For my next part of the journey, I will be investigating the question:
How can a mathematics teacher differentiate for students in need of extension or support in an inquiry learning experience?
This is a question that really interests me. I know in the past when I have embarked on inquiry experiences in History or Geography, I have usually held small groups to practise skills to support their inquiry, or met with children one on one. But these are usually longer time frames that allow for this to happen. Inquiry in Maths can be short, I’ve learned, so how do I support students with less mathematical ability and how do I design tasks that can cater for extension students?
I will be using ProQuest education for this search. I have never used ProQuest before so I am interested to see what it will be like. To begin, I again compiled my search terms and their synonyms into a mind map.
This time, I decided to use the “subject” field code to look for maths and differentiation under the subject of inquiry learning. I chose the Education databases and plugged in my search.
|SU(inquiry OR “inquiry-based” OR “problem-based”) AND (maths OR mathematics) AND (differentiation OR extension OR support OR ability)||1,336
|Some of these results centred around some of the search terms but not all. Some used the term inquiry as teacher inquiry and others had studies on differentiation in Maths, but not Inquiry-based Mathematics. There were articles on the effects of Inquiry-based Mathematics on students, but not on methods of differentiation.
There was one result of note.
The Impact of Problem-Based Learning Curricula and Teachers’ Mathematical Knowledge for Teaching on the Mathematical Development of Second Grade Students highlighted the need for effective differentiation to be proactive rather than reactive, which means “planning a lesson, from the outset, which addresses the needs of all learners instead of planning a “one size fits all” lesson” (p125). The document goes on to list methods such as use of small, homogenous teaching groups, where students are placed into in purposefully-planned groups so the teacher can meet their common needs and are expected to collaborate and work together. This would require a depth of knowledge about what the learner knows. Each group (and sometimes individual) is also provided varied materials based on their abilities, and pacing. While differentiation was planned, opportunities arise where differentiation can occur in a teachable moment. The article points out that in order to take advantage of these moments, teachers must have a strong content knowledge, teaching knowledge and student knowledge.
This was a great resource, but I needed more. This time, I decided to put all my search terms under a subject field code. I hoped that this could turn up results where these terms were more frequently mentioned. I deleted the word “ability” as I found it was turning up too many unrelated results.
|su(“inquiry learning” OR “inquiry-based learning” OR “problem based learning”) AND su(differentiation OR extension OR support OR gifted OR ability) AND su(mathematics)||21 results||This reduced my results significantly, and terms such as gift, talents and inclusive learning began turn up in the titles.
However, there are still a lot of irrelevant results about undergraduate courses and other subject fields, mainly science.
2 helpful results.
Gifted Students: Differentiating Mathematics and Science Instruction. It’s Just Good Teaching Series also spoke about grouping students based on abilities, but also according to preferences.
“Students will decide how much information they want to work with, how complex their solutions will be, and how they will demonstrate their learning. The teacher can also provide varying levels of guidance. Some students will need more assistance with defining the problem and planning their work.” (Stepanek, 1999, p.34).
This showed many consistencies with the first source I found. I wonder if grouping students according to preferences would be more viable in a science classroom. Perhaps you could do interest-grouping with some students.
Student Wonderings: Scaffolding Student Understanding within Student-Centred Inquiry Learning. This study spoke about methods of scaffolding students in their individual Zone of Proximal Development by anticipating conceptual misunderstandings. Again, this requires a deep level of understanding of the student’s abilities and pre-planning. The study specified six tutor actions for differentiation: “recruiting interest in the task; reducing the degrees of freedom (simplifying the task); maintaining direction towards the goals of the task; marking critical features; controlling frustration; and modelling the preferred procedures by demonstrating”.
This was a very long study and only some of it was relevant, but it had some concrete examples from teachers using inquiry learning. This study also spoke briefly about learning disabilities, which I included in my next search.
|su(inquiry OR “inquiry-based learning” OR “problem based learning”) AND su(learning disabilities) AND su(mathematics)||15||
I changed “inquiry learning” to inquiry in this search, as I didnt get any results of note. This didn’t have a significant effect on results, and many were still the same. There was one good result however.
The Inclusive Classroom: Mathematics and Science Instruction for Students with Learning Disabilities. It’s Just Good Teaching seems to be from the same series as Gifted Students: Differentiating Mathematics and Science Instruction. It’s Just Good Teaching Series which I referenced earlier. This book advocated for “mapping” topics, requiring teachers to understand what essential concepts students need to know and what they would need to know before this. It made me consider how I could use the Scope and Sequence for Mathematics in my planning.
This was a very frustrating search process. I felt like I was looking for a needle in a haystack. With Google, it was often immediately possible to tell whether or not your results would be helpful, but some of the complex wording in these documents, their long titles and the lack of a preview underneath made it sometimes difficult to determine what the article was about. While I did find a few good results that helped build my understanding, it was difficult to work out how to cut out out the results I didn’t want, as they all seemed to come from different fields. Perhaps if I had done some google searching on this topic first, I would have a better idea of what terms I was looking for.
Nevertheless, I came away with some good ideas on differentiation. Happily, my methods of group work and one-on-one appear to be a good start. My next step seems to be anticipating and planning for student understanding and needs, grouping for required skills and investigating the “before and after” skills using the scope and sequence before beginning a new inquiry with my students.
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