Lehrer and Schauble, 2015), which led to the fact that most LPCM did not really reflect the important role of big ideas in the setting of the upper anchor. For example, the LP should not only describe the process from unscientific to scientific understanding of the particle nature of matter: low-level students believe that particles are embedded in matter and high-level students realize that matter is composed of particles (Johnson, 1998; 2013). It should also describe the different learning performances that students should have in explaining everyday phenomena, which reflects the competency of students to solve practical problems. Regarding the particle nature of matter as a guiding framework helps students develop a more comprehensive understanding and in turn guides them to make more complex causal explanations about phase change or other daily phenomena, which is seen as the power behind the construction of LPCM (Krajcik, 2012). However, we found that students showed a low level of competency in this regard (Hadenfeldt et al., 2016; Morell et al., 2017).

The basis for selecting progress variables

Progress variables identify the critical dimensions of knowledge, skill, or ability development over time, and can be used to track students’ performance at different levels (Alonzo and Gotwals, 2012). What is the basis for selecting progress variables in the process of constructing LPCM? This question is an important issue that guides researchers in carrying out related work.

We found that the selection of progress variables in constructing LPCM was based on the summary of personal experience. For example, based on the literature review, Morell et al. (2017) proposed a hypothetical LP on molecular theory, which initially included six dimensions: properties of objects, measurement and data handling, density and mass & volume, changes of state, macro evidence for particulate structure, and atomic–molecular theory of macro properties (Black et al., 2011). After discussion with scientists, science education experts and elementary and secondary school teachers and further review of the literature referred to in such studies and empirical data results, Morell et al. (2017) redefined the structure of this LP. The selection of progress variables in the above research is based on an empirical summary. In other studies of constructing multi-dimensional LPCM, the selection of progression variables also reflects the characteristics of attaching importance to personal experience or considering curriculum standards (e.g., Liu and Lesniak, 2005; Stevens et al., 2006; Rogat et al., 2011). As a result, although the multi-dimensional structure of the concept of matter has been empirically confirmed (Hadenfeldt et al., 2016; Emden et al., 2018), researchers have not reached consensus regarding the primary issue of “what dimensions should be included in the multidimensional nature of the concept of matter.” To resolve this issue, the selection of progress variables should consider the integration of theoretical and empirical perspectives. Research on the philosophy of chemistry may provide some help at the theoretical level.

In addition, researchers rarely define the progress variables in their studies in detail, resulting in the second problem where the relationship between concepts (e.g., matter, change, and energy) in existing research about LPCM has not been well understood. For example, Claesgens et al. (2009) proposed that matter, change, and energy are big ideas in high school and college general chemistry. However, they found that there was a correlation between students’ performance in the two variables of matter and change (r = 0.68). When these highly related concepts are used as progress variables to construct LPs without distinguishing them, researchers encounter difficulties in assessment. Kristin et al. (2012) found that there are coding limitations and data analysis limitations when matter and energy were used as two progress variables at the same time in their research of assessing 4th–12th grade students using the developed carbon LP. Specifically, the younger students did not distinguish between the two concepts of matter and energy. The data showed that the scores in these two dimensions were highly correlated (r = 0.959). These data warn follow-up researchers that the empirical use of concepts can easily lead to confusion in the meanings of terms. In order to avoid unclear use of terms, it is recommended that researchers clarify the theoretical meanings of the concept used (e.g., matter, change, energy, structure, and properties).

The dimension of constructing LPCM

In 2009, Wilson discussed the relationship between LPs, “construct maps,” and progress variables, which provide theoretical support for the development of different types of LPs (unidimensional or multidimensional). A progress variable presents learning performance at different levels in an orderly manner, which constitutes a construct map. The simplest LPs only focus on one progress variable to form a construct map, in which the levels of the construct map are the levels of the LPs. With the multi-dimensional structure of the matter concept being revealed, constructing multi-dimensional LPCM can be seen as a set of construct maps. The progress variables can be multiple, and the levels of the construct map are related to the levels of the LPs. Specifically, when there are multiple progress variables, as the levels increase, multiple construct maps may show some similarity in complexity from level to level (e.g., Stevens et al., 2010). Different construct maps may also be located at different levels of LPs. For example, Liu and Lesniak (2005) found that 7th grade students reached the level of understanding the aspect of matter conservation; 8th and 12th general students developed an understanding of physical and chemical properties and change; 12th grade math and science specialization students developed understanding of the structural and compositional aspects of the matter concept. They then described five different levels of understanding based on all four aspects of the matter concept (Hadenfeldt et al., 2014; 2016). Finally, the four construct maps formed by these four progress variables appear at different levels of LP. In the LPCM revised by Morell et al. (2017), the relationship between LP and construct maps is similar to the above example. As four progress variables—macro properties, physical changes and other changes of state, physical changes of particulate explanations, and chemical changes of particulate explanations—are used to construct four construct maps. They correspond to different levels of the LP. On the whole, the theoretical viewpoints proposed by Wilson (2009) can be confirmed by relevant empirical studies found in the reviewed articles.

Constructing a single-dimensional linear LP is the most common and simplest. Stevens et al. (2007) pointed out that linear assessment separates the connections between concepts, which is not conducive to students’ understanding of big ideas in science. Current evaluation emphasizes the ability to apply big ideas to a series of natural phenomena or contexts (e.g., Kubsch et al., 2018; Nie et al., 2019). In order to promote students’ understanding of the big idea of matter in science education, students should first understand the big idea of matter proposed in chemistry education. The formation of big ideas is slow and spans larger grade bands. The different components of a core idea should be explicitly related to each other. At present, in the field of chemistry education, the multidimensional structure of the matter concept has been confirmed. In order to answer the question of how students establish the connection between the different aspects of the matter concept, future research must pay attention to the relationship between multiple progress variables. Through empirical studies, researchers can identify how concepts are connected in the progression path. The identified promoting conception integration stepping stones may help students to better integrate the components of larger concepts learned at different grade levels and lead to a more sophisticated understanding of big ideas. For example, using different particle models to explain physical/chemical changes involves the connection between structure and properties. Although there are theoretical studies of the structure–property relationship (Talanquer, 2018) and empirical studies of carrying out teaching at university level (Cooper et al., 2012), how to construct an appropriate LPCM based on the curriculum setting in K–12 education is worth exploring.

In addition, as a crosscutting concept in science education, the construction of LPCM can select progress variables based on the interdisciplinary perspective, which would help students’ thinking in breaking the boundary between disciplines, avoiding the dilemma of students being unable to think about physical content in the field of chemistry (Taber, 2005). Research in this direction will also provide suggestions for the setting of curriculum content in different disciplines. In the LPCM on the two progress variables of “atomic structure” and “electrical forces” constructed by Stevens et al. (2010), the researcher considered the statement “There are different types of inter-atomic interactions, all governed by electrical forces” as the learning performance at level 4, which reflects an interdisciplinary perspective. Students at this level can better understand the way that atoms interact to form chemical bonds (Levy Nahum et al., 2007). That is, by mastering these crosscutting concepts, students have the framework to organize the knowledge from the various disciplines into a coherent understanding (NRC, 2012). In particular, after the crosscutting concepts were proposed, the strengthening of the connections between different disciplines and cultivation of interdisciplinary competence were emphasized (Song and Wang, 2021). The value of knowledge integration in cultivating interdisciplinary competence cannot be ignored. Researchers also set crosscutting concepts such as reasoning and scale as progress variables when constructing LPCM (e.g., Mohan et al., 2009; Jin et al., 2013). Mohan et al. (2009) identified four levels of achievement about students’ understanding of carbon-transforming processes at multiple scales, describing the different patterns of reasoning. That is to say, students explained the same phenomenon with different complexity and scientific accuracy possibly because their ability to integrate knowledge was at different levels of reasoning (e.g., McLure et al., 2022). Their studies confirmed the important role that cross-cutting concepts play in understanding a complicated phenomenon.

Conclusions and implications

This study systematically reviewed 21 studies about LPCM in science education published between 2005 and 2021. Most existing studies focused on developing a theoretical or empirical LPCM with varying spans and grain sizes. Generally speaking, it is difficult to directly link the research results for the big idea of matter to guide constructing the content of K–12 curriculum standards and materials. There were some inconsistencies among the 15 studies that focused on constructing LPCM. They used different terms to represent the big idea of matter, which reflected researchers’ different understandings of the big idea. When the same term was used to express the dimensions of matter, its connotations also differed. Selecting progress variables based on experience led to an inconsistent focus and development path in LPCM. Different types of stepping stones were laid along the path that develops from the lower anchor to the upper anchor. A degree of consensus has been reached in the empirical LPCM: the multidimensional structure of the matter concept has been empirically confirmed by researchers. We identified three primary aspects of the current characteristics of the process of constructing LPCM; this should provide a direction for researchers to conduct follow-up research.

The LPCM tested by classroom instruction would provide curriculum developers with instructional components, which are useful for building curriculum materials. The review found that researchers in this field focused on the development and validation of LPCM, weakening the value of LPCM for guiding curriculum and instruction. These LPCM have not been widely applied in practice. Guiding researchers in related fields need to carry out more solid research that is conducive to the development of follow-up curriculum standards and the efficient development of classroom teaching. Finally, we put forward the following implications for future researchers engaged in related fields.

The notion of LPs arose from an early focus on the curriculum, instruction, and assessment in science education (NRC, 2005; 2007), which meant that the development of an LP had to define its value in guiding these three factors. In instruction interventions carried out under the guidance of LPCM, one of the challenges is how to help students move to the next level and finally form the new understandings that constitute the upper anchor. Studies have confirmed the impact of curriculum on conceptual understanding. In particular, students in higher grades have a higher level of understanding regarding the concept of matter (Margel et al., 2008; Hadenfeldt et al., 2016). But it is possible that over time students will return to a lower level of understanding (Margel et al., 2008). How to use the spiral curriculum to promote conceptual development is a question that should be considered in the future. To establish associations between concepts, Corcoran et al. (2009) pointed out that repeated concepts are helpful, which is an advantage of the spiral curriculum. Regarding specific curriculum design, Wiser et al. (2009) suggested that course designs based on LP should shift the focus from “topics” to “concepts.” For example, students were found to have difficulty understanding the concepts of matter and gas. Early students’ understanding was that “matter is something that can be seen and touched.” Gas did not meet this condition. By associating weight and volume, younger students gained a stepping stone to understand the materiality of gases. Such a detailed curriculum really requires researchers to design small and fine-grained learning steps.

Considering that the constructed multi-dimensional LPCM have particulars at different levels of learning performance, strategies or methods for identifying key ideas connecting different dimensional concepts—the “critical points” mentioned by Stevens et al. (2007)—should also become the focus of researchers in the future. Wiser et al. (2009) identified the “lever concepts” of volume, density, and matter as weight, size, and material, which need to be further developed in subsequent learning. These “lever concepts” are similar to the “critical points” proposed by Stevens et al. (2007), which are key concepts that appear in lower-level anchors, to establish the links between concepts and promote the integration of concepts. They are important stepping stones in the process of conceptual development.

The development of statistical analysis tools has contributed to the implementation of this study. Emden et al. (2018) obtained a variety of possible paths about structure of matter and chemical reaction through Bayesian networks. They found that different ideas played different roles in learning paths. An understanding of describing chemical elements and compounds as pure substances, which can differentiate them from each other, could be achieved even if students had not achieved an understanding of the idea of identifying substances by their properties. Their study reported the conditional probability for achieving the upper performance expectation. Research based on this method would help in discovering the “critical points” connecting different dimensions, which would provide a teaching direction to follow-up with the question of how to strengthen the connection between different dimensions of the concept of matter.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the Key Project of Basic Education Teaching Reform of Shandong Province in China in 2019 (3700014).

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