Textbooks and the Mathematics Curriculum

I have taught Intermediate math almost exclusively in my first 12 years of teaching and I did it strictly out of the textbooks that were provided for me. Eventually, I progressed to be very selective of the textbooks in influencing our school's purchasing so that the textbooks were a "best fit" to the current version of the Mathematics Curriculum. I didn't do any PD nor read any research. I taught math out of the textbook as that is what I thought had to be done. Differentiation as far as general lesson delivery wasn't much of a presence. Everyone received the same lesson independent of their current understanding. When the students were assigned independent work to do, that is when the grunt work began to get to as many students as possible in the limited time to help them see the main strategy that I was teaching. It wasn't about students developing conceptual understanding or learning it in their own way. It was about getting students to follow the set rules in math and just decoding the questions in order to connect the only correct procedure so that they can get the only right answer. Since, I switched to Primary (Grade 3) two years ago (this is my third year teaching Grade 3) and I immediately went to the textbook (Minds on Math) to run my math program. I quickly noticed that my set ways of teaching math (which I really wish I could go back and redo in a more inquiry based model) were my way of learning math and that this wasn't working for pretty much everyone. They needed more guidance as they worked through the task. Students needed more chunking into smaller parts in order to be able to handle the tasks. I was seeing past the procedures and seeing that I needed to get the students to buy into the concepts first in their own way. I tried for two years to run an inquiry model, but fell back onto the traditional textbook way quickly as I wasn't understanding how to run a program in that way. This year, I have been fully committed to an complete inquiry model with 3 Part lessons that focus on the individual student and I am struggling to build lessons and tasks for students that take all aspects into consideration. When I do this well, the students flow with the learning so smoothly, but when I make a mess of the partnered tasks, the students are left with so much confusion and lack of clarity in where to go, what strategies to use, and how to solve the problems. I have much more learning to do in so many aspects of my math program, but I am committed to creating the best math program possible for each of my learners and when it works well, it is so amazing to see the learning (again, I wish I could go back and redo my 12 years of traditional mathematics teaching as I am sure I'd be more effective then I was for those years).

As to how my use of textbook changes when implementing a newly released curriculum guideline, there wasn't a whole lot of change in the use of textbooks. The focus just shifted on the types of questions used for the independent tasks and often supplementing the base work with additional problem solving work or sometimes the use of manipulatives. But, the base of my program at that time built off of the textbook.

This year, I do not use a textbook at all (I actually gave them all to another teacher that doesn't run an inquiry program that was very much in need of the books). As of right now, I am very happy to not be using the textbooks. This is because of the work I did this summer in Mathematics Part 1 and now Part 2 where I have learned to more effectively analyze all aspects of the curriculum and construct very thought out long range plans for the whole year in Mathematics. This has given me a much deeper understanding of where the students should have gotten to in Grade 2 and where they will be going in Grade 4 to have a much clearer vision of what is necessary for Grade 3. I have never looked at the expectations and compared/connected across the strands and into other subjects to deeply. This has given me the base I need to stay focused as to what curriculum needs to be covered and when with connections to other subjects. From here, I use various authentic assessments to determine where each learner is in their understanding of math concepts and what misconceptions need to be clarified. At the beginning, this was a huge amount of work to build tasks with multiple entry points and parallel tasks giving students choice of meaningful rich tasks to explore their learning. I really like the inquiry approach and building unique authentic tasks for students as this engages them immediately in what they are doing and learning seems to be moving so fluidly.

I don't think the current textbooks we have in our school meat the teaching approaches in the curriculum guidelines as there isn't a whole lot of students building their learning using their own strategies and analyzing other strategies for effectiveness and efficiency. From what I have seen, the tasks are geared towards following the example strategy which can really limit creativity and stifle learner where students might discredit their own reasoning. Also, there isn't a whole lot of communication built into many of the lessons where students share their strategies and justify their reasoning. From personal experience, building this on my own from scratch helps to shape the lens of what I am looking for as indicators of student learning and this really helps me be more effective as I facilitate the learning throughout the 3 Part lessons.

Right now, I have the best understanding of the math curriculum then I've ever had and I owe it to having to shred the curriculum and make my own connections to build an overall plan for implementation. Having done this, my focus is very strong (may the math force stay with me!) when building rich authentic tasks for the needs of my students. I am not thinking of every going back to a textbook. But if one were available that I would consider, it would have to include samples of questions that would scaffold to meeting overall expectations. These samples would model the thinking and timeline of scaffolding to build the learning. I wouldn't need lessons on delivery, rather how the problems connect and relate to the culminating tasks that are coupled with direct learning intentions and support in building success criteria with my students. The problems don't even need to be fully written problems, rather prompts of things to consider in a diverse equitable classroom where I can plug in a context and vary the entry points for my learners. Samples of parallel tasks would also model how to differentiate for a group of learners. In addition, up to date assessment strategies (for, as, and of learning) and what to look for in the learning as indicators and flags to support descriptive feedback. This would be a great tool that would empower me to be more effective in building the appropriate program that keeps my learners' unique learning strengths at the forefront.

Culture and Gender Influences in Mathematics

From the article "Gender, Culture, and Mathematics Performance" we learn that there has been previously a gender difference in mathematics performance between the genders that existed until the recent few decades. The article states females have matched the males in mathematical performance, a narrowing of gap between the genders in scoring above the 95th or 99th percentile, and that although not recognized frequently as males, that they have documented females with  profound mathematical talent. In looking past the numbers for explanation, the researchers recognize that a gap that may have existed but has either dissolved or is narrowing and can be directly connected to sociocultural factors rather than a biological distinction.  As we read through the article we learn that over a hundred years ago, women didn't have access to programs/courses that would extend their skills. The equality of access can be attributed to some of the differences that may have been present in previous studies early in the 20th century and have gradually faded out leading to the elimination of the gender gap. We know today through the mandatory nation wide every grade testing attached to the "No Child Left Behind" US government initiative, that females are taking on par many of the courses that they used to not take and now they are seeing a parity in performance levels. This is then connected to a change in jobs that were held by females several decades ago to today. Over time, females have almost equaled(49%) the males in attaining jobs that required math and science. This can be directly attributed to a change in sociocultural and environmental issues that have changed the access females have to science and mathematics courses as well as having equally high expectations of females as those of males to learn in these fields. Access to and gaining jobs is also connected to a change in sociocultural ideologies where females have arguably equal access to jobs as males. This has contributed to a national culture where all learners are on par.

Connecting this to my classroom, I take from this that gender learning is connected to the cultural and environmental climate of the community that influences that of the students and builds into our class learning climate. I feel that separating the genders would be a limiting move by removing learning experiences that will build a more comprehensively skilled collaborative learner. It is then incumbent on the teacher to filter out any limiting community influences that would be barriers to females learning mathematics and facilitate the building and maintaining of a gender equal inclusive student centred classroom that maintains high expectations for each and every learner. This environment needs to be coupled with specific intentional assessment that aims at the individual strengths in acquiring and mastering skills necessary to meet the learning targets along their own learning path.