**Lesson study. Practice** **research**

**Шалкенов Жаслан** – учитель математики в Назарбаев Интеллектуальной Школе Нурсултан.

*Abstract:* The purpose of the research is to explore five (5) horizontal differentiation strategies in mathematics lessons and their effectiveness by researching the literature in this area.

The main question of this research is: What are the strategies of horizontal differentiation in mathematics lessons?

Key questions in order:

- What is differentiation in the classroom and on what basis can students be differentiated?
- What differentiation strategies are common in math lessons and how effective are they?
- How exactly is horizontal differentiation applied in mathematics lessons?

*Аннотация:* Целью исследования является изучение пяти (5) стратегий горизонтальной дифференциации на уроках математики и их эффективности путем изучения литературы в этой области.

Главный вопрос исследования: каковы стратегии горизонтальной дифференциации на уроках математики?

Ключевые вопросы по порядку:

- Что такое дифференциация в классе и по какому признаку можно дифференцировать учащихся?
- Какие стратегии дифференциации распространены на уроках математики и насколько они эффективны?
- Как именно горизонтальное дифференцирование применяется на уроках математики?

*Keywords:* lesson study, action research, practice research, differentiation.

*Ключевые слова**:* изучение урока, исследование действия, исследование практики, диффиренциация.

I want to evaluate the effectiveness of five horizontal differentiation strategies in the classroom. It is easier for me to assess the effectiveness of strategies with an ordinary coefficient of effectiveness, that is, to compare the results of students before and after applying the strategy, as well as take into account the time spent by the teacher to apply the strategy. For example, a teacher can apply a certain strategy for six months and, as a result, students' results will change by a certain number of points. Thus, it will be possible to assess how effective the strategy is. In this case, it is necessary to clearly define in advance in what quantitative characteristics the goal of a particular strategy can be measured. I am planning to use a quantitative experimental correlational design. According to Creswell (2014), a correlational research design “provides an opportunity to predict scores and explain the relationship among variables using the correlation statistics” (p. 364). This design is appropriate for delivering the study when seeking to correlate two or a number of dependent and independent variables and investigate if they affect each other (Creswell, 2014). In my research, I plan to look for a correlation between the amount of time spent using statistics in hours (in my case, in lessons) and the resulting gain in learners for each of the five horizontal differentiation strategies. If the correlation coefficient is high enough, I can compare the linear functions formed by the ratios of hours to results and identify the most positive trend among the five strategies. Also, using the extrapolation method, it will be possible to calculate how long it will take to achieve a certain result or what result can be achieved in a certain time. The independent variable will be the number of hours; the dependent variable will be the result.

I believe that such a study, although it examines the effectiveness of strategies from a purely numerical perspective, it saves me from any subjectivity when comparing strategies and gives clear numerical indicators. When comparing the effectiveness of something, the numbers are the most understandable and convenient tool.

**Name of the Method**: Interview

**Format or approach: **Focus Group

**Participants: **Secondary school math teachers

**Reflection**: This method is appropriate for my research study because the topic of my research is effectiveness of horizontal differentiation strategies and the best way to identify if strategy is really effective on math lessons or not – is to ask math teachers directly. This method aligns well with my research problem and purpose statement. This method will help me answer my research questions by analyzing the responses of the interviewed teachers. I am interested in the practical application of strategies in mathematics lessons. No matter how good and effective a strategy looks on paper, it is much more important to demonstrate its effectiveness in practice. And only practicing mathematics teachers can confirm this. As a mathematics teacher, I am sure that all mathematics teachers are faced in their practice with the need to apply differentiation strategies. There is usually an urgent need to apply vertical differentiation strategies, but I think many teachers have tried horizontal differentiation as well. I plan to structure the questions in my interview in such a way as not only to get feedback from teachers about how effective a particular strategy is, but to try to come to my own conclusion based on their answers. Indeed, in terms of the effectiveness of teaching, it is difficult for a teacher to objectively assess how effective his strategy was in the lesson. I will also include questions about how the teachers learned about a particular strategy they used. Perhaps some of them have already done research like mine. Then I will ask about it much deeper and the information obtained from interviews with such teachers will be even more valuable for my research.

In conclusion, I believe that any study that examines the effectiveness of any strategies or other things that can only be tested in practice will get a lot of benefit from interviewing people who implement these strategies in practice, this is obvious.

**Type of instrument**: Questionnaire

**Participants: **Secondary school mathematics teachers

**Reflection**: The design of my study is quantitative and I am going to use the analysis of the numerical data obtained by calculating the correlation coefficient between the specified two variables. In the future, if the correlation is strong enough, I will use the extrapolation method to predict how effective certain horizontal differentiation strategies will be or how long it will take to successfully apply the strategies. This method is suitable for my research, since with a sufficiently large sample of math teachers, conducting a survey can give all the interesting and useful numbers. So using a classic questionnaire with answer options attached to scores from 1 to 5, you can get numbers that characterize the opinion of teachers on certain questions. For example, I can create a series of questions about how teachers apply their strategies and get a number that indicates how a particular teacher is applying a particular strategy. Also, questions can be made about what teachers think about the effectiveness of a particular strategy, and again, we will get the numerical equivalent of their opinion. I can also use the questionnaire to formulate questions about the narrowly focused specifics of teachers. That is, ask how exactly they apply horizontal differentiation in mathematics lessons and thus, the resulting numbers will be able to answer one of my research questions. In addition to direct questions regarding the effectiveness of strategies, I can also ask many leading questions, based on the results of the answers to which I can draw certain conclusions regarding the effectiveness of strategies. For example, I will ask how much time the teachers spent on applying the strategy and what results they achieved. Later, using the data obtained, I will be able to independently calculate the effectiveness of a particular strategy.

*References*

- Creswell, J. W. (2014).
*Research design qualitative, quantitative, and mixed methods approaches*. Thousand Oaks, CA: SAGE Publications. - Monitoring of inclusive education in the Republic of Kazakhstan. (2017). MESRK, JSC “IAC”.
- T. M. “Schools’ Transition Toward InclusiveEducation in Post-Soviet Countries: Selected Cases in Kazakhstan”. (2020)SAGE OpenApril-June 2020: 1–13.

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