A framework for analyzing the quality of mathematics lessons

There are only few studies on teachers’ professional development that involves providing teachers with a research-based lens through which they can analyze and think about their lessons. In this paper.

UP NISMED’s Lesson Study Program honored at the 2019 Gawad Tsanselor

UP NISMED’s Lesson Study Program honored at the 2019 Gawad Tsanselor The Lesson Study Program of the University of the Philippines National Institute for Science and Mathematics Education Development (UP NISMED) was honored as one of UP Diliman’s Natatanging Programang Pang-ekstensyon...

World Association of Lesson Studies (WALS) International Conference 2017

NISMED staff as well as teachers from partner schools presented papers at the World Association of Lesson Studies (WALS) International Conference 2017 held at Nagoya University, Japan on 24-17 November 2017.

PALS Inaugurated

The Philippine Association of Lesson and Learning Studies (PALS) Inc. was inaugurated on 10 December 2016 at the Pearl of the Orient Tower in Manila.

Wednesday, August 30, 2017

Students Answering Their Own Questions: Voices from High School Chemistry Classroom through Lesson Study

by Amelia E. Punzalan and Arlene P. de la Cruz apdelacruz@up.edu.ph

Mas napapa-isip ako sa pagsagot sa tanong ko. Celyn, 15 years old (I think more of answering my own questions.)

nasasagot ‘yung hindi namin maintindihan. Ann, 14 years old (… the things we do not understand are being answered.)

The two statements above are part of several explanations given by third-year high school chemistry students during an interview on why they would rather ask questions (and answer them) than answer questions from the teacher. This paper presents the results of the second and third cycles of one of the two high school chemistry lesson study groups under UP NISMED’s three-year lesson study project in public schools in Metro Manila. The focus of the discussion is on the interview responses of the students after the second cycle of the study. It includes comments on teaching and learning science, the students’ questions and answers, and lesson study as a professional development activity and research opportunity in teaching science. 

The lesson study group, which was formed in May 2010, was composed of three chemistry teachers (designated as T1, T2, and T3) and two researchers from the UP NISMED Chemistry Group. These three teachers were all seasoned ones with more than two decades of high school chemistry teaching experience. Both T2 and T3 retired from the service at the end of school year 2012-2013, having reached the optional retirement age of 63 years. T1 and T2 were usually assigned to handle the relatively low-ability sections of about 40 students. As reported earlier (Punzalan, de la Cruz, Nudo, Baltazar, Mindo, & Fernandez, 2013), some of the students in these sections were repeaters. On the other hand, T3, acting as observer, knowledgeable other, and documenter, had been teaching in the top three third-year pilot science classes of the school. 

The lesson study group members decided to adopt the same goal and sub-goal of the 1st lesson study cycle, which are stated thus: The goal is to develop and nurture self-directed learners who have enduring understanding of science concepts that can be applied to real-life situations; The sub-goal is to participate actively in communicating the students’ ideas by asking questions and finding answers to their questions. They also decided Gas Laws as their research lesson. 

At the end of the four-day lesson on Boyle’s and Charles’ Laws, an intact group of six students were randomly selected by T1 and T2 from each of their classes, and interviewed by the two NISMED staff. These two groups of 12 students were composed of 10 girls and 2 boys aged 14 years (50%), 15 years (41.7%), and 17 years (8.3%) years. The purpose of the interviews was to get students’ feedback up close regarding their experience of raising and answering their own questions. The group interviews were conducted right after their respective classes. The students were instructed to be brief and direct to the point in writing down their responses which could be in English or Filipino. The interviewers saw to it that all the students had finished writing before proceeding to read the next question in Filipino. The interview questions were the following: 

1. What was your reaction when you were told to make your own question regarding the activities in your science class? 
2. What was your reaction when you were told to answer your own questions? 
3. Was it difficult for you to ask questions and answer your own questions? Explain. 
4. Which do you prefer the teacher asking questions or yourself asking questions? Explain. 
5. Did you learn science when you were given an opportunity to ask and answer your questions? Explain. 

Based on the students’ responses, as well as their reaction when told by their teacher that their task was to ask questions and answer them, the students expressed that they were excited and surprised, and that they happily welcomed and liked the idea. Therefore, they set themselves to immediately think. On the other hand, they also felt nervous and anxious, thinking they might give wrong answers. However, the students appreciated the teaching style of the teacher; because of which, their questions opened up discussions among them and they were able to freely express their thoughts about their observations and answers to their questions. It was just like imitating their teacher where she elicited from them answers to her questions. 

In this study it was also shown that students did not find the task of answering their own questions difficult. Half (six students) of those interviewed said it was not difficult, while the other half mentioned that it was just a bit difficult. They prefer being the ones asking questions, so much so that they learned their science well. 

Further, it is worth mentioning that the observers noted from the classroom observations that the students were fully engaged in the activity as well as in posting papers on the board, reading their reports, and listening to other group reporters. Students participated actively in communicating their ideas among themselves in both the small groups and the whole class, and to the teacher. 

The students’ explanations about why it was not difficult to ask and answer their own questions at all were further discussed. They reasoned that they made actual observations during the lesson and that they could confidently express themselves because they were using the mother tongue. Tagalog is the base of the national language, Filipino, which is the lingua franca in the area. Additionally, four out of the 12 students interviewed specifically mentioned the advantage of using the mother tongue in communicating and expressing their questions and answers, as well as in understanding their lessons. Their explanations affirmed previous findings regarding the use of the mother tongue (Saong & Punzalan, 2013; Punzalan et al., 2013). The students expressed their reasons for their difficulty: not knowing the correct answers to their own questions and needing to do some more thinking. 

Meanwhile, given a choice based on interview question 4, students overwhelmingly preferred that they be the one asking questions rather than the teacher. Students were learning the things they would like to know, be clarified with, and understand. They would like to ask things they were curious about. The enumerated reasons about the benefits to learning affirmed other studies mentioned in this study (Chin & Osborne, 2008, Eshach et al., 2013, Weinstein, et al., 2010, Carpenter, et al., 2006, Karpicke & Roediger, 2007, McDaniel et al., 2007 cited in Weistein et al., 2010). Students had an idea where the lesson is going to proceed. Interesting questions were asked by other students, which they understood and for which knew the answers very well. Answers were accepted and the wrong answers were corrected. However there were students who got nervous when the teacher asked questions. They said that they learned nothing when the teacher does the questioning. Perhaps, questioning, both a teacher behavior and an important instructional strategy (Kim & Kellough, 1987) does not need to be dominated by the teacher any longer. 

In consonance with the research lesson sub goal ”communicating the students’ ideas…” being able to verbalize what they know, or think of what they know is an important aspect of learning (Developing Communication Skills, n.d.). When students listen to each other, they have the opportunity to hear the same things they already know as well as other questions and ideas different from their own. Along with explanations or answers, they come to realize, first hand, that it is “alright” to have many questions and ideas about an event (Jelly, 1985). Only when ideas are made to surface will there be active learning as opposed to passive or memory learning (Chin, 2001 p. 99). 

The full version of this article is published in the UP NISMED’s Lesson Study Book 2: Learning more together, growing in practice together.

Tuesday, August 29, 2017

Three Teachers, One Lesson on Teaching Trigonometry through Problem Solving in a Lesson Study

by Allan M. Canonigo amcanonigo@up.edu.ph

This article discusses the different ways students solved a given problem involving trigonometry and how the teacher made use of the students’ solutions in introducing and developing conceptual understanding of sine, cosine, and tangent. In this study, the teacher introduced a problem to the class and then allowed the students to solve the problem in groups using their prior knowledge and understanding of some mathematics concepts. There were five teachers who were involved in the lesson study, three of whom implemented the same lesson in their respected classes. Results show that in all three classes, students used graphical representation to understand the problem and to present the solution. The diagrams or graphical representations were essential tools for students’ mathematical thinking. This is consistent with the study of Greeno and Hall (1997), particularly regarding the algebraic, numerical, and graphical representations. In particular, most of them used the unit circle to arrive at their solutions. 

In all these classes, the students were not able to provide much reasons to justify or explain their solutions. However, the problem has already provided opportunity for students to make connections, justify their solutions, and make sense of sine, cosine, and tangent. Two of the teachers emphasized the unit circle method in introducing sine, cosine, and tangent. Two other teachers utilized the students’ solutions in introducing the concept of sine, cosine, and tangent. Although these teachers vary in their approaches to utilizing students’ answers and solutions, two of them attempted to ask probing questions to elicit students’ justifications to their solutions. This helped the students to make a clear connection of previous mathematical concepts which were needed to solve the problem. 

In planning a lesson, the teachers involved in the lesson study team realized that in order to be effective in teaching, students’ current knowledge and interests must be placed at the center of their instructional decision making. Although they wrote all their intentions in the plan prior to the implementation of the lesson, they learned to adjust their instruction to meet the students’ learning needs. They also realized that instead of trying to fix weaknesses and fill gaps, they can make use of students’ existing proficiencies – by making use of the students’ solution to the problem in order to help them understand the concept of trigonometric functions. 

As shown in this study, the students could solve a problem in different ways when they were given the opportunity to do so. The students were able to work in groups effectively and came up with a solution and the reasoning behind that solution. On the other hand, it is very important that the teachers are able to process these solutions to develop conceptual understanding of sine, cosine, and tangent. For the teachers involved in this study, it was a challenging task for them to introduce the lesson and develop students’ conceptual understanding through problem solving by utilizing students’ solutions and answers. 

The teachers found the lesson study a rich learning experience. Through planning the lessons collaboratively, they were able to deepen their subject matter knowledge as well as their understanding of how to teach sine, cosine, and tangent. It provided them with the opportunity to actually see and be sensitive to how students processed their thinking, how students’ misconceptions and difficulties could arise, and how it was an eye-opener to observe how the students struggled with the problem, and how teachers used students’ solutions to develop conceptual understanding in different ways. They were able to see that a good lesson is one that meets the learning needs of the students. Such teachers are responsive both to their students and to the discipline of mathematics. It is therefore recommended that, whenever mathematics teachers use “real-world” contexts for teaching mathematics, they maintain a focus on mathematical ideas. 

The full version of this article is published in UP NISMED’s Lesson Study Book 2: Learning more together, growing in practice together.

Thursday, August 24, 2017

Learning the Nature of Inquiry-based Teaching through Lesson Study

by Ivy Mejia

A number of reform-based initiatives in science education are focusing on inquiry as an approach to science teaching. A case in point is the K to 12 Science Curriculum of the Department of Education (DepEd, 2016). The general standard for this curriculum is for students to acquire an “understanding of basic science concepts and application of science inquiry-skills” (DepEd, 2016, p. 4). However, there are varied conceptions of inquiry both in preservice and in-service education (Akerson, Abd-El-Khalick, & Lederman, 2000). To regulate accurate understanding of inquiry in science instruction, teachers needed support in this area. To reconcile the need for the development of inquiry and support, the University of the Philippines National Institute for Science and Mathematics Education Development (UP NISMED) initiated a collaboration with five science teachers at a typical public school in the National Capital Region. It was a three-year project whose main goal was to enhance the capacity of science teachers to strengthen the inquiry skills of the students. This article will not describe the entire project but only the results of the first year of implementation of a professional development model, which is referred to as lesson study. 

The study employed a case study design where the case is a group of five teachers and two UP NISMED staff. The data collected were drawn from the several stages of lesson study: planning, implementation, and post-lesson discussion. The research lesson is on “evidence of chemical change.” Two classes of first-year students were selected to gather data on teaching and learning with a focus on inquiry skills. The transcript of the group discussions and lesson implementations were subjected to content analysis. These were coded and categorized to draw patterns on science inquiry skills gained both by the teachers and students. 

Figure 1. Students synthesizing their observations drawn from the activity on evidences of chemical change (Photo credit:  High School Earth Science Workgroup).
The entire process of lesson study brought realizations to teachers that unpolished process skills of students served as barriers to the development of inquiry skills. During the first lesson implementation, students had an alternative conception on initial and final observations. For example, they had to describe a piece of bread before and after it was burned. Their initial observation was that the bread looks brown while their final observation was that the bread became toasted. Another instance was ignoring the changes on the surface of a sliced eggplant once it was exposed to air. For them, they have been used to this appearance and did not consider it as a change. The group had to revise the lesson by revisiting observation as basic process skill. Students were taught what is meant by initial and final observations. On the second implementation, students were able to describe the physical and chemical changes. They provided explanations based on evidence brought by employing careful observations on changes as drawn from the activity. 

On the first year of lesson study, the members concluded that enhancement of inquiry skills of students was dependent on prior process skills of students. The group focused on the inclusion of inquiry but it overlooked the prior readiness of students to engage in inquiry. The planning, implementation, and lesson study discussion, as part of lesson study cycle, served as a way for the group to understand the factors affecting the acquisition of inquiry skills both to teachers and students. Although students were observed to have been discussing their explanations based on evidence, this does not guarantee that they have understood this feature of inquiry. The students should not only undergo the process of inquiry but also demonstrate an understanding of the process of inquiry. This is achieved when teachers are both competent in knowledge and skills about inquiry. 

The full version of this article is published in UP NISMED’s Lesson Study Book 2: Learning more together, growing in practice together.

Thursday, August 10, 2017

World Association of Lesson Studies (WALS) International Conference 2016

On September 3-5, 2016, four NISMED staff presented their papers* in the 10th World Association of Lesson Studies International Conference at the University of Exeter, the United Kingdom. The theme of the conference was on the role of lesson study in transforming teaching and teacher learning in professional learning communities.  The entire conference highlighted the benefits of collaboration which is built on lesson study.  When teachers collaborate with their colleagues they start to build self-efficacy, gain new idea on how students learn which results in deep learning, receive moral support, and predict future success as an effect of working together.  During the conference, there was also a presentation on countries that managed to sustain lesson study, such as Cambodia and Indonesia.  It was also suggested that lesson study has to be the culture of school even if the principal leaves the school.  The relationship between the principal and the faculty is far more important than the top-down approach to sustain lesson study. Investing in social relationship such as principal-to-teacher and teacher-to-teacher is what Andy Hargreaves, the keynote speaker, referred to as Social Capital.  
*Title of papers presented in WALS 2016
Sustaining the culture of collaboration in lesson study through fostering a collegial atmosphere:  A practice-based case study
Ms. Jacquieline Rose Gutierrez

Students’ answering their own question:  Voices from high school chemistry classroom Ms. Arlene dela Cruz
Influence of culture in adapting lesson study
Ms. Ivy Mejia and Mr. Eligio Obille