- Title: Understanding Verbal Probability Expressions: How Secondary School Students Interpret Probability Language
- Authors: Ran Peleg, Rosalyn Hyde & Christian Bokhove
- Access the original paper here
- Watch a video overview:
Paper summary
Uncertain scientific information is often communicated with words such as “likely” or “rarely” in place of numbers. This study asked how secondary school students in England turn those words into numbers. 184 students from five schools completed an online questionnaire with 29 sentences, each containing a probability word, and moved a slider from 0 to 100% to show how probable they thought the event was. Students disagreed most on words at the extremes (“certain”, “impossible”) and on words for events that are more likely than not (“very likely”, “usually”). They agreed most on words near 50% (“maybe”, “sometimes”) and words for unlikely events. Older students gave more extreme and more consistent answers than younger ones. There was no significant difference between boys and girls on 28 of the 29 words.
If teachers remember one thing from this study, it should be…
Students in this study read probability words less strongly than adults do, and they disagreed with each other a lot. “Certain” averaged 83% and “impossible” averaged 13%. A phrase like “very likely” may not carry the meaning you intend. The paper notes that numbers are less open to interpretation.
*** PAPER DEEP DIVE ***
What are the key technical terms used in the paper?
- Verbal probability expressions (VPEs): words or phrases that describe chance, such as “likely” or “rarely”.
- Numerical interpretation: the percentage a student gives for a probability word.
- Between-student agreement: how closely different students’ percentages match for the same word.
- Benchmark: an agreed percentage range attached to a word.
What are the characteristics of the participants in the study?
The 184 students came from five urban state comprehensive secondary schools (ages 11 to 16) in the South of England. 119 were in Key Stage 3 and 65 in Key Stage 4; 103 identified as male and 74 as female. 204 responded; 20 were excluded for not engaging.
What does this paper add to the current field of research?
Research on how people turn probability words into numbers has mostly involved adults, and one earlier study suggested children match adults by about age nine. This study finds secondary students still differ from adults, and it offers word groupings based on how young people actually responded.
What are the key implications for teachers in the classroom?
- Put a number next to the word when the exact chance matters. Students’ answers for “very likely” averaged 74%, while published guidance from bodies such as the Intergovernmental Panel on Climate Change treats it as above 90%. “Almost certain” averaged 78%. If you tell a class that an outcome is “very likely”, add a percentage or a fraction so they know how strong a claim you are making.
- Spend lesson time agreeing what probability words mean. The authors point out that these words are rarely taught because teachers presume students already know them. You can borrow the study’s task as a starter. Put “unlikely”, “possible”, “probable” and “almost certain” on the board, ask students to write a percentage for each on mini-whiteboards, and look at the spread across the room before you settle on shared meanings.
- Check that students treat “impossible” as 0 and “certain” as 100%. In maths these two words have exact values, yet they were among the words students disagreed on most. Most students were close (the middle answers were 0 and 97%), but enough were not to pull the averages to 13% and 83%. Some of that may come from students not engaging with the slider, and the sentences were about everyday situations. It is still worth asking “what number goes with impossible?” when you introduce the probability scale, and following up with anyone who doesn’t say zero.
- Be careful with the word “possible”. Students placed it at about 53%, close to “maybe”, while “impossible” sat near the bottom of the scale. So a student who hears “it’s possible the experiment will fail” may take that as roughly an even chance. If you mean “it could happen but probably won’t”, say exactly that.
- Expect younger students to be less sure. Key Stage 4 students gave more extreme answers than Key Stage 3 students and agreed with each other more, and adults in an earlier study went further again. With Year 7 and 8 classes, allow extra time for discussing these words, and don’t assume a phrase that works with Year 11 will be heard the same way lower down the school.
- Agree a short list of words as a department. The authors sort the 29 words into five groups based on students’ answers: certain not to happen (“never”, “impossible”), more unlikely than likely (“unlikely”, “rarely”, “doubtful”), about even (“maybe”, “possible”, “sometimes”), more likely than unlikely (“likely”, “probable”, “usually”) and certain to happen (“always”, “certain”). Words in the same group often scored almost identically. “Likely”, “usually” and “generally” all averaged about 65%. Choosing one or two words per group and using them consistently across maths and science gives students fewer meanings to guess at.
Why might teachers exercise caution before applying these findings in their classroom?
This was a one-off questionnaire in five schools in the South of England, and the authors had limited means of checking students engaged. Each word appeared in only one sentence, which may have shaped answers. Students’ language backgrounds weren’t recorded, and the adult comparison comes from a Dutch study.
What is a single quote that summarises the key findings from the paper?
“Results show that VPEs indicating extreme certainty or moderate probability elicited the most variability, while those near 50% or suggesting low probability showed greater agreement. Older students demonstrated more consistent and polarized interpretations, a trend strengthened when comparing our data with that of adult audiences.”
