Strategies for Achieving Deep Understanding and 1 Improving Learning Skills: New Approaches to 2

Instruction and Lesson Study in Japanese Schools 3

Yuri UESAKA1, Tatsushi FUKAYA2, and Shin’ichi ICHIKAWA1 4 1: The University of Tokyo, 2: Gunma University 5

Abstract. Education that facilitates the achievement of deep understanding and 6 the improvement of learning skills to help students prosper in the society of the 7 future has become an important topic worldwide. To achieve this goal in daily 8 instruction, in this study, new approaches to in-class instruction and teacher 9 professional development – ‘thinking-after-instruction’ and ‘three-way review’ 10 – are proposed by a psychological research group in Japan. This chapter de-11 scribes and exemplifies these approaches and discusses their benefits. It then 12 presents empirical data on their effects in maths education at a school in which 13 they were implemented over a two-year period. The data suggest that the ap-14 proaches significantly improved the quality of teachers’ instructional strategies 15 and, as a result, also improved students’ use of learning strategies and their 16 maths performance in national tests. 17

Keywords: deep understanding, learning strategy, thinking-after-instruction, 18 lesson study, three-way review, education in Japan 19

1   Global Change in Education Goals 20

One of the most active discussions related to education around the world regards 21 changes in the goals of school education: traditionally, the focus was more on teach-22 ing content that was deemed important, whereas educators have now shifted their 23 focus more to helping students obtain competencies that will allow them to prosper in 24 contemporary society. This tendency emerged with the proposal of ‘key competencies’ 25 by the DeSeCo (The Definition and Selection of Key Competencies) project. This 26 project was conducted by the Organisation for Economic Co-operation and Develop-27 ment (OECD), from 1997 to 2003, and the final reports were published in 2003 28 (Rychen and Salganik, 2003). This project became the basis for the Programme for 29 International Student Assessment (PISA), an international assessment in maths, sci-30 ence, and reading literacy, which targets 15-year-old students. The idea of ‘21st-31 century skills’ (Griffin, McGaw, and Care, 2012) is also in the same line, in that it 32 encourages skill development as a means to prosper in society. Even at the policy-33 maker’s level, valuing the development of students’ competencies for life in contem-34 porary society has recently been emphasized (e.g. SDGs (Sustainable Development 35 Goals) 4.7 by UNESCO, 2015). 36

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As elsewhere, Japanese educational policies and discussions around curricu-1 lum reform have come to place more emphasis on the development of students’ com-2 petencies (called 資質・能力 in Japanese). Although the idea of developing students’ 3 ability to prosper in society is not new in Japan and previous discussion on curriculum 4 reform at the Central Council for Education has also focused on this issue (called, at 5 the time, ‘zest for living’ (生きる力) (e.g. Minister of Education, Culture, Sports, 6 Science and Technology of Japan (henceforth MEXT), 1996), this previous discus-7 sion did not consider concrete strategies to attain this end. On the other hand, recent 8 discussion regarding the next curriculum reform has included perspectives on how to 9 achieve the goal of fostering students’ competencies. For example, ‘active learning’ is 10 considered important, and in this respect, deep learning (深い学び), collaborative 11 learning (協同的学び), and subjective learning (主体的学び) are valued as general 12 principles for instruction (MEXT, Japan, 2016). However, it remains unclear how 13 these principles can be realised in classroom instruction, and quite a few Japanese 14 teachers are confused about how to adjust their instruction methods in this regard. 15

In addition, the practical research conducted by our research group, which 16 we termed ‘cognitive counselling’, suggests that a number of problems need to be 17 addressed in regard to students’ learning by in-class instruction. The ‘cognitive coun-18 selling’ conducted by our group (Ichikawa, 1989, 1993, 1998, 2005) comprised a 19 psychologist engaging directly in personal tutoring using psychological perspectives. 20 The clients in cognitive counselling are students who struggle with aspects of learning 21 such as ‘I cannot remember well’, ‘I cannot perform well academically even if I take 22 a very long time to learn’, or ‘I cannot get motivation to learn’. The goal of this per-23 sonal tutoring is not to teach those things that students cannot solve or understand but 24 rather to make them autonomous learners by enabling them to spontaneously use 25 learning strategies that psychological research has revealed to be effective. While the 26 materials used in this counselling vary, this practical research reveals common prob-27 lems underlying students’ learning difficulties: The first is a lack of conceptual under-28 standing and reliance on rote memorization, the second is inappropriate learning be-29 liefs that underlie the underuse of effective learning strategies (e.g. beliefs that value 30 rote memorization alone, or an orientation that neglects the value of the process and 31 relies solely on obtaining the correct answer). In many cases, students’ poor achieve-32 ment or suffering occurs because inappropriate learning beliefs result in the poor use 33 of learning strategies, and as a result, poor achievement. Furthermore, this often caus-34 es a serious decrease in learning motivation. It has also been suggested that students’ 35 problems do not occur due to their own lack of competencies, but rather due to the 36 poor quality of instructional methods at schools. 37

Based on this recognition, in order to address these problems, our psycholog-38 ical research group proposes two approaches: the ‘thinking-after-instruction’ ap-39 proach, to be implemented as part of instruction in class, and ‘three-way review’, as 40 part of lesson study. Both are proposed based on educational psychological perspec-41 tives. Lesson study is an approach to the professional development of teachers’ in-42 struction skills that is widely conducted in Japanese schools. In lesson study, a teacher 43 designs an actual classroom lesson by collaborating with other teachers and uses 44 his/her class to demonstrate how his/her idea works in an actual class with students. 45 After the class, all teachers participating in this demonstration engage in a discussion. 46 This process has been considered to contribute to enhancing teachers’ professional 47

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skills. This chapter first introduces both approaches in detail and then examines data 1 on students and teachers from a school in which both approaches have been used for 2 two years to discern the effects. 3

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2   The ‘Thinking-after-Instruction’ Approach in Class 5

2.1 Core Idea and Background of This Approach 6 Discovery learning, which aims at minimizing instruction and encouraging students to 7 discover targeted knowledge for themselves, and direct instruction, which aims to 8 provide instruction about targeted knowledge from teachers, are two common and so-9 called controversial approaches to instruction that have been in place for a long time 10 (e.g. Lee and Anderson, 2013). The conflict between these two approaches has been 11 called the ‘assistance dilemma’ by Koedinger and Aleven (2007), which relates to the 12 fact that teachers must decide whether they provide instruction or refrain from provid-13 ing instruction. Although the two approaches are basically considered incompatible, 14 the ‘thinking-after-instruction’ approach combines these two approaches (e.g. Ichika-15 wa, 2004, 2008, 2015; Ichikawa, Uesaka, and Manalo, in press; Ichikawa and Uesaka, 16 2016). Furthermore, two new phases – for checking comprehension and self-17 evaluation respectively – have been integrated in addition to the simple integration of 18 direct instruction and discovery learning. Although the detailed design principle of the 19 thinking-after-instruction approach will be described in more detail in a later section, 20 the outline of this approach is as follows. A class using the thinking-after-instruction 21 approach consists of four phases: teacher’s explanation (direct instruction), checking 22 comprehension, deepening understanding (discovery learning), and self-evaluation. 23 The more essential point of this approach is achieving deep understanding and im-24 proving students’ learning strategy use, as will be explained in more detail in the next 25 section. This is because the practical research of cognitive counselling (e.g. Ichikawa, 26 1993, 1998; Uesaka, 2010), as described above, showed that students lacked concep-27 tual understanding, had poorly constructed knowledge, and rarely used effective 28 learning strategies. These problems were also considered to have occurred because of 29 lack of instruction methods in school classes. Based on this recognition, this approach 30 was proposed to address problems in education in Japan specifically. Thus, this sec-31 tion first provides a more detailed background to the approach relating to methods of 32 instruction in Japan and then gives a concrete example from the classroom. 33

One of the important background factors in the thinking-after-instruction ap-34 proach is related to the excessive emphasis on discovery learning in elementary 35 school education in Japan, where discovery learning is usually more valued than di-36 rect instruction. Let us show an example of the typical discovery style class in Japan. 37 When instructing in mathematical formulas, such as calculating the area of a triangle 38 or parallelogram in a typical Japanese class, the teacher might encourage students to 39 identify a mathematical formula for the area of a triangle or parallelogram. In this 40 type of class, the formulas found by students are introduced and shared with class-41 mates at the end of the class. This active discussion to uncover and justify target 42 knowledge in collaboration between teachers and students is called neriage (練り上43

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げ) and is traditionally considered one of the most important processes in Japanese 1 education. It is considered more effective than direct instruction as students them-2 selves discover why the target knowledge is found. After the targeted knowledge has 3 been shared with the class, drill practice using that knowledge usually follows. 4

Despite its advantages and its dominance in elementary school education in 5 Japan, discovery learning also has several defects. For example, although targeted 6 knowledge is shared among all class members, the reality is very often that only the 7 top students give substantive explanations for this knowledge and it is often unclear 8 how well other students understand. In fact, many students who visit our cognitive 9 counselling practice report that they cannot understand the discussion between teach-10 ers and top students. Second, many students have already become familiar with target 11 knowledge as a result of attending after-hours education institutions like cram schools. 12 Third, even if teachers try to convey a conceptual understanding of target material, 13 many students focus only on the procedural aspect. One of the reasons for this is that 14 even if the teacher explains the conceptual aspects, the follow-up activities that many 15 teachers request students to complete merely comprise drilling. It is rare that opportu-16 nities are provided for all students to explain the conceptual aspect and thus to check 17 their understanding. As a result, as shown in case reports from cognitive counselling, 18 many students struggle because they rely solely on rote memorization and pattern 19 learning in various subjects. 20

Another important background aspect of thinking-after-instruction is that 21 junior high school and high school teachers in Japan overly rely on direct instruction 22 and rarely provide students with opportunities for discovery learning. In contrast to 23 elementary schools, teachers at these school levels in Japan value direct instruction 24 more than discovery learning. The typical flow of this type class is as follows: first, 25 the teacher explains the concepts to the students; second, the students are asked to 26 solve related problems; and finally, students’ understanding is confirmed. Although 27 students receive conceptual explanations, they are never afforded opportunities to 28 produce the knowledge by themselves. 29

Although direct instruction is valuable in that the targeted knowledge is pro-30 vided explicitly and students will not struggle to ‘discover’ it, this approach also has 31 several defects. For example, case studies of cognitive counselling show that many 32 students struggle to follow direct instruction in class. In addition, students may find 33 that they can solve basic problems using target concepts, but not applied problems, as 34 they do not understand the material deeply and conceptually (see the case studies 35 reported in Ichikawa, 1993). Another problem is that many students may lose interest 36 in learning content if there is no scope for independent engagement with the material 37 or for challenging oneself. In a related criticism, this style of instruction may not help 38 students learn to express their ideas. 39

In order to address these problems, the ‘thinking-after-instruction’ approach, 40 to be applied in class, has been proposed (e.g. Ichikawa, 2004, 2008, 2015; Ichikawa, 41 Uesaka, and Manalo, in press; Ichikawa and Uesaka, 2016). As described above, clas-42 ses designed using this approach consists of four phases. To help students understand 43 the reasoning behind target knowledge more deeply, the teacher first provides explicit 44 explanation of the concept and relevant or underlying concepts (the conceptual aspect 45 of knowledge), as in direct instruction. Even if the knowledge is more procedural, 46

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explicit instruction may be given as to why this procedure is used or points that stu-1 dents should pay attention to. 2

In the next phase, checking comprehension, the teacher provides students 3 with activities that they can do to help themselves and the teacher ‘understand their 4 understanding’. As part of this approach, for example, the teacher asks the students to 5 explain their reasoning and process in pairs as the teacher has done (in many cases, 6 they are asked to explain by imagining that the student with whom they are paired 7 does not know about the topic). When students find they cannot explain well, it may 8 mean that they do not sufficiently understand. 9

In the third phase, the deepening understanding phase, the teacher provides 10 students with an exploratory task to complete in groups, to deepen their understanding. 11 Such a task may focus on an aspect that students might easily misunderstand; for 12 example, in a class on the mathematical formula for calculating a parallelogram, the 13 task might focus on ensuring that the students understand the concept of ‘height’. 14

In the final phase, the self-evaluation phase, students are asked to articulate 15 what they do and do not understand. They are encouraged to articulate strategies to 16 determine points about which they are unsure (e.g. ‘I can calculate a parallelogram’s 17 area by transforming it into a shape whose area I already know how to calculate’). 18

If we compare this new approach to the usual Japanese discovery style class 19 which is common at elementary school level, the latter tries to help students discover 20 knowledge in the textbook, but the new approach tries to help them discover 21 knowledge beyond the textbook (that is, it uses textbooks but transcends them). Also, 22 if we compare this new approach to the usual Japanese direct instruction style class 23 which is common at junior high or high school level, the latter instruction style does 24 not afford the opportunity to check students’ understanding by explaining what they 25 understand or through discovery learning, but the new approach tries to create such 26 opportunities for students. Particularly at high school level, discovery learning in 27 groups is rarely conducted in traditional Japanese education, but has begun to be con-28 sidered important in recent discussion about ‘active learning’ (MEXT, 2016). 29 30 2.2 Learning Strategy Use Enhancement with the Thinking-after-31 Instruction Approach in Class 32 A central point in this chapter is that the thinking-after-instruction approach effective-33 ly promotes students’ learning skills—especially use of learning strategies such as 34 cognitive and meta-cognitive strategies—and deepens their understanding. For exam-35 ple, the underlined parts in Table 1 show instances in which the teacher intentionally 36 tried to promote students’ use of meta-cognitive learning strategies. To do so, for 37 instance, the teacher encouraged the students to read the textbook before class as 38 preparation. In this stage, a teacher encourages the students to find what they have 39 and have not understood. Moreover, especially by the 5th or 6th grade, teachers may 40 advise students to set their own goals to achieve in class. In one class, a student men-41 tioned, ‘I’ve got an idea how we can calculate the area of a circle using a mathemati-42 cal formula, but I do not understand why this kind of math formula works, so my goal 43 in this class is to understand the reason why this math formula can work’ (Tamashima 44 TV, 2013). In the teachers’ instruction phase, the teacher encourages students to focus 45 on the points that they do not understand when listening to the teacher. In the follow-46 ing checking comprehension phase, the teacher provides a task that allows both the 47

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teacher and students to check their conceptual understanding. Students are asked to 1 solve a task or to explain conceptual aspects ‘as the teacher did’, often in pairs or 2 small groups. When they find that they cannot provide some explanation well, they 3 become aware of the gaps in their understanding. In the final phase, students once 4 more express what they do and do not understand. By repeating this cycle, students 5 are expected to develop their meta-cognitive skills and to use meta-cognitive learning 6 strategies spontaneously in their own learning without any instruction from the teach-7 er. 8

9 Table 1. Framework for Using the Thinking-after-Instruction Approach Prior to and 10 During Class (Parts Relating to Meta-Cognitive Learning Strategies are Underlined 11 and Cognitive Learning Strategies are Italicized) 12 13 Teacher’s Action Students’ Expectation Before class: Preparatory Read-ing

Encouraging students to read their text-books to prepare for their upcoming clas-ses.

Checking what they have un-derstood about the topic, but al-so what they have not under-stood. Setting their own goal to achieve in class (especially in 5th and 6th grade) and writing these goals down in their note-books.

In class: Teacher’s Instruc-tion

Explaining the mean-ing rather than just focusing on the pro-cedure.

Focusing on points that they do not understand when listening to the teacher’s instruction.

Checking Com-prehension

Asking students to solve problems or ex-plain as the teacher did in the teacher’s instruction phase by focusing on concep-tual aspects in pairs or groups.

Checking understanding, when they cannot solve or explain, becoming aware that they do not understand. The other mem-ber of a pair (or group) should support understanding.

Deepening Under-standing

Providing task(s) ap-plying what they have learned; de-signed to deepen their understanding fur-ther.

Collaboratively solving the task with other peers, and utilizing the knowledge that they have learnt.

Self-evaluation Asking students to re-flect what they have understood and what they have not under-stood.

Checking what they have un-derstood, but also what they have not understand. Writing not only conceptual aspects but also strategy aspects.

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1 Additionally, as mentioned above, this approach tries to develop students’ 2

cognitive learning strategies and general orientation toward cognitive learning. The 3 parts in italics in Table 1 are places where the teacher intentionally and explicitly tries 4 to promote cognitive learning strategy use and orientation. As our research group’s 5 background is in cognitive psychology, we consider it important to foster students 6 who value conceptual rather than just procedural understanding, focus on process 7 rather than simply obtaining the correct answer, and prize failure that fosters im-8 provement (rather than simply hating failure as such). To achieve this in the teacher’s 9 instruction phase, teachers focus on reasoning and process rather than simply on tar-10 get content. Additionally, in the checking comprehension phase, the teacher encour-11 ages students to explain as the teacher has done. This suggests to students that the 12 goal of the class is to deepen and refine their understanding until they can explain in 13 their own words, rather than simply solving problems. Then, in the deepening under-14 standing phase, students are asked to utilize the knowledge learnt in different contexts, 15 suggesting to them that applying knowledge across contexts is another important goal. 16 Finally, in the self-evaluation phase, students are expected to refer to conceptual as-17 pects of the material and strategic aspects of their learning process, reinforcing the 18 goal of deep understanding. By conducting this kind of class every day, teachers 19 should help students to value conceptual understanding as a whole and encourage 20 them to start using cognitive and meta-cognitive learning strategies spontaneously in 21 their own learning even without special instruction from teachers (for analysis of how 22 students spontaneously use cognitive and meta-cognitive learning strategies in a 23 thinking-after-instruction context, see Uesaka (2014)). 24 25 2.3 Example of Thinking-after-Instruction in Class 26 In this section, we will introduce three example of real class design based on the 27 thinking-after-instruction approach. When designing a class, it is important to consid-28 er what kinds of difficulties students will meet in the class (‘difficulty assessment’; 困29 難度査定; Ichikawa, 2016). Thus, the difficulties predicted when designing the clas-30 ses are introduced as well as the goals and overall class design. 31 The first example involves a 6th-grade class whose goal was to achieve con-32 ceptual understanding of the mathematical formula to calculate the area of a circle. 33 One difficult point for students that was identified before class was that some students 34 already knew the mathematical formula in question (radius x radius x 3.14) but did 35 not fully understand why it was effective. Others might have been able to calculate 36 the area of a circle but did not fully understand the meaning of the formula itself (es-37 pecially the fact that the radius is multiplied twice). To overcome these difficulties 38 and ensure that students had learned the formula effectively, the teacher first gave 39 explicit instruction on the formula and why it worked, using ICT tools and diagrams. 40 In the next phase, the comprehension check, the teacher asked students to explain in 41 pairs how the formula could be represented diagrammatically on a worksheet and also 42 asked them to calculate the area of those circles. In the deepening understanding 43 phase, Figure 1 was provided and students were asked to ‘[p]lease consider in groups 44 what the students who said the areas of these several diagrams are equivalent are 45 thinking, so that I can know about it without using actual calculation!’ By engaging in 46 this task, students were expected to understand the deeper structure of the mathemati-47

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cal formula: that the radius is multiplied twice. More concretely, if we consider the 1 radius of the left part of Figure 1 to be 1, then the circles in the middle and right parts 2 are respectively 1/2 x 1/2 = 1/4 and 1/3 x 1/3 = 1/9. However, there are four circles in 3 the former case and nine in the latter, so that they have the same overall area as the 4 one left circle. In the final phase, students articulated points that they had or had not 5 understand. 6 7

8 Figure 1. Diagrams shown in Deepening Understanding Phase of the First Example 9

10 The second example comes from a 3rd-year class whose goal was conceptual 11

understanding of the word ‘diameter’. This class was conducted by the third author 12 when he was dean of the Faculty of Education at the University of Tokyo (our re-13 search group has a policy whereby even psychologists must demonstrate instructional 14 methods to help teachers understand how psychological perspectives can be utilized 15 in class design. For this reason, we went into an elementary school and demonstrated 16 this method to show teachers that psychological perspectives are useful in class de-17 sign). Although many of the students already knew the word ‘diameter’ and the con-18 cept’s features (such as that it is the longest line that can be drawn within the circle 19 and must always pass through the centre), a lack of conceptual understanding was 20 projected to be a problem. Thus, activities were set in which students measured the 21 diameter or found the centre of a circle. Before class, students were asked to read the 22 relevant material in the textbook as preparation for the upcoming class. In class, dur-23 ing the teacher’s instruction phase, the teacher instructed the students on the definition 24 and features of the diameter of a circle, and ways to measure it. In the class, students 25 approximated the measurement of diameter by using a straight ruler and two triangle 26 rulers, with which students were familiar (Figure 2). In the comprehension check 27 phase, students were asked to measure the diameters of Japanese coins (10, 100, and 28 500 yen) in pairs. In the deepening understanding phase, students were asked to find 29 the centre of a circle on a piece of thick paper and use it to make a spinning top in 30 groups (see Figure 3). Several groups discovered that they could find the centre of the 31 circle by relying on the feature whereby the diameter always crosses the centre—thus, 32 multiple diameter lines can be used to locate the centre by triangulation. Finally, stu-33 dents were asked to articulate what they had and had not understood. 34

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Figure 2. Tool Used for Measuring Diameter in the Second Example 3 4

5 6 7 8 9 10 11 12 13

Figure 3. Students Involved in Checking Comprehension Phase (left) and Students 14 Presenting Their Ideas for the Deepening Understanding Phase (right) 15

16 Although the examples described above all involved elementary school 17

mathematics topics, the approach is not limited to the mathematics context or to the 18 elementary level. Ichikawa and Uesaka (2016) introduced 20 lesson plans using this 19 approach in various fields including maths, Japanese language, science, social studies, 20 moral education, and English. In addition, lesson plans at the junior high and high 21 school levels have also been presented (e.g. Ichikawa, 2015), and the practice has 22 been used in the context of higher education (Uesaka, 2011). Let us consider one 23 example from a non-maths context, from a 5th-grade Japanese language class con-24 ducted by the first author. The material used is a famous Japanese story, ‘God in straw 25 boots’ (わらぐつの中の神様) by Mikiko Sugi. An outline is as follows: 26

27 A girl, Masae, hated her straw boots because they did not look cool; but her 28 grandmother encouraged her to use them when the shoes she usually wore in 29 the snow were wet. The grandmother started to tell Masae that God was in 30 the straw boots, and that once upon a time, a young girl named Omitsu 31 wanted to get cute Japanese wooden clogs but could not ask her parents as 32 her family was too poor. So in order to get the clogs, Omitsu started to make 33 straw boots herself for selling. The first boots she made did not look good at 34 all, but she cared a lot about the wearers and wove the straw tightly, not 35 leaving any space. The boots were very ugly, and when she was selling them, 36 a lot of people laughed at them, but one young carpenter bought the straw 37 boots every time she sold them. When she asked him why, he said that ‘the 38 value of the work is not decided by its appearance. How much the maker 39 considers the users is more important. Objects made with sincere considera-40

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tion for the user include God within them’. After saying that, he proposed to 1 Omitsu that they get married as ‘a person who makes such things is next to 2 God, so would you come to my house? I will treat you as God’. (After these 3 words of the carpenter, we return to the scene of the grandmother and Ma-4 sae.) Masae learns that Omitsu is her grandmother and the young carpenter 5 is her grandfather. After listening to the story, Masae starts to articulate the 6 comments, which suggests she is changing her sense of values, and that she 7 believes that everything in which one can sense sincerity contains God. 8 9

The unit that goes with this story has the following goals: first, understanding the 10 story from three perspectives (structure, scene description, and personalities of the 11 characters) and developing the skills to interpret its message; and second, writing the 12 short advertising messages to accompany other stories written by Mikiko Sugi using 13 the skills for interpreting messages that they have gained in class. The characters’ 14 personalities in particular were expected to help students understand the message, but 15 a difficulty was predicted: students did not have any concrete strategies for under-16 standing the characters’ personalities. Thus, this class focused on ‘sense of values’ as 17 an aspect of personality and instructed students on how to identify sense of values in a 18 literary work. Finally, to help students apply those perspectives when reflecting on 19 their own lives and develop their own values, the class also included activities to help 20 them review their own lives in terms of the sense of values emerging from the story. 21

The concrete flow of this class was as follows. As this targeted class was the 22 7th class out of 10 hours in total for this unit, students already knew the story. Thus, as 23 preparation before class, students were asked to write down what the young carpenter 24 considered important and why. In class, the teacher first instructed them that it is 25 sometimes possible to understand the message of a literary work by understanding the 26 sense of values of its important character(s), and taught them to identify the sense of 27 values with the aid of a diagram (Figure 4). In Figure 4, the square parts represent 28 what the character says and does, while the oval parts show the underlying sense of 29 values, captured by considering what ideas unite what the character said and did. The 30 teacher presents a concrete example from the story (from his comments to Omitsu and 31 his behaviour, for instance buying the ugly straw boots, we might think that the young 32 carpenter’s sense of values posit that ‘it is more important for something to be made 33 with sincerity rather than to be of good appearance’). In the checking comprehension 34 phase, Masae’s sense of values before and after listening to her grandmother’s story 35 were analysed in groups by filling in a values diagram worksheet, based on examples 36 shown by the teacher. The answers were shared with the whole class. In the deepen-37 ing comprehension phase, students were asked to review their lives from Masae’s 38 perspective. The teacher asked the students ‘Are there any objects around you that 39 you feel include God inside when you get the perspective of Masae, or are there any 40 objects around you that you treated badly even though you think they might include 41 God inside from the current perspective of Masae?’ Students engaged in this task in 42 groups and also shared their responses in class. At the end, students articulated what 43 they had understood and not understood. 44

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1 Figure 4. Diagram Used for Analysing Sense of Values in the Third Example 2

3   A New Approach to Lesson Study: ‘Three-Way Review’ 3

3.1 Background to the Use of Three-Way Review in Lesson Study 4 Our research group also proposed a new approach to lesson study, called ‘three-way 5 review’ (三面騒議法) (Ichikawa and Uesaka, 2010; Ichikawa, 2016). Lesson study is 6 a Japanese system used to enhance the quality of instruction among teachers in a 7 school. It is a cultural institution in Japanese elementary schools, and almost every 8 elementary school in the country has several chances per year for all teachers to con-9 duct lesson study. Lesson study is also conducted in junior high and high schools. 10 This system has contributed to keeping the quality of Japanese education high and 11 also to maintaining high standards across schools. Traditionally, the typical process of 12 lesson study is as follows: first, participants watch a class together; second, they share 13 comments with all participants (without prior discussion in small groups; cf. below). 14 External commenters like academic university staff may also add some comments. 15

Although this system is valuable, traditional lesson study has several prob-16 lems. For example, participants sometimes find it difficult to speak honestly, as they 17 do not want to damage their relations with the teacher giving the class. Also, partici-18 pants may find it easier to comment honestly to younger teachers showing their class 19 but more difficult with older teachers; finally, from a cultural perspective, Japanese 20 people tend to hesitate to contribute to discussions, such as asking questions, so some 21 people may have trouble commenting even if they do have something to say. When 22 such problems occur, even if the teachers share their comments, it may be difficult for 23 these to lead to deep discussion or contribute to enhancing the development of the 24 teachers’ instruction skills. 25

Based on these considerations, three-way review in lesson study was pro-26 posed as a way of conducting lesson study more actively. Recently, a new style of 27 lesson study has been proposed in Japan, that is, workshop style lesson study, which 28 includes an active session such as small group discussion rather than simply providing 29 a lecture from a knowledgeable person (Murakami, 2012); three-way review can be 30 positioned within this style of lesson study. The procedure is slightly different from 31

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the traditional style of lesson study. First, participants watch a class together, and each 1 participant writes comments on sticky notes of three colours (red: good points, blue: 2 points for improvement, yellow: points that can bring in learning from other units or 3 subjects). After watching the class, participants first get together and share their ideas 4 in small groups (3–6 participants per group). Second, each group presents all the 5 comments it has heard to the other groups. Finally, facilitators may pick up some 6 points and discuss them with all participants. In some cases, external observers like 7 university researchers may add comments. 8

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Figure 5. Teachers in ‘three-way review’; Discussing methods of instruction with 12 small groups (left) and Sharing comments with all members (right). 13

14 This approach has several important features. First, the structure of the pro-15 cess encourages all participants to talk sufficiently, especially with the inclusion of 16 the small group phase, which may help Japanese participants in particular to feel com-17 fortable sharing their views. Second, devices are incorporated to encourage partici-18 pants to provide negative as well as positive comments. First, all comments shared in 19 small groups are shared with all participants, but without specifying which individual 20 person has made them; this anonymity addresses the problem of participants worrying 21 about their relations with the teacher who is showing his or her class. A second im-22 portant device is that when participants suggest points for improvement, they are en-23 couraged to provide alternatives (e.g. another method of instruction or of conducting a 24 task) by imagining what they would do if they themselves were the teacher. This too 25 is expected to contribute to meaningful discussion. 26 27 3.2 Combining Thinking-after-Instruction with Three-Way Review 28 Although three-way review can be used in any type of lesson study, it works most 29 effectively if combined with thinking-after-instruction. This is because, compared to 30 the usual Japanese three-phase class structure (introduction, main work, and sum-31 mary), thinking-after-instruction clearly points to what aspects participants in lesson 32 study should consider in each phase. For example, in the teachers’ explanation phase, 33 participants should evaluate the appropriateness of instruction according to whether 34 students achieve deep conceptual understanding and, if not, consider what other in-35 structional strategies might have been effective alternatives. In the checking compre-36 hension phase, participants should consider whether the task at hand is appropriate to 37 allow checking of conceptual understanding for both students and teachers, and if not, 38 not only to point out problems but also to propose a more effective alternative. In the 39

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deepening understanding phase, participants should similarly check whether the task 1 is really deepening students’ understanding. In the self-evaluation phase, participants 2 should evaluate students’ writing from the perspective of whether the students have 3 achieved appropriate understanding, and if not, again, consider what points should be 4 changed and what kinds of student observations might indicate that the goals of the 5 class have been achieved. 6

We will now introduce one real example of the use of three-way review in a 7 school. This school had been using the thinking-after-instruction approach in Japanese 8 language classes for two years and all lesson studies had been conducted using three-9 way review. This example is taken from around the middle of the academic year, so 10 all of the students and teachers were by this stage familiar with both thinking-after-11 instruction and three-way review. In the example, a teacher presented a 1st-grade Jap-12 anese language class in the second part of unit construction, in which the aim was for 13 students to learn to write sentences by themselves. 14

All teachers from that school and several teachers belonging to other schools 15 watched the students’ actual responses during class observation by standing at the 16 back of the classroom. As they watched, participants wrote comments on coloured 17 notes as described above, which they brought to the discussion. In the small group 18 discussion, many teachers highly evaluated the students’ responses in class, saying 19 that the students were really active and pleasant. At the end of this class, some stu-20 dents said things like, ‘Oh, is it already time? I want to do more!!’ ‘It is OK if it is 21 extended until 50 minutes!’ (Japanese elementary school is 45 minutes per class). The 22 comments indicated that the teacher had guided the students well, and that they were 23 easily able to write sentences by summarising in a table, explaining what they would 24 write to peers before writing it, and using appropriate conjunctions. On the other hand, 25 some comments said that students might have more clearly understood the important 26 points about writing (the aim of the class). Some participants proposed alternative 27 ways of instruction, such as showing an example of bad writing in the checking com-28 prehension phase and asking students to answer why it was not appropriate (e.g. ‘it 29 does not use conjunctions at all’). Those comments were shared with all teachers after 30 the small group discussion. 31

Next, a visiting academic, the first author of this chapter, commented briefly. 32 From the perspective of meta-cognitive awareness, the author proposed that, as an 33 alternative approach to those seen, the teacher could establish a flow that would help 34 students more consciously understand the process of writing. In more detail, the au-35 thor suggested that in the teacher’s instruction phase, using material from the textbook, 36 the teacher could outline concrete steps or points to help students write sentences. For 37 example, they might first decide what to write about (decide on a specific type of car 38 to write about), and might then make a table and organize the material they want to 39 write (the function and car shape are important, so those cells should be included in 40 the table), explaining to peers what they plan to write based on a note or table that 41 they make before writing, and finally the writing phase itself. In the checking com-42 prehension phase, the teacher models examples of intentionally bad student behav-43 iours (e.g. starting writing without making notes or a table, or without explaining to 44 peers – the last strategy was emphasized in this unit as useful for students’ under-45 standing and writing), and encourages students to identify inappropriate points based 46 on what they have learnt. In the deepening comprehension phase, information about 47

14

new material (a fire truck) is shown on a TV screen, and students are encouraged to 1 construct sentences in groups (in a 1st-grade context like the one discussed here, a 2 certain amount of guidance from teachers may be necessary and effective). Finally, 3 students are encouraged to provide writing advice for other students who will write 4 sentences in the future. 5

While three-way review expects the audience to propose alternatives and is 6 usually challenging for them, using it in conjunction with thinking-after-instruction 7 makes it easier to generate, as the design principles of the lessons are much clearer 8 than in a typical class design. Furthermore, one of the teachers who joined in the les-9 son mentioned above wrote on the feedback sheet for the lesson study that ‘this style 10 of lesson study is very effective and good. I was able to ask questions more easily and 11 I could learn a lot even though I am not very familiar with the thinking-after-12 instruction approach in class. I hope to use this style of lesson study in my own 13 school’. 14

4.   Empirical Data from a School Using the Two Approaches 15

4.1  About the Site School and the National Test 16 In this section, empirical data are presented from a school where both thinking-after-17 instruction and three-way review were used in maths learning over a period of two 18 years (this is the content of a paper presented at the International Congress of Psy-19 chology in 2016, in Yokohama, by Uesaka, Fukaya, and Ichikawa). The targeted 20 school is an elementary school in Shinagawa-ku, Tokyo. Before starting this educa-21 tional practice, the overall achievement at this school was comparatively high, but 22 bipolarization of achievement was considered a major problem, as teachers struggled 23 to conduct a class that both higher- and lower-achieving students could benefit from. 24 To address this problem, thinking-after-instruction was implemented, with the aid of 25 the three authors of this chapter. The collaboration between the school and researchers 26 happened because the principle of the school deeply approved of the thinking-after-27 instruction approach, and thus requested the three authors to support the school. The 28 authors agreed to join this school project only once they had achieved consensus from 29 the teachers in the school, and so the project started in April 2014 once the school 30 principle had obtained this consensus. The authors anticipated that the following pro-31 cess and change would happen: First, the instructional methods used by this school’s 32 teachers would change; second, students’ learning behaviours would change; and 33 finally, academic performance such as in national tests would be improved. Based on 34 these expectations, the authors designed a survey to capture these changes as well as 35 collaboratively designing classes with teachers. We will briefly report the results of 36 the survey in the remaining part of this section. 37

Over two academic years (2014 and 2015), all maths classes in all six grades 38 were conducted using the thinking-after-instruction approach. In addition, to help all 39 teachers share their thoughts on this approach, this school conducted lesson study 40 with all teachers once a month, again with the participation of the researchers, and 41 three-way review was used in those discussions. After the two-year period was over, 42 the national test results demonstrated an improvement in the overall performance in 43

15

maths in this school. In Japan, national tests are conducted annually for all 6th-grade 1 students in both maths and reading, including both ‘A-type’ and ‘B-type’ problems 2 (that is, basic and applied). In the site school, as shown in Figure 6, the difference 3 from the national average scores increased after the practice had started. 4

To ensure that this difference was not an outlier (a cohort effect), school and 5 national test scores for (reading) literacy were checked, and, as shown in Figure 7, no 6 such increasing difference between the score of this school and the national average 7 was found. This suggests that the result for maths was not simply because the cohort 8 taking the test was unusually good. 9 10 11

12 13

Figure 6. Results of National Test in Mathematical literacy. Results of A-type prob-14 lem (left) and B-type problem (right) 15

16

17 18

Figure 7. Results of National Test in Reading literacy. Results of A-type problem 19 (left) and B-type problem (right) 20

21

4.2  Students’ Learning Strategy Use and Teachers’ 22 Improvements to Instructional Strategies 23

To examine the reasons for improved student performance in maths and the processes 24 by which it improved, students’ learning strategy use was investigated. Several math-25 ematical word problems were given to students (e.g. ‘Make a regular square with 26 sheets of paper, the height of which is 12 cm and the width of which is 16 cm. An-27 swer how many sheets of paper are necessary to make it. Explain how you get the 28 answer using diagrams, formulae, sentences, etc.’) and the responses were analysed. 29 From the viewpoint of learning strategy use, if students are interpreting and solving 30 such problems conceptually, they might tend to use diagrams to understand and ex-31 plain the situation, and tend to get the correct answer. On the other hand, if they do 32

16

not use any diagrams and cannot solve the problem, this may indicate that they are not 1 using sufficient (cognitive and external resourcing) learning strategies. On this basis, 2 the number of student responses that contained ‘correct answers with diagrams’ and 3 ‘incorrect answers without diagrams’ were counted. The results, shown in Figure 8, 4 indicate that over the two-year period the number of correct answers with diagrams 5 increased and that of incorrect answers without diagrams decreased significantly. This 6 suggests that students’ strategy use improved, and might therefore be a meaningful 7 element underlying the improvement of the students’ maths performance on the na-8 tional test. 9 10

11 Figure 8. Results of Students’ Strategy Use 12

13 Moreover, we also examined how teachers’ approaches to instruction 14

changed after they started to use the thinking-after-instruction approach in class. In 15 the site school, almost every month, teachers conducted lesson study and shared the 16 information gained about classroom design. However, the number of classes for 17 which all teachers participated in lesson study was limited, also limiting our under-18 standing of changes in their teaching strategies. Thus, we explored changes in teach-19 ers’ methods of instruction by developing a new ‘lesson plan construction task’. In 20 this task, all teachers in the school were asked to construct a lesson plan using a text-21 book from 2014 and one from 2015. To counterbalance, two textbook excerpts (one 22 about the concept of line symmetry and another about calculating the area of a trape-23 zoid) were prepared; half the teachers did the line symmetry task first (2014) and the 24 trapezoid task second (2015) and the other half did the reverse. The teachers’ re-25 sponses were coded and counted. 26

Figure 9 shows the several points in which the teachers’ methods of instruc-27 tion changed during the period of the educational intervention. As shown in the figure, 28 increases were observed in teachers’ adoption of collaborative learning situations, 29 multiple-answer tasks, and consideration of points of difficulty faced by students. 30 These changes might meaningfully underlie the changes in students’ strategy use that 31 seemed to enhance their performance on the national test. 32

Finally, we looked at students’ responses to the thinking-after-instruction ap-33 proach. To the question ‘What do you think about this style of class?’, more than 90% 34

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Incorrect answer without diagrams

correct answer with diagrams

Num

ber of problems average)

2014 (n =100)

2015 (n =111)

17

of students responded positively, as did more than 90% of students who indicated that 1 they did not like mathematics. More concretely, students who answered that they did 2 not like maths said things like: ‘This style of class is good even for poorly achieving 3 students like me!’, ‘This is very good: very easy to follow the class instruction’, and ‘I 4 hope this style of class continues’. This is a good sign for this school, with the chal-5 lenge of learning polarization that it faces, and for the broader value of these methods: 6 both high- and low-achieving students reacted positively to this style of class. 7 8

9 Figure 9. Results of ‘Lesson Plan Construction Task’, Points that Increased were Ob-10

served 11

5.  Conclusion 12

The thinking-after-instruction approach not only strikes a balance between direct 13 instruction and discovery learning but also integrates perspectives in Japan before and 14 after 1990. Before 1990, Japanese education greatly emphasised procedural aspects 15 and direct instruction from teachers at all school levels (it comprised to some extent a 16 cramming system of education). On the other hand, after 1990, the value of discovery 17 learning was focused on and, particularly in elementary school, the focus shifted to 18 discovery learning. The slogan ‘support rather than instruction’ became very popular, 19 and many schoolteachers, especially in elementary school, tried not to instruct stu-20 dents until they had found the knowledge by themselves (this was sometimes called 21 teachers’ encouragement of thinking without instruction; thinking-without-22 instruction). The thinking-after-instruction approach is one example of a new trend 23 toward integrating these two extreme ideas of previous periods. 24

Although Japanese teachers and researchers with whom the present authors 25 have discussed this approach sometimes misunderstand thinking-after-instruction as a 26 simple return to the old ways of teaching—didactic, rote learning, or cramming 27 knowledge—this is not the case: as shown in this chapter, thinking-after-instruction 28 comprises the integration of direct instruction and discovery learning, leading to high-29 er-level discovery based on both a full understanding of the value of discovery learn-30

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18

ing and the deeper understanding of basic knowledge. That is, while traditional clas-1 ses in Japan tried to discover the knowledge in the textbook, our approach tries to 2 discover knowledge not obviously presented in the textbook; that is, it focuses on 3 achieving a deeper level of knowledge and learning. Furthermore, our approach tries 4 to help all, not only some, students articulate their discoveries and new understanding. 5 In addition, this approach tries to improve students’ cognitive and meta-cognitive 6 learning skills in daily subject classes. This is because this approach has been pro-7 posed by cognitive psychologists, who have a keen consciousness of the value of 8 cognitive strategy and meta-cognitive awareness of the meaning of knowledge and 9 students’ understanding of their own state of understanding. 10

Lesson study, particularly three-way review, might work very effectively 11 when understanding this approach and designing a class with it. Some teachers who 12 do not understand this approach well sometimes just use the four stages (teacher’s 13 instruction, checking comprehension, deepening understanding, and self-evaluation) 14 when designing a class based on this approach. However, it is important to understand 15 the deep parts of this instructional idea as described above. To achieve this purpose, 16 using three-way review in lesson study is effective, as teachers can more actively ask 17 questions in lesson study in small groups. Furthermore, the rule whereby participants 18 try to create alternative ideas when they find problems may contribute to developing 19 teachers’ competencies at creating effective tasks to check and deepen students’ un-20 derstanding in many situations. The data from lesson plan construction tasks designed 21 by teachers shows this empirically. Teachers in the school never joined the lesson 22 study dealing with the task material, but they can write more sophisticated lesson 23 plans by experiencing three-way review as well as daily practice of thinking-after-24 instruction. Although the effects of three-way review alone should be examined more 25 empirically, it can at least work very effectively when combined with thinking-after-26 instruction. 27

To conclude, let us further discuss the applicability of thinking-after-28 instruction in class and three-way review. We often receive questions like ‘Do you 29 think it is necessary to use the thinking-after-instruction approach to conduct all clas-30 ses?’ We do not argue that this approach is always applicable, for the following rea-31 son. We consider that in school education, two types of learning exist: mastery-32 oriented learning (including deep and conceptual understanding) and inquiry-oriented 33 learning (see Figure 10). This figure is a slightly modified version of the one included 34 in Ichikawa (2004). Mastery-oriented learning typically includes general subject 35 learning, in which the teacher has a clear goal to achieve: inculcating certain 36 knowledge among students. In contrast, inquiry-oriented learning means learning 37 where students themselves set their own goals. A typical example of this type of 38 learning is independent research, which is often assigned as a summer task in Japan. 39 Thinking-after-instruction is, as suggested in Figure 10, a strategy for mastery-40 oriented learning, and it is not appropriate to apply this approach to inquiry-oriented 41 learning. Additionally, even in mastery-oriented learning, teachers may spend time 42 promoting proficiency at certain technical or rote tasks: calculation, or (in Japan) 43 writing Chinese characters, or others. In such cases, thinking-after-instruction might 44 not be a good strategy. However, we maintain that this approach is useable as a stand-45 ard tool in general mastery-oriented learning, which might account for (very roughly) 46 80% of school education, and of which, in turn, around 80% might focus on under-47

19

standing rather than proficiency at skills. Thus, we suggest that thinking-after-1 instruction might be effective across around 64% (80% x 80%) of the whole school 2 curriculum. Although in Japan the word ‘instruction’ is perceived as somewhat nega-3 tive because of the strong trend away from direct instruction since the 1990s, schools 4 have started to come around to this more balanced perspective, and around 50 to 100 5 schools are currently engaged in thinking-after-instruction practice, with many 6 schools also using three-way reviews. We hope that this idea, which emerged from 7 the cognitive psychological perspective, will be correctly understood and will con-8 tribute to students’ development of the necessary skills to prosper in the unpredictable 9 world of the future. 10

11

12 Figure 10. Two Cycles in School Education (slightly modified version of the one 13 included in Ichikawa, 2004). 14 15

Furthermore, it might be important to consider the applicability of this ap-16 proach in other cultures or countries. Although this approach was proposed in Japan 17 and all of the current practices relating to these approaches occur in Japan, these ap-18 proaches may also be effective in other cultures or countries. One of the reasons is 19 that the issue of balancing direct instruction and discovering learning in education 20 may be a more general topic that needs to be addressed in education all over the world. 21 In particular, east Asian countries traditionally have a strong culture of direct instruc-22 tion, so a very important topic is how to effectively integrate discovery learning. In 23 such a situation, our proposal can provide one solution to this annoying problem. In 24 addition, the issue as to how to achieve conceptual understanding and students’ cogni-25 tive and meta-cognitive skills in daily subject learning is very important in the context 26 of international discussion that values competences that promote prospering in society. 27 The combination of thinking-after-instruction and three-way review would work ef-28 fectively, even in other countries. However, of course, the effectiveness of these ap-29 proaches should be examined empirically. Our research groups strongly expect that 30 not only will Japanese teachers and schools engage in these approaches but also that 31 teachers and schools in other countries will understand the value of these approaches 32 and that the practices relating to these approaches will thus be extended. If so, the 33 answer to the question as to whether or not these approaches can work effectively will 34 be demonstrated with empirical evidence. This point is one of the most important 35 future issues for our research group. 36

20

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29 Acknowledgement: 30 The authors' work in writing this chapter was supported by a grant-in-aid (26245075, 31 15K13126, and 15H01976) received from the Japan Society for the Promotion of 32 Science. We would like to express sincere appreciation and gratitude to Emmanuel 33 Manalo for advice and support during the preparation of this manuscript. 34