There is concern in some circles that scores on standardized mathematics and literacy tests are declining.1 This fear has raised questions about the importance of teaching the basics and the impact of inquiry learning. Some critics attribute the perceived dip in test results to the recent emphasis on “inquiry teaching.”2 Media reports frequently present a polarized debate between two camps: “back to basics” versus “inquiry or discovery learning.”3 The resulting impression that educators must choose between one or the other is the kind of exaggerated position that often propels the educational policy pendulum to oversimplify and overreact. In this article, we seek to explain how learning the basics and inquiry teaching can be reconciled, and to document the effects of doing so.
In education, we frequently get ourselves into difficulty by treating complicated concepts as though they are “black or white” labels.4 Certainly this has been true of the basics versus inquiry debate. But there is nothing inherently contradictory about these two concepts.
Before looking for the diversity within these notions, let’s agree on the defining features of each of these terms:
- Teaching the basics: a belief that there are core ideas and facts that every student needs to master.
- Inquiry: “to inquire” is essentially to pursue an answer to a question that is not already known by the individual. In other words, students’ answers to an inquiry question will require some examination or investigation on their part.
With the rote practice method, students repeat an action time after time exactly as before, without necessarily understanding why each step must be done as directed. Instructions are offered as recipes to follow verbatim. This is how many of us may have learned the standard algorithms for most mathematical operations. A teacher we work with recently recounted that she was taught to divide fractions by memorizing the phrase “Tis not for me to question why, just invert and multiply.” With an inquiry approach, instruction and repetition may still feature. Instruction, however, is intended to provide a platform from which students can explore options and variations. The repetition is mindful in that students are imagining possibilities, observing the effects of each trial and making further critical adjustments as needed. In mathematics and other highly skill-based subjects, we have found this a more effective way to empower students with the “basics” for a 21st century arena where conditions are changing and unpredictable, where creativity and innovation are key to success, and where high levels of complex performance are needed. Properly implemented, inquiry is a powerful method to deepen student understanding of the curriculum, increase student engagement and develop competency in critical, creative and collaborative thinking.
One of our earliest documented experiences with these two approaches occurred while working with mathematics teachers in India. By Grade 6, students in one of the schools we were assisting had had two previous years of memorizing the formula for calculating profit and loss, and applying the formula as prescribed in countless problems. Despite repeated drill, many students were unsuccessful with the problems and most didn’t really understand what they were doing as they applied the formula. With support from our team, teachers created several scenarios of simple commercial operations where the profit or loss was to be calculated. Working in groups, students were asked to figure out the answers as best they could, and then to formulate a sentence using as few words as possible (or only symbols if they were able) to represent all of the elements they needed to consider and the relationship among the variables. Students tested their draft formulae with various problems to see if they worked in each case, and shopped their version around to the other groups to see if they could arrive at more complete, reliable and concise formulations. In reflecting on this experience in a learning log, one student remarked that while this was the third time he had been exposed to the topic, for the first time he understood what he was doing. He wasn’t worried that he would forget the formula at exam time, because now that he understood it, the formula was more memorable to him. He went on to explain that even if he did happen to forget the formula, he was confident he could reconstruct it because of the recent learning experiences.
Criticisms of inquiry approaches
While the previous example suggests that students can figure out some formulae on their own, critics will counter that students can’t possibly discover everything we want them to learn. We agree that expecting students to invent everything for themselves is inefficient and unrealistic. In fact, this is where our approach differs from “discovery learning.” If the teachers in the situation described above thought that solving the profit and loss problems and generating original formulae would be too difficult or time-consuming for their students, they could have shifted the focus of the inquiry by providing students with possible formulae to consider. In this case, the inquiry would be to determine which version of the supplied formulae would be the best to recommend for use by students at this particular grade level. As this modification suggests, inquiring into a topic does not require that students re-invent everything for and by themselves. On the other hand, inquiry learning does require some investigation; students can’t simply be expected to accept answers.
A second criticism leveled against inquiry approaches is the suggestion that many of the basics can be acquired only through drill and memorization. While we agree that students should be expected to master and remember many basic facts, it is important to recognize that drill is one form of practice, and memorization is one way to remember something. In our view, the issue is not whether students need to remember and master basic facts, but how best to help them satisfy this need. It is well known that students are more likely to remember something if they understand what they are being asked to learn. Consider the following sentences:
- My best friend is Peter Pan.
- Gy hepl gfiern iv Qelef Qaw.
Most will agree that the first sentence would be easy to remember, whereas the second sentence would be very difficult. This is true even though all the vowels are identical and there is the same number of words and letters in both sentences. The point being made here is the same one that the student from India was making about remembering the formula for profit and loss. He had struggled to remember the formula that he had been taught (and expected to memorize) over the two previous years because he didn’t understand what he was learning. Yet, as soon as he understood the formula, he became more confident in his ability to remember it. The more we help students comprehend what we want them to remember, the less students need to learn by memorization.5 Before expecting students to memorize number facts such as “5 + 5 = 10” we should ask them to visualize this fact, manipulate objects to demonstrate it and predict the result to help them understand its meaning.
The more we help students comprehend what we want them to remember, the less students need to learn by memorization.
Not only must students remember many basic facts; there is much that students need to learn that can be mastered only by repetition. But what is the best way to structure repetition? Recognizing that drill is but one form of practice helps to address this question. Some drill may be useful from time to time, but without meaning, repetition is unlikely to increase understanding and fluency. On the other hand, mindful practice guided by ongoing questioning and testing is a more effective and engaging form of repetition. Instead of “drill” worksheets where students use rote memory to solve multiple problems involving a basic operation, a more productive strategy is to ask students to detect the various kinds of problem types present in the worksheet (for example, distinguishing subtraction problems involving regrouping of none, one or more placeholders) and to solve one example of each type. Students would repeat this process with other worksheets until they could quickly identify a wide range of problem types across all of the four basic arithmetic operations. This kind of mindful practice conducted in a spirit of inquiry is more likely to develop genuine mastery in mathematics.
As we hope these examples make clear, “learning the basics” and “inquiry,” properly understood, can be complementary components of a successful educational program.
Adopting robust inquiry that nurtures and builds from the basics (what some call moving “forward with the basics”) can lead to improved and often spectacular results. We base these conclusions on 20 years of experience working with approximately 80 districts and 200 schools involving over 125,000 teachers worldwide.
Our work with teachers ranges from a few face-to-face sessions over the course of a year to ongoing sustained professional learning programs. We focus on helping teachers problematize the content of the curriculum using a critical inquiry approach. We support teachers in embedding critical thinking questions into every aspect of their teaching, and then model how to systematically introduce and practice the “tools” needed to successfully complete each task.
Qualitative data and anecdotal evidence repeatedly suggest positive results. As well, a number of schools with improved results on standardized tests in areas such as literacy, mathematics and student engagement have attributed these results, in large measure, to our work with them. Typically they credit our approach with deepening student understanding and increasing student engagement. The extent of improvement is often significant. For instance, one Ontario school reported a 54 percent increase in combined Grade 3 Reading and Writing scores on EQAO tests.6 The same school saw a 75 percent increase in Grade 6 Mathematics in procedural and conceptual understanding. A group of four elementary schools in a partner district reported increases of 15 percent in the number of Grade 3 students and an increase of 36 percent in the number of Grade 6 students achieving levels 3 (grades B or B+) or 4 (grades A- to A+) in Mathematics.
Our approach has shown positive results with students from across the spectrum of ability. For example, a school with students considered to be at high social risk reported a 168 percent increase in the number of Grade 6 students reporting that they liked math most of the time. Not surprisingly, the number of those students achieving at or above the provincial standard on EQAO tests increased from 15 percent to 50 percent during the same period. In another school with a challenging student population, 85 percent of Grade 6 students were performing at or above standard in Mathematics after working with our team. In the previous year, only 49 percent of the Grade 6 students had reached this level.
Our results are consistent with a larger study involving 5,000 students in 117 Chicago-area schools.7 Newmann and his team found that providing Grades 3, 6 and 8 students with “challenging intellectual work” resulted in greater-than-average scores on standardized measures of basic numeracy and literacy skills. These researchers found that students in disadvantaged as well as mainstream classrooms benefited from these challenging tasks. In fact, students with low prior achievement levels in Mathematics experienced greater gains from this approach than did students with high prior achievement levels.
It would be unfortunate if the idea of inquiry per se were discredited merely because some interpretations of the concept are ineffective. This regrettable situation would be further compounded if support for inquiry were replaced by the very approach to teaching the basics that was dismissed in the past because it was ineffective in preparing students for an increasingly complex world. We believe that a rigorous critical inquiry that moves “forward with the basics” offers a fruitful middle ground that draws on the best of both approaches and steers clear of the less desirable extremes. While this article may raise as many questions as it resolves, we hope it will foster thoughtful debate about the role of the basics and inquiry in 21st century classrooms.
En Bref: Les préoccupations concernant les résultats aux épreuves normalisées ont soulevé des questions concernant l’importance d’enseigner les éléments de base et l’impact de l’apprentissage par l’enquête. Souvent, l’impression que les éducateurs doivent choisir entre « le retour aux savoirs de base » et « l’enseignement par l’enquête ou la découverte » entraîne le pendule des politiques éducatives vers des simplifications et des actions extrêmes. Cet article clarifie les interprétations contradictoires possibles de l’enseignement des éléments de base et l’enquête. Il examine comment il peut s’agir de composantes complémentaires d’un programme éducatif fructueux. Les auteurs documentent l’efficacité de cette approche par les résultats favorables des mesures normalisées de réussite et d’engagement des élèves de diverses écoles où le TC2 (Critical Thinking Consortium) a travaillé. Les preuves démontrent clairement la valeur d’une enquête critique rigoureuse qui progresse avec les savoirs de base.
First published in Education Canada, December 2015
1 According to the 2012 PISA results, mathematics scores are declining in several Canadian jurisdictions. However, results from the Pan-Canadian Assessment Program for 2013 indicate that scores for Grade 8 students in math and reading are on the rise across the country.
2 Caroline Alphonso, “Why Discovery-Based Learning Doesn’t Add Up,” Globe and Mail, September 20, 2013: L3; “New Math Equals Trouble, Education Expert Says,” CBC News, September 21, 2011. www.cbc.ca/news/canada/new-math-equals-trouble-education-expert-says-1.1058161
3 David Staples, “The Top Nine Reasons Why Education Minister Jeff Johnson Is in Such Hot Water,” Edmonton Journal, May 16, 2014.http://blogs.edmontonjournal.com/2014/05/16/the-top-nine-reasons-that-education-minister-jeff-johnson-is-in-such-hot-water/
4 See Roland Case, “Our Crude Handling of Educational Reforms: The case of curricular integration,“ Canadian Journal of Education 19, no. 1 (1994): 80-93; and Roland Case, “Educational Reform in British Columbia: Bold vision/flawed design,” Journal of Curriculum Studies 24, no. 4 (1992): 381-387.
5 Robert Sternberg, “Assessing What Matters,” Informative Assessment 65, no. 4 (2008): 23.
6 EQAO (Ontario Education Quality and Accountability Office) reports on province-wide literacy and mathematics achievement tests and questionnaires, administered yearly.
7 Fred Newmann, Anthony Bryk and Jennny Nagaoka. Authentic Intellectual Work and Standardized Tests: Conflict or coexistence? (Chicago: Consortium on Chicago School Research, 2001).