Measuring pre-service chemistry teachers’ graph and table interpretation skills: when performance meets confidence

2.1 Visual representations

To convey scientific information, visual representations such as graphs, tables, diagrams, schematics, and models are commonly employed. Interpreting data using graphs and tables is a fundamental skill when learning science. ⁷ For scientists, organizing data in graphs and tables is an invaluable method for identifying relationships between variables and understanding the properties and reactivity of materials. ⁹ These visual tools help reveal patterns that might be difficult to discern in textual descriptions, making them essential for both understanding and communication in science.

The structure of tables is connected to the structure of graphs, as tables serve as a way to display data, creating a relationship between organized tables and their graphical representations. ¹⁰ However, students often confuse graphs with symbolic representations of data, which affects their ability to analyse information effectively. ¹¹

Although mathematics education has long emphasized tables and graphs, recent research shows growing attention to these skills in science education. ⁷ PISA has consistently included graph- and table-based items as core components of scientific literacy frameworks. ^{12 , 13} This global emphasis is further reflected in national education standards in multiple countries, ^{14 , 15} where data interpretation and visualisation belong to key learning goals.

Scientific literacy, including graph interpretation skills, is shaped by factors such as data characteristics and content. ⁷ Despite this, research shows that students across all educational levels struggle with interpreting graphs and often make similar mistakes. ^{16 , 17 , 18 , 19}

Moreover, educators have much to learn about the processes involved in reading, analysing, and interpreting information presented in data graphs and tables. ¹⁰ A frequent cognitive error in graph reading occurs when students perceive a graph as a literal picture rather than an abstract representation, leading to confusion between slope and height or intervals, and points. ⁷ Although the ability to read graphs is crucial, it is not an innate skill that develops automatically. Dreyfus and Eisenberg ²⁰ stressed that reading graphical data is a learned ability that requires explicit instruction. As a result, research on this topic has gained increasing attention not only in the natural sciences but also in other disciplines. ¹⁰

Research shown that reading and interpreting graphs are two cognitively distinct processes. Reading typically involves the extraction of explicit features (e.g., value, trends), and is therefore less demanding for students, ²¹ whereas interpreting data requires drawing inferences, connecting data to underlying principles and evaluating implications, therefore a more cognitively demanding task ²² which is reflected in students’ results. ^{7 , 23 , 24}

The design of learning materials can therefore significantly influence students’ abilities to work with non-textual components. Several studies analysing the visual components of textbooks ^{25 , 26 , 27 , 28} highlight the unequal representation of different types of representations. In a study by Rusek et al. ²⁶ all lower-secondary chemistry textbooks submitted to the analysis included almost all textbook components, however, the textbooks differed in the amount of attention to particular components. Technically, each textbook includes both a table and a graph. However, the emphasis placed on these elements varies, which signals to teachers how important it is to integrate them into their teaching. ^{29 , 30 , 31} In addition, Dhakulkar and Nagarjuna ³² found that in a sample of Indian science textbooks, the presence of graphs was relatively limited and, in some cases, even lower than in mathematics textbooks. Other comparative analyses have similarly shown that the frequency and type of graphs differ significantly between mathematics, science, and engineering textbooks, pointing to notable variability across disciplines. ³³ Moreover, even when graphs are present, the cognitive demands they place on students are not always clear. Slough and McTigue, ³⁴ for instance, observed that despite a trend toward more visually rich science texts, the integration of visual and textual information – the graphical demands – often remains underexplored. Likewise, Khine and Liu ³⁵ found that in a sample of primary science textbooks from the UAE, graphical content was primarily static and iconic, with relatively little use of data-driven graphs. Importantly, the mere presence of graphs and tables does not guarantee that students are supported in learning how to interpret them.

Currently, the literature on this topic in science education appears heavily skewed, with the vast majority of studies originating from physics education, ^{36 , 37 , 38 , 39} while representations in chemistry education are predominantly examined from macroscopic, sub-microscopic, and symbolic perspectives, ^{4 , 40} graphical and tabular representations are often overlooked.

2.2 Student skills diagnostic tests

As mentioned above, reading and using data from graphs and tables belongs to one of central student skills in science education. To test students’ skills in general, researchers have been using various diagnostic tools, including open-ended tasks, multiple-choice tests, and multiple-tier tests such as two-tier, three-tier, and four-tier tests and recently also eye-tracking mostly in combination with other methods such as think aloud. ⁴¹ Each method has its own advantages or disadvantages.

Multi-tier tests, due to their capacity to evaluate understanding, skills as well as disclose misconceptions have recently been used by researchers more frequently. ⁴² In contrast to traditional tests, a two-tier test includes a first tier with a multiple-choice question and a second tier presenting possible justifications for the selected answer. These tests allow for identifying and measuring incorrect answers with correct reasoning and correct answers with flawed reasoning (i.e., false positives and false negatives). However, they do not differentiate between a lack of knowledge and misconceptions, which can lead to an overestimation or underestimation of students’ scientific understanding. ^{43 , 44} Using a three-tier test allows differentiation between errors and lack of knowledge, ⁴⁵ incorporating the confidence tier (third tier). ^{42 , 46 , 47} The Confidence rating factor or confidence judgement refers to diagnostic questions where students are asked to choose an answer and assess their degree of certainty about that answer. ⁴⁸ Confidence’s evaluation differs across individual studies. The simplest approach are “sure” and “not sure”, or “very confident”, “not confident” and “do not know” options (see e.g., ^{49 , 50 , 51 , 52} ) followed by reporting confidence on Likert scale: four-point ^{42 , 53} or six-point ^{54 , 55 , 56 , 57} or a 10-point scale suggesting percentage. ^{48 , 54 , 56 , 57}

While all misconceptions are a form of error, not all errors stem from misconceptions. Yet, misconceptions are errors that are strongly held and advocated with high confidence. ^{45 , 55 , 56} A four-tier test is a multiple-tier diagnostic assessment designed to address limitations found in two-tier and three-tier tests. ⁵⁰ Three-tier tests address some weaknesses of two-tier tests, but they still don’t clearly separate confidence in the answer (first tier) from confidence in the reasoning (second tier). As a result, they may overestimate students’ scores and underestimate their lack of knowledge. ⁵⁸ In a four-tier test, the first tier consists of a standard multiple-choice question, with distractors specifically targeting misconceptions. The second tier requires students to indicate their confidence in their chosen answer from the first tier. The third tier prompts them to provide reasoning for their initial answer. Finally, the fourth tier asks students to express their confidence in the reasoning they provided in the third tier. ^{45 , 47 , 55}

2.3 Confidence judgement

With a focus on lifelong learning, self-regulated learning ⁵⁹ plays a crucial role in fostering autonomy and adaptability in learners. It represents a crucial element individuals need to develop not to remain dependent on external evaluation of their progress. Their metacognition, i.e., their awareness of their own knowledge, cognitive processes, mental state as well as the ability to monitor and regulate them is a vital element. ⁶⁰ As the scope deepens and knowledge expands, experts find it increasingly challenging to precisely define the boundaries of metacognition. ⁶¹ In metacognition research, scholars typically examine how individuals monitor their own cognitive processes and the extent to which they can regulate them. ⁶²

The aforementioned multi-tier tests became a useful tool to evaluate students’ metacognition in science education research. ^{42 , 53 , 58 , 63}

With respect to this paper’s focus, confidence in data interpretation is key to working with graphs and tables effectively. When analysing numerical and visual information, individuals must assess their comprehension and make decisions based on patterns, trends, and relationships. Confidence judgments (CJ) allow individuals to evaluate how well they understand a concept. ^{55 , 56} However, perceived confidence does not always correspond to actual accuracy – both overconfidence and under-confidence can impede effective data interpretation. ⁴² Overestimating one’s skills may lead to misreading trends or overlooking inconsistencies, while insufficient confidence can discourage deeper analysis and limit the ability to draw meaningful conclusions. ^{53 , 64}

Aligning confidence with actual analytical proficiency enhances data literacy by improving self-evaluation accuracy. Excessive confidence, particularly when based on incorrect assumptions, can result in misinterpretation of data. However, when misunderstandings are corrected through targeted feedback, confidence can drive a more thorough and insightful approach to analysis. ⁶⁵ On the other hand, moderate confidence, often associated with intellectual humility, encourages a more careful and adaptable approach to working with data. ⁶⁶ Effective strategies help individuals calibrate their confidence levels to match their actual understanding, refining their analytical skills and decision-making processes. ^{67 , 68} Therefore, cultivating accurate confidence judgments is essential, among others, for developing strong data interpretation skills.

2.4 The use of multi-tier tests to diagnose student’s engagement with tables and graphs

Research on students’ ability to interpret data remains relatively limited, particularly in studies employing multi-tier test formats. However, several studies have explored how students process and understand data representations, particularly through the use of graph-based assessments. ^{36 , 37 , 69} These studies provide insights into students’ conceptual understanding, confidence levels, and metacognitive abilities, revealing common misconceptions and differences in field of science.

One of the early applications of a multi-tier test in this area was conducted by Klein et al. ³⁷ who examined representational competence in kinematics using a two-tier test. This assessment included multiple-choice combined with a confidence rating tier, allowing for the identification of representational misconceptions. The findings indicated that students exhibited higher confidence (over 80 %) when answering purely data-interpretation-based items compared to the overall confidence level across all items (mean confidence = 75 %). However, students were less confident when dealing with pictorial representations or a combination of pictorial and algebraic representations. Crucially, the study revealed that students often misjudged their ability to interpret graphs accurately. For instance, in graph-based items, even students who expressed high confidence performed no better than those who guessed, suggesting a disconnect between perceived and actual competence. Conversely, in non-graph-based items, students were more aware of their knowledge limitations and did not overestimate their abilities.

Further analysis of students’ performance and confidence judgements highlighted specific misconceptions in the interpretation of motion graphs. A common difficulty involved associating a motion schema with a corresponding velocity-time graph when velocity changes due to direction shifts. Likewise, students struggled to assign a correct motion schema to a given velocity-time graph. One prevalent misconception was the assumption that the direction of motion corresponds directly to the shape of the graph, leading to errors in interpretation, Additionally, students exhibited misunderstandings related to acceleration, particularly regarding terminal velocity and the influence of air resistance. The gap was observed in their interpretation of curve curvature, indicating fundamental misunderstandings of graphical representation. ^{36 , 37}

Building on the work of Klein et al., ³⁷ a later study by Klein et al. ³⁶ investigated graph comprehension in a broader academic context, comparing the abilities of physics and economics students in interpreting data from graphs. The study focused specifically on slope graphs and the area under a curve, using an instrument that combined a content tier with a confidence judgement tier. The results demonstrated that physics students outperformed economics students in tasks requiring data interpretation from graphs. Interestingly, while both groups exhibited similar overall confidence levels (mean confidence rating: 62 %), physics students demonstrated greater accuracy in evaluating the correctness of their answers.

This study also provided evidence that the type of graph related concept impacts metacognitive accuracy. Both physics and economics students were more precise in assessing their answers when dealing with slope graphs than when working with area-under-the-curve concepts. This suggests that students’ ability to evaluate their own understanding is influenced by the nature of the concept, reinforcing the findings of Klein et al. ³⁷ regarding the difficulties associated with more complex graphical formats.

While the two-tier and confidence-based approaches in the studies by Klein et al. provided insights into students’ misconceptions and confidence misjudgements. Turmanggor et al. ⁶⁹ expanded on this methodology by introducing a four-tier test to further diagnose conceptual misunderstandings in this area. This test included usual four-tier structure. ^{45 , 47 , 55} This extended multi-tier approach was specifically designed to detect misconceptions among prospective physics teachers in the domain of waves and wave motion. The results revealed several recurring misconceptions, such as misunderstanding wavelength, failure to differentiate between particle motion and wave motion, incorrect assumptions about external factors affecting wave properties.

Together, these studies demonstrate the utility of multi-tier tests in diagnosing conceptual understanding and metacognitive accuracy in data interpretation. These findings suggest that multi-tier testing can serve as an effective tool for identifying misconceptions in students’ data interpretation abilities not just their knowledge. ^{42 , 55 , 70}

For this reason, this study brings two novel approaches: it is aimed to disclose the neglected field of students’ engagement with graphs and tables delivering chemistry content and employed a more elaborated, multi-tier tasks to measure their skills.

4.1 Research procedure

This study is a part of a larger project focused on students’ ability to engage with learning materials containing non-textual components, whose phases are illustrated in Figure 1. This present study employed a mixed-methods approach that included multi-tier tasks designed to assess students’ data interpretation skills, their ability to justify their responses (RQ 1), and their reflection on their own performance (RQ 2).

Figure 1:

Design of the project.

Except for the information about students’ ability to engage with data in graphs and tables, the results will be used to select a sample of successful and unsuccessful students for further investigations into the graphs and tables reading strategies students employ.

4.2 Sample

The study sample consisted of 55 pre-service chemistry teachers from four universities in Czechia, all at the outset of their university studies. These included students from the Faculty of Education, Charles University (N = 20); the Faculty of Education, University of West Bohemia (N = 11); the Faculty of Science, Palacký University (N = 15); and the Faculty of Science, J. E. Purkyně University (N = 9). The test was administered at the beginning of the winter semester of 2024.

4.3 Research tool

This study used a four-tier Graphs and Tables Engagement (GATE) test previously piloted and adjusted by the authors of this study. ²¹ The GATE test consisted of nine tasks: three focused on interpreting tables and six on interpreting graphs in various forms (see Table 1). Each task consisted of four parts: a content tier, a confidence judgement tier for the answer, an explanation tier, and a confidence judgement tier for the explanation. To assess confidence, a 100 mm visual analogue scale was used. ^{21 , 71 , 72} An exception to this format were items 2A and 2B, which were presented in a two-tier structure as the response directly required an explanation. ⁷³ The average time required to complete the GATE test was approximately 40 min. The example of one item with all four tiers is shown in Figure 2.

Figure 2:

Example of GATE test item (4B) on solubility.

4.4 Data analysis

The closed-ended content tier was evaluated either as correct (1) or incorrect (0). The open-ended explanation tier was evaluated independently by two researchers according to the framework shown below.

Item 1

1. Question: Determine the overall air quality rating based on pollutant data in the table.

2. Correct answer: Satisfactory

3. Model explanation: Determine the air quality index for each pollutant from the table. The worst index value determines the overall rating. NO₂ has an index of 3 (satisfactory), worse than the others, so the total is satisfactory.

4. Correct response code: According to the worst measured value

5. Incorrect response code: Estimate; Repetition of the question; Average; Average + intermediate value; Average + incorrect interpretation of table data; Average + wrong calculation; Average + rounding; Majority, prevalence, ratio

Item 2A

1. Question: What evidence supports the conclusion that the rise in global temperature is affected by the increase in CO₂ emissions?

2. Model correct answer with an explanation: The overall trend in both graphs is upward, suggesting a possible relationship between global temperature and CO₂ emissions.

3. Codes: Included in the response evaluation.

Item 2B

1. Question: Which part of the graph does not support the conclusion that the rise in global temperature is influenced by the increase in CO₂ emissions and why?

2. Model correct answer with an explanation: For example, the period from 1940 to 1960, when temperatures increased rapidly, but CO₂ emissions remained stable.

3. Codes: Included in the response evaluation.

Item 3A

1. Question: Which vitamins in the tablet are below the Recommended Daily Intake?

2. Correct answer: Vitamin C and Vitamin K

3. Model explanation: Compare tablet content with RDI. Vitamin C (65 mg < 80 mg) and Vitamin K (70 μg < 75 μg) are below the recommended amounts, so tablets alone do not meet the RDI for these vitamins.

4. Correct response code: Compare RDI versus tablet content (identify C and K as below RDI); Cite specific values from table (e.g., 65 < 80; 70 < 75); State that all other vitamins meet or exceed RDI; General statement “RDI is higher than tablet content” (for C and K)

5. Incorrect response code: Unit-conversion confusion/failed conversion; Incomplete comparison (mentions only one vitamin or gives partial data); Vague/guessing/no justification

Item 3B

1. Question: Which of the three selected vitamins has an intake from the given foods that is below the RDI?

2. Correct answer: Vitamin E

3. Model explanation: Total intake from two oranges + 200 g liver is below 12 mg RDI for Vitamin E, so it is insufficient despite other vitamins being sufficient.

4. Correct response code: Accurate calculation & comparison for all three vitamins; Correct classification without numbers; Cites specific values and correctly sums; Logical explanation showing correct reasoning process

5. Incorrect response code: Misclassifies adequacy for any vitamin; Confuses units leading to wrong conclusion; Partial answer not covering all three; No explanation or unrelated reasoning; Only copies data from table without evaluation

Item 4A

1. Question: Which salt has the highest solubility at room temperature?

2. Correct answer: NaNO₃

3. Model explanation: At 25 °C, NaNO₃ has the highest solubility on the graph (∼100 g per 100 g water). At this temperature, its curve is the highest.

4. Correct response code: Identifies NaNO₃ as having the highest solubility at ∼20–25 °C; Cites approximate correct value from graph; Describes highest curve at relevant temperature; Compares salts and correctly selects NaNO₃; Uses correct reasoning from graph shape

5. Incorrect response code: Names wrong salt; Gives incorrect solubility value; Misreads temperature axis; Provides irrelevant or no explanation; Describes unrelated table data instead of graph

Item 4B

1. Question: Which salt(s) dissolve in ice-cold water (0 °C)?

2. Correct answer: NaCl, KNO₃, KCl

3. Model explanation: At 0 °C, these salts have solubility above 0 g/100 g water, so they dissolve in ice-cold water.

4. Correct response code: Identifies KClO₃ as the only salt with zero solubility at 0 °C; States that other salts have non-zero solubility at 0 °C; Refers to graph values above zero for the other salts; Describes curve position relative to zero at 0 °C; Explains difference between KClO₃ and other salts in terms of solubility at 0 °C

5. Incorrect response code: Names the wrong salt; Claims all salts dissolve or all have the same value; Misreads the temperature or mass axis; Gives irrelevant statement about curve shape without reference to 0 °C; Does not identify any salt or provide explanation

Item 4C

1. Question: Which salt’s solubility is most sensitive to temperature change?

2. Correct answer: KNO₃

3. Model explanation: Its solubility curve rises most steeply with temperature, showing greatest sensitivity to temperature change.

4. Correct response code: Identifies the substance (KNO₃) with the greatest increase in solubility as temperature rises; Recognises that KNO₃’s solubility curve has the steepest slope/largest change across the temperature range

5. Incorrect response code: Makes only a general statement about solubility increasing with temperature without identifying the correct substance; Misidentifies the substance or misinterprets the graph’s trends

Item 4D (NaCl)

1. Question: What happens if you add 48 g of NaCl to 100 g water at 40 °C?

2. Correct answer: Saturated with crystals

3. Model explanation: At 40 °C, solubility is ∼38 g/100 g water; adding 48 g exceeds solubility, so undissolved solid remains.

4. Correct response code: Correctly compares given masses with maximum solubility from the graph at 40 °C and concludes that all of the KNO₃ will dissolve while some NaCl will remain undissolved; Identifies from the graph that KNO₃’s solubility exceeds the given amount, while NaCl’s does not

5. Incorrect response code: Makes vague or unrelated statements about solubility without using the given quantities; Misinterprets or misreads the graph; Incorrectly concludes that both salts will fully dissolve or that neither will

Item 4D (KNO₃)

1. Question: What happens if you add 53 g of KNO₃ to 100 g water at 40 °C?

2. Correct answer: Clear solution

3. Model explanation: At 40 °C, solubility is ∼64 g/100 g water; adding 53 g is below the limit, so all dissolves.

In case of inconsistency, consensus by agreement was reached through discussion with the third author. Each response was assessed individually using elements of open coding. The researchers evaluated the correctness of the justification (1/0). Partially correct responses were not considered, as insufficient justifications indicate either a lack of knowledge or the ability to make appropriate connections.

In addition to the overall results obtained using standard statistical methods, item difficulty, the discrimination index, reliability as well as item correlations were calculated.

To evaluate how the GATE test items are effective in distinguishing between strong and weak students, the discrimination index (D) was used. It was calculated using the formula:

interpreted according to Mitran et al. [74] as follows:

1. D > 0.40 → Excellent discrimination (The item effectively distinguishes between strong and weak students)

2. 0.30 ≤ D ≤ 0.39 → Good discrimination (The item differentiates fairly well)

3. 0.20 ≤ D ≤ 0.29 → Acceptable discrimination (The item is useful but could be improved)

4. D < 0.20 → Weak discrimination (The item does not effectively differentiate between students)

5. D < 0.00 → Problematic item (Weaker students performed better than stronger students, suggesting possible issues with the item)

The students’ confidence judgement (CJ) was given on a 100 mm visual analogue scale with on end marked “not at all confident” and the other “completely confident” with correctness of their response either the content or the explanation. Using a ruler, the responses were transcribed to numbers ⁷¹ ranging from 0.00 to 10.00.

1. The data were analysed using the approach by Caleon and Subramaniam, ⁴⁶ widely used in later studies. ^{42 , 48 , 49 , 51 , 52 , 54 , 75} The metrics included: Content Score (CS) – the correctness of students’ response,

2. Explanation Score (ES) – the correctness of students’ explanation of the given response,

3. Total score (TS) – the product of the two aforementioned scores, where 1 is given to correct content and evaluation and 0 to the rest of the possible combinations,

4. Mean Confidence (CF) – the sum of all confidence ratings for the given tier(s), divided by the total number of responses,

5. Mean Confidence for Correct Responses (CFC) – the sum of confidence ratings for all correct answers, divided by the total number of students who provided them calculated separately for C, E and TS,

6. Mean Confidence for Incorrect Responses (CFW) – the sum of confidence ratings for all incorrect answers, divided by the total number of students who provided them,

7. Confidence Discrimination Quotient (CDQ) – indication of students’ ability to distinguish between what they know and what they do not know calculated as ((CFC – CFW)/SD) where SD is the standard deviation of all confidence ratings for the given tier. ⁵⁵

Higher values of CDQ indicate better metacognitive discrimination, meaning a person is good at distinguishing when they are right or wrong based on their confidence. Lower or negative values indicate poor metacognitive discrimination. In such cases an individual might be overconfident in incorrect responses or underconfident in correct ones. ^{54 , 76 , 77}

Reliability of the GATE test was examined using Cronbach’s alpha and Spearman-Brown split-half coefficient. The Shapiro–Wilk test (p < 0.05) indicated that the data were not normally distributed. Therefore, we used Spearman’s correlation to examine relationships between first-tier (CS) and third-tier (ES) scores, and between students’ results and their confidence judgments. To further identify the differences, higher-order statistics was used. Mann-Whitney U test was used to investigate the differences between the successful and unsuccessful task solvers with r to examine the effect-size interpreted according to Cohen. ⁷⁸

5.1 Psychometric evaluation of the test

The strong psychometric properties of the GATE test observed during the pilot testing ²¹ were confirmed on a larger sample of students from multiple universities. To specify them, reliability, correlation analysis, discrimination index and item difficulty were evaluated.

5.2 Students’ performance analysis (RQ1)

Table 3 summarises student performance across test items based on three measures: Content Score (CS), Explanation Score (ES), and Total Score (TS). CS reflects students’ ability to extract data from graphs and tables, ES evaluates their capacity to justify answers, and TS combines both dimensions.

On average, students achieved a Content Score (CS) of 0.66, indicating moderate success in retrieving data from graphs and tables. However, their ability to explain their reasoning was notably lower, with a mean Explanation Score (ES) of 0.51, and the combined Total Score (TS) dropped to 0.48. This decline suggests that many students struggled to justify their answers adequately, revealing important gaps in deeper understanding and interpretive skills.

Item-level analysis provides further insight into these patterns. The easiest item was 4C where students were asked to identify the most temperature-sensitive salt in a solubility graph, i.e., the steepest curve (CS = 0.98, ES = 0.60). Although nearly all students selected the correct answer, many explanations lacked key ideas such as curve steepness or axis relationships. This echoes concerns raised by Friel and Bright ⁷⁹ or Planinic et al. ⁸⁰ Similarly, items 3A (CS = 0.73, ES = 0.75) and 4A (CS = 0.89, ES = 0.62) involved straightforward comparisons of tabulated or graphical values and were among the highest-performing tasks. These findings align with previous research showing students perform well on basic extraction tasks. ^{81 , 82 , 83}

In contrast, more challenging tasks like Item 4D (CS = 0.29, ES = 0.15) required students to predict the outcome of mixing solutions based on solubility data, i.e., compare numerical values once they understood their meaning. This task revealed major challenges in inference-based interpretation and conceptual reasoning. ^{84 , 85 , 86} Similarly, Item 3B (CS = 0.78, ES = 0.49) showed a gap between retrieving values and justifying them. Students often misread table columns or failed to synthesise key information. ^{82 , 83}

In Item 3A, ES exceeded CS, indicating that students could verbally justify the correct approach but failed to select the right answer. This highlights the cognitive challenge of turning understanding into correct action. ^{47 , 87 , 88}

This gap between surface-level identification and deeper reasoning was evident across several items, supporting findings from Aydeniz et al., ⁸⁹ Espinosa et al., ⁴² and Yang. ⁹⁰ For instance, Item 4B (CS = 0.56, ES = 0.44) involved determining solubility at a specific temperature. While students often selected correct values, they struggled to justify them using concepts such as saturation or temperature dependence.

Students who gave correct explanations to Items 1 and 4A–C were significantly more likely to select the correct response. This reinforces the link between conceptual understanding and performance. ^{46 , 86 , 91}

Only a few items (3A, 4A, 4C) exceeded the 60 % TS threshold, confirming that students performed best on tasks with clear structure and minimal inference demands.

These findings indicate that multi-tier diagnostic testing is effective in exposing not only content knowledge gaps but also discrepancies in reasoning and self-awareness. While most items fell within the optimal difficulty range (0.3–0.7), Item 4C may be too easy and Item 4D too difficult, warranting revision to improve their discriminatory power.

In summary, students were reasonably competent in basic data retrieval and comparison, but faced clear challenges when tasks required them to explain, infer, or apply information in new contexts. Instruction that strengthens higher-order skills – such as graph reasoning, explanatory depth, and metacognitive self-monitoring – could make students more effective and confident in using tabular and graphical data in chemistry education. ^{39 , 85 , 86}

5.3 The role of confidence in student performance on multi-tier tests (RQ2)

7.1 Implications for teacher education and curriculum design

1. Embed explicit instruction on interpreting and reasoning with data-rich visuals across courses, rather than treating it as an assessment-only skill.

2. Incorporate multi-tier tasks (answer + explanation + confidence judgment) in assignments and exams to develop explanatory reasoning and metacognitive monitoring.

3. Train students in confidence calibration by having them predict and then reflect on their accuracy, reducing overconfidence in incorrect answers.

4. Use scaffolded tasks progressing from simple data retrieval to complex comparative and predictive reasoning to build competence step-by-step.

7.2 Implications for assessment practice

1. Adopt multi-tier assessments to separate content knowledge from explanation quality and confidence, revealing hidden weaknesses not visible in single-answer formats.

2. Use GATE results to inform targeted feedback, particularly for students who recall data but cannot justify it.

3. Analyse performance patterns to revise curricula, focusing on representations (e.g., multi-graph comparisons) that consistently cause difficulty.

7.3 Implications for research and policy

1. Adapt the GATE model to other STEM disciplines to expand understanding of visual data literacy across contexts.

2. Encourage policymakers and accreditation bodies to set explicit benchmarks for graph and table interpretation in teacher training standards.

3. Explore integration of GATE-style assessments with learning analytics tools (e.g., eye-tracking, digital response tracking) to provide adaptive feedback in real time.