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Running head: Knowledge Threshold
1
How Much Knowledge is too Little?
When a Lack of Knowledge Becomes a Barrier to Comprehension
Tenaha O’Reilly
Zuowei Wang
John Sabatini
Educational Testing Service
Suggested citation:
O’Reilly, T., Wang, Z., & Sabatini, J. (2019). How much knowledge is too little? When a lack of
knowledge becomes a barrier to comprehension. Psychological Science, 30(9), 1344-1351.
https://doi.org/10.1177%2F0956797619862276
*This is final accepted version from the authors, which may have slight differences from the final
published version.
Running head: Knowledge Threshold
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Abstract
Have you ever found it difficult to read something due to your lack of knowledge on the topic?
We investigated this phenomenon with a sample of 3,534 high school students who took a
background knowledge test before working on reading comprehension tasks on the topic of
ecology. Broken-line regression revealed a knowledge threshold such that below the threshold
the relationship between comprehension and knowledge was weak (
=.18), but above the
threshold a strong and positive relation emerged (
=.81). Further analyses indicated that certain
topically relevant words (e.g. ecosystem, habitat) were more important to know than others when
predicting the threshold, and these key words could be identified using natural language
processing techniques. Collectively, these results may help identify who is likely to have a
problem comprehending information on a specific topic, and to some extent, what knowledge is
likely required to comprehend information on that topic.
Key words: background knowledge, reading comprehension, knowledge threshold hypothesis,
broken-line regression, content area reading
Acknowledgement: The research reported here was supported by the U.S. Department of
Education Institute of Education Sciences, Award No. R305A150176 & R305F100005, to
Educational Testing Service. The opinions expressed are those of the authors and do not
represent views of the U.S. Department of Education or Educational Testing Service.
Running head: Knowledge Threshold
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How Much Knowledge is too Little? When a Lack of Knowledge Becomes a Barrier to
Comprehension
While research has shown that background knowledge can facilitate reading
comprehension (e.g. Ahmed et al., 2016; Elbro & Buch-Iversen, 2013; Gough, Hoover, &
Peterson, 1996; Ozuru, Dempsey, & McNamara, 2009; Shapiro, 2004), much less is known
about precisely how much knowledge is necessary to understand a text, and whether there is a
specific amount of knowledge required before understanding is compromised. In this study, we
explore whether we can quantitatively identify a point below which a lack of students’
background knowledge impedes their understanding, and above which background knowledge
starts to facilitate comprehension. We call this point the knowledge threshold. We also explore if
it is possible to predict whether students fall below or above the threshold from their basic
knowledge of topically-relevant keywords, many of which do not appear in the texts they read. If
successful, this approach would be useful for helping identify who may have difficulty
understanding a text on a particular topic.
Why Knowledge Matters? Theoretical Perspectives
Background knowledge is critical in many models of reading (Cromley & Azevedo,
2007). In the Construction Integration Model (Kintsch, 2004), knowledge is necessary to form a
“situation model”, the reader’s interpretation of the text, by integrating background knowledge
and the text contents. Activation models such as the resonance model (Myers & O'Brien, 1998)
highlight the importance of background knowledge for reading comprehension. The text not only
activates words and concepts in the readers’ mind that are directly mentioned in the text, but also
words and concepts that are not directly mentioned, but highly relevant to the concepts in the
text. The activation of knowledge can have immediate impact on comprehension, especially
when the text is closely related to what one already knows (Cook & O'Brien, 2014). When a
Running head: Knowledge Threshold
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reader knows more about a topic, reading texts on the topic would result in more activation of
related knowledge (or knowledge schema) compared to a reader who knows less, and this
contributes to differences in comprehension between high and low knowledge readers through
mechanisms such as inference making (McNamara & O'Reilly, 2009).
The Existence of Thresholds in the Literature
Researchers have suggested that readers need a minimal level of decoding and word
recognition skills (Duncan et al., 2013; Juul, Poulsen, & Elbro, 2014; Wang, Sabatini, O'Reilly,
& Weeks, 2018) or general vocabulary (Hsueh-Chao & Nation, 2000; Laufer, 1989; Schmitt,
Jiang, & Grabe, 2011) to read and understand text at a sufficient level. It is estimated that people
need to know the meaning of between 95-98% of the words in text in order to comprehend it
well (Hsueh-Chao & Nation, 2000; Laufer, 1989; Schmitt et al., 2011). Research has shown that
English language learners need to have a vocabulary size of over 3000 in order to achieve
acceptable performance on a comprehension test (Laufer, 1992). The consequences of falling
below a threshold are striking. Fifth through tenth grade students who fell below a decoding
threshold showed little growth (< .05SD per year) compared to peers who were above the
decoding threshold (about 0.2SD per year; Wang et al., 2018).
It is important to note that the above studies focused on exploring whether there are
specific decoding and vocabulary thresholds for reading comprehension. A lack of knowledge,
as reflected by not knowing important keywords on a topic, will likely create difficulties in
understanding topical texts similar to those caused by a lack of general vocabulary, thus resulting
in a threshold that is domain specific, that is, the knowledge threshold.
The idea of a knowledge threshold is implied in the stage Model of Domain Learning
(Alexander, 1997, 2003; Alexander, Jetton, & Kulikowich, 1995), which provides a framework
Running head: Knowledge Threshold
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to understand how people gain expertise in a domain as they accumulate domain knowledge. On
the path to achieve expertise, the learner needs to construct a knowledge framework that
provides the scaffold for subsequent learning. In doing so, they move from the “acclimating
stage” to the “competent stage” (Alexander, 1997). Specifically, their knowledge transitions
from fragmented to well-structured, which helps the learner become skilled in attending to
important information for more efficient learning. This transition implies that the role of
background knowledge undergoes a qualitative change as students develop knowledge in a
domain. Because a large part of domain learning relies on reading and comprehending new
materials, it also implies that the relation between background knowledge and reading
comprehension might change during this transition.
Measuring Knowledge with a Topical Vocabulary Task
While previous studies have mostly used factual statements in the form of multiple-
choice questions to evaluate background knowledge, the development of these items often
requires expertise in the topic and is time-consuming. For example, Cromley and Azevedo
(2007) had to read the passages in a reading comprehension test and identify the background
knowledge that could be important for students to know in order to understand the content. They
then developed items around the identified background knowledge. Finally, they also developed
distractor items. Even after all these procedures, not all items turned out to be usable because
some items were too easy or too difficult. These complications limit the assessment of
background knowledge.
In this paper, we propose a different method to measure background knowledge.
According to the resonance model, one’s knowledge on a topic can be evaluated by examining
one’s knowledge activation when introduced to a topic. To elicit knowledge activation, we
Running head: Knowledge Threshold
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present students with a list of words--some related to the topic and others unrelated--and have
them decide whether each word is related to the topic to be read. The selection of topically
related key words was achieved through using a natural language processing database, which
was generated by calculating co-occurrences of words in a corpus of over one billion words of
natural texts (Deane, 2012). The database provides a topical association index for each keyword
in a given topic. Words that occur more often in a topic generally have higher topical association
index. We also selected as distractors a similar number of topically irrelevant words that matched
in general word frequency (in the overall English language) of the topically relevant words.
Consistent with the resonance model, which posits a connection between knowledge activation
and comprehension (Myers & O'Brien, 1998), we predict that students’ performance in such a
keyword recognition task would be correlated to comprehension.
In short, we ask two research questions: first, whether we could identify a knowledge
threshold below which comprehension is limited and not predicted by knowledge, and above
which the two constructs are correlated; second, whether knowledge of a few topically-related
keywords identified through natural language processing could be used to identify who is below
the knowledge threshold.
Method
Participants
Participants were 3,534 grade 9-12 students from 37 schools in two states in the West and
Midwest of the United States. The data was collected as part of a separate, multi-school study
conducted by colleagues of ours in another organization. Our organization was responsible for
the design, administration, scoring, and psychometric analyses of the measures. Consequently,
the sample size was determined by the needs of this allied study. Due to agreements with the
Running head: Knowledge Threshold
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schools, we do not have individual demographic information available. However, we were able
to obtain demographic information for the whole recruitment pool from which our participants
were drawn. For the whole recruitment pool of 14,747 students, 49% were female; 14% were
English language learners; 56% were eligible for free or reduced-price lunch and 61% were
nonwhite students.
Materials
Comprehension was measured with a scenario-based assessment on the topic of
ecosystems (O’Reilly, Weeks, Sabatini, Halderman, & Steinberg, 2014). The reading
comprehension test had 34 comprehension items (34 total points). Reliability as reflected by
Cronbach’s alpha calculated from the current sample was .88. Items measured single text
understanding such as the ability to recognize and provide accurate paraphrases, the ability to
summarize text, and the ability to recognize opinions and incorrect information. The reading
comprehension test also contained items that measured students’ ability to apply what they read
across multiple texts and reason about scientific content. This included items that required
students to interpret data, apply classifications to given scientific abstracts, and apply scientific
definitions to given vignettes. Thus, the measure included some traditional style reading items, as
well as items that measured students’ ability to reason and apply the information they read. The
length of the two primary content passages in the reading comprehension test were 814 and 304
words, with Flesch Kincaid (Kincaid, Fishburne Jr, Rogers, & Chissom, 1975) grade levels of
9.8 and 15.4 respectively. The respective text complexity grade level estimates using the
TextEvaluator® system (Sheehan, Kostin, Napolitano, & Flor, 2014) were 10 and 12 which was
within the grade range of this sample.
Running head: Knowledge Threshold
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Before students worked on the reading comprehension tasks, they were also given a
background knowledge measure with two types of items. The first was a topical vocabulary task
(44 items). Students saw a list of keywords and they were asked to indicate whether each
keyword was either related or unrelated to the topic of “ecology”. Only 9 of the 26 topical words
in the topical vocabulary task were explicitly mentioned in the texts. A topical association index
was obtained for these keywords from the natural language processing database provided by
Deane (2012). The second type of item tested students’ factual knowledge related to the topic
ecosystems, in the form of a multiple-choice test (13 items). The analyses below were performed
with both topical vocabulary and factual multiple-choice items as the background knowledge
measure. Using topical vocabulary items alone as the background knowledge measure yielded
similar results. For both item types, students were told that their performance on these items
would not count towards their final score, and that they were allowed to select an “I don’t know”
option, if they decided that they did not know the answer to that question. For the purposes of
this paper, the “I don’t know” option was scored as incorrect. Reliability of background
knowledge items as reflected by Cronbach’s alpha was .91.
Because the topical vocabulary task we used is a vocabulary measure, questions arise
regarding whether the knowledge threshold identified with this measure is actually a result of a
general vocabulary threshold as discovered by Laufer (1989) as opposed to a threshold that is
realted to the topic of the texts. To deal with this, a small subset of all the students (n=303) also
completed a history vocabulary test that included 44 items. In the test, students saw lists of words
and they needed to indicate if each word was related to the topic of the history of U.S.
immigration in the 19th and early 20th centuries. Thus, the format of this history vocabulary test
Running head: Knowledge Threshold
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was exactly the same as the topical vocabulary test used on the topic of ecology. Reliability of
these history vocabulary items calculated from the 303 students was .88.
Procedure
Students took the reading comprehension test along with the background knowledge
section online during their regular 55-minute class period. Selected response items were
automatically scored, and constructed responses were manually scored by two trained raters
following a rubric developed for these items. When the two raters disagreed in their initial
scoring, they discussed to reach an agreement before providing a final score. There were four
constructed response items, including three summary items and one paraphrase item. Each of the
three summary responses was scored on a 0-3 scale. The paraphrase response was given a binary
score of 0 or 1. To evaluate inter-rater agreement, 300 student responses on each of the four
constructed response items were independently scored by the two raters. For the summary items,
72% of the 300 responses were given the exact score by both raters, and on another 21% of the
responses the two raters only had 1 point score difference, thus adjacent agreement was 93%. For
the paraphrase item, the two raters provided the exact score on 86% of all responses. For the
purpose of final score calculation, each summary score was rescaled to a one-point scale by
dividing the manual score by three, so that each item in the reading comprehension test task was
worth one point.
Analysis
To answer our first research question about the identification of a knowledge threshold,
we used broken-line regression (Adams, 2014; Muggeo, 2008). Broken-line regression is a
statistical method that identifies a changepoint in linear regression and it provides significance
level and confidence interval for the changepoint (i.e. threshold). Instead of estimating one
Running head: Knowledge Threshold
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regression slope as in linear regression, broken-line regression estimates two regression slopes,
divided by the identified changepoint. This method has recently been used in educational
research (Wang et al., 2018) and could be useful for making future binary decisions (e.g., teach
background knowledge before reading or not).
To answer our second research question regarding whether students’ knowledge
threshold status could be determiend by their recognition of topical keywords, we selected the
six keywords that had the highest natural language processing topical association index and used
performance on these six keywords to predict students’ knowledge threshold status using logistic
regression. This was to show the specificity of the topical knowledge and the utility of using
natural language processing topical assocation index to select keywords to test students’
knowledge threshold status.
Results
Students’ background knowledge and reading comprehension were scored separately.
Mean score on the background knowledge questions was 38, SD=10, range [0, 54]. Mean score
on the reading comprehension section was 15, SD=7, range [1.33, 34]. To improve the
interpretability of results, these scores were also transformed to Z-score (mean=0, SD=1) before
we performed broken-line regression.
Broken-line regression (Adams, 2014; Muggeo, 2008) confirmed that the relation
between background knowledge and reading comprehension was affected by a knowledge
threshold at a background knowledge score (standardized scores in parentheses) of 33.5 (-.40),
p<.01, with 95% confidence interval [29, 36] ([-.79, -.16]). When predicting reading
comprehension with background knowledge, the regression slope was relatively flat B= .12 (
Running head: Knowledge Threshold
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=.18) with 95% confidence interval [.09, .15] ([.13, .23]) for students having a knowledge score
below the threshold, and became significantly steeper B= .56 (
=.81) with 95% confidence
interval [.51, .61] ([.73, .89]) for students whose knowledge score was above the threshold
(Figure 1). Eighty-seven percent of students in the below threshold group (n=835) had a
comprehension score lower than 15, which was equivalent to the grand mean comprehension
score across all students in this sample. On the other hand, 91% of students (n=1356) whose
comprehension score was above the mean also scored above the knowledge threshold. These
results supported the idea that knowledge does not play the same facilitative role to
comprehension when it was below vs. above the threshold.
To evaluate whether the threshold was specific to knowledge related to the reading topic,
i.e., ecology terms, the broken-line relation was replicated with the subset of 303 students who
also took the history topical vocabulary test, controlling for this history vocabulary. For this
subsample, performance on the background knowledge section was M=38, SD=11; performance
on the comprehension section was M=15, SD=7, almost identical to the whole sample, thus
representative of the whole sample. Using this subsample, a knowledge threshold was identified
at background knowledge (using ecosystems background knowledge) score of 30 (-.73), p<.01,
with 95% confidence interval [22, 40] ([-1.51, .16]). When students’ background knowledge was
below the threshold, their background knowledge failed to predict comprehension B=0 (
=0)
with 95% confidence interval [-.13, .13] ([-.26, .26]); when students’ background knowledge was
above the threshold, background knowledge was positively related to comprehension B=.51 (
=.79 with 95% confidence interval [.37, .64] ([.63, .85]). Importantly, this broken-line relation
remained significant even after controlling for the effect of history vocabulary: the threshold
Running head: Knowledge Threshold
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remained at background knowledge=30 (-.73), p<.01, with 95% confidence interval [21,41] ([-
1.52, .25]). Thus, the threshold has a topic specific component.
Figure 1. Non-linear relation between background knowledge and reading comprehension;
shading of the dots reflects the number of overlapping cases.
As another test of the specificity of the threshold to relevant ecology knowledge, we
identified which keywords were most predictive of students’ knowledge status (above vs. below
threshold). We calculated the correlation between student’s performance on each keyword and
the student’s knowledge threshold status. The keywords differed in their predictability to
students’ knowledge threshold status (Figure 2). The most predictive keyword was
“ecosystems”, which explained almost 30% of variance in students’ knowledge threshold status.
Running head: Knowledge Threshold
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In contrast, other keywords were less predictive of students’ threshold status. For example, the
recognition of “densities” or “fauna” explained less than 3% of variance in students’ threshold
status.
Not surprisingly, many of the highest ranking topical keywords were also mentioned in
the texts of the reading comprehension task (Figure 2, marked with asterisk). The correlation
between students’ comprehension and performance on the keywords that were mentioned in the
reading texts was r(3532) = .36, p<.01, with 95% confidence interval [.33, .39]; the correlation
between students’ comprehension and performance on the keywords that were not mentioned in
the reading texts was r(3532)=.38, p<.01, with 95% confidence interval [.36, .41].
Figure 2. Threshold status variance explained by topical keywords. Keywords marked with an
asterisk (*) appeared in texts in the reading comprehension task.
0%
5%
10%
15%
20%
25%
30%
35%
ecosystem*
habitat*
climate*
species*
environment*
atmospheric
aquatic*
freshwater
biodiversity*
lakes*
streams
tropical
pollution
extinction
biotic
groundwater
temperate
vegetation
biomass
precipitation
trophic
predation
terrestrial
bioremediation*
densities
fauna
Threshold Variance Explained
Running head: Knowledge Threshold
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Interestingly, the ranking of keywords based on how much variance of threshold status
they explained (Figure 2) converged well with the ranking of these words based on how likely
these keywords occur in natural texts on the topic, the latter of which was reflected by the topical
association index provided by Deane’s (2012) database. The correlation of the two rankings
(Spearman correlation) were r(23)=.65, p<.01, with 95% confidence interval [.34, .83]. After
controlling for general word frequency, the two rankings were still significantly correlated,
r(22)=.62, p<.01, with 95% confidence interval [.29, .82]. Thus, a measure of topical association
that accounts for how frequent a word is in a given topic, is more predictive of threshold status
than a measure based on how frequent a word appears in the general language. In other words,
the threshold has a topic specific component beyond general vocabulary.
To evaluate the utility of the topical association index in identifying “must-know”
keywords, we further compared both threshold groups’ (above vs. below knowledge threshold)
performance on a few keywords that had the highest topical association index to determine how
many keywords we would need to reliably identify students who might be below the knowledge
threshold. After some exploration by varying the number of the keywords, we found that by only
using the top six keywords that had the highest topical association, we were able to correctly
identify 74% of the students who were below the knowledge threshold, with 26% false alarm
rate. While the above-threshold group had an average accuracy of 95% on these items
(SD=10%), the below-threshold group’s mean performance was only 64% (SD=33%). Thus, it
appears that knowledge on these six words is critical for students to stay above the knowledge
threshold.
Running head: Knowledge Threshold
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Discussion
Our results support the knowledge threshold hypothesis. Using broken-line regression,
we were able to identify a quantifiable point (59% correct on the knowledge test) at which there
was a qualitative change in the relationship between background knowledge and reading
comprehension. Below the threshold, the slope was relatively flat (B=.12), but above the
threshold, increases in the level of a student’s knowledge were strongly associated with increases
in comprehension (B= .56). Importantly, the knowledge threshold seems to be specific to the
knowledge on the domain of texts to be read. After controlling for the effect of history
vocabulary in the subset of 303 students, a domain different from the reading comprehension
texts, the knowledge threshold remains significant. The existence of this threshold suggests that
students might need a minimum amount of knowledge of a topic to comprehend a text about that
topic. Eighty-seven percent of the students who fell below the threshold scored below the mean
on the comprehension assessment, whereas 91% of the students whose comprehension score was
higher than the mean were above the knowledge threshold. Thus, there seems to be a qualitative
change in the relationship between background knowledge and comprehension, this point can be
quantifiably identified, and it is associated with different comprehension profiles.
We also found that some words were more predictive of exceeding the knowledge
threshold than others. For instance, the words ecosystems, habitat and species are more
predictive than other words such as bioremediation, densities and fauna. Interestingly, these
more predictive words were also among the highest topically associated words as reflected by
natural language processing-based statistics (Deane, 2012). The above threshold group achieved
near ceiling performance (i.e. 95% correct) on six of the keywords that had the highest topical
association index. This suggests that these words might be “must know” words for students in
Running head: Knowledge Threshold
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order to perform above the knowledge threshold. Indeed, simply using students’ performance on
these six words, we were able to correctly identify the great majority of students who were below
the knowledge threshold with an acceptable false alarm rate (26%).
The results lend some support to activation models of reading comprehension such as the
resonance model (Myers & O'Brien, 1998), which posits that the words in the text activate
information described previously in the text as well as relevant background knowledge not
included in the texts. Indeed, 17 of the 26 topical words in the knowledge measure were not
mentioned in the text. The fact that these associated but not mentioned words were predictive of
students’ comprehension (r=.38, p<.01) supports the knowledge activation process of the
resonance model (Myers & O'Brien, 1998). In other words, not only activation of keywords that
are explicitly mentioned, but also those that are not mentioned in the texts are predictive of
comprehension performance.
The current results have implications for instruction. Identifying which students may
have a problem reading a given text on a particular topic is informative for teachers. While there
are many reasons why a student may not comprehend, ranging from weakness in decoding
(Wang et al., 2018), vocabulary (Hsueh-Chao & Nation, 2000; Laufer, 1989; Schmitt et al.,
2011), or inference making (Cain, Oakhill, Barnes, & Bryant, 2001), the current study explored
another possibility: limited background knowledge. Knowledge measures such as the one
described here, would not take too much time (less than 3 minutes) from instruction or reading.
We were able to correctly identify the great majority of students who fell below the threshold
based on the six most frequently seen keywords for the topic. Having a quick measure of
students’ knowledge might be able to reveal the transition where knowledge starts to facilitate
reading comprehension. In terms of the model of domain learning, such a transition may signal a
Running head: Knowledge Threshold
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possible shift from beginning (acclimating stage) to more capable levels of knowledge
development (competent stage). More importantly, identifying those students who fall below the
threshold is important as they are likely to have comprehension difficulties and should be
targeted for additional instruction.
Limitations
While the results of the current study are encouraging, there are a number of limitations.
First, although the comprehension assessment used in this study included a range of source texts,
they were all on the same general topic (ecology). Future research is required to determine
whether these results generalize to different topics or domains. Second, while we used two item
types (topical vocabulary choice and factual multiple choice), future research should employ
other item types as measures of knowledge to examine the generalizability and robustness of the
threshold hypothesis. The position of the knowledge threshold may depend on the knowledge
measure used. For example, an easier knowledge test might result in the threshold identified at a
higher knowledge score, but the nonlinear relation between knowledge and comprehension
should still be observed. This should be examined in future studies. Third, future research should
explore whether the effects observed in this study transfer to different comprehension
assessments (e.g., traditional reading comprehension test), or varying levels of text complexity.
Fourth, future studies should examine the knowledge threshold hypothesis in different
populations (e.g. middle school or college students). In short, while the precise numerical value
of the threshold may change for different populations or materials, future research should explore
whether an identifiable threshold may limit comprehension under different conditions.
Running head: Knowledge Threshold
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Conclusion
Measuring students’ background knowledge before they read a text may reveal which
students are likely to have a reading comprehension problem and which may need to build
additional background knowledge before reading. But how much knowledge is too little? The
answer to this question is complex but is likely discernable with an empirically identifiable
knowledge threshold.
Running head: Knowledge Threshold
19
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