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Incorporating the First Peoples Principles of Learning (FPPL) – Educating Now
In this blog I’m going to continue to explore some of the ways we can incorporate the First Peoples Principles of Learning (FPPL) into our daily math lessons. Last blog, we looked at incorporating experiential learning and multiple strategies and so I’d like to continue to unpack this principle:Learning is holistic, reflexive, reflective, experiential, and relational (focused on connectedness, on reciprocal relationships, and a sense of place). Holistic:My ethnomathematics experiences have taught me the value of holistic learning. I consider holistic learning to include learning in authentic contexts as well as learning that is centered on the wellbeing of the person and their communities. Learning in authentic contexts is integrated or cross-curricular learning (can also be problem-based or project-based learning). In terms of learning that is centered on the well-being of the learner, I think about the different worldviews and value systems as well as choice, being outdoors and moving while learning. Examples:a) This lesson centered on the Gorge Waterway incorporates different subject areas such as Social Studies, Science, Math, English Language Arts and focuses on the importance of the waterway for the Lekwungen peoples and all of us who live in Victoria. b) As a class discuss some problems that are specific to your community (classroom, whole school, surrounding community) and then students will work in groups to solve them or at least understand the problems in more complex ways. An example for teachers at Cedar Hill is to approach the owners or managers at Fairways grocery stores and discuss food waste while also looking at the statistics for how many folks in Victoria use food banks. Students can use different charts, maybe percentages and will likely perform many other operations as they determine the total food waste per day, week, month, year, etc. Ideally, they’ll be able to provide some ideas for reducing food waste and supporting those who don’t have enough to eat. Reflexive and Reflective:I’ve had a lot of experience with reflective learning and teaching but reflexive was a new term to me. I’ve found different definitions but have found the following ones useful: Reflexive:When we encourage students to be self-reflexive, we are asking them to understand what they are learning as they are learning. Additionally, self-reflexivity not only allows students to understand what they learned but why they learned it.(https://www.chronicle.com/blogs/profhacker/reflexive-pedagogy/22939) Reflective:Teachers who promote reflective classrooms ensure that students are fully engaged in the process of making meaning. They organize instruction so that students are the producers, not just the consumers, of knowledge. To best guide children in the habits of reflection, these teachers approach their role as that of "facilitator of meaning making."(http://www.ascd.org/publications/books/108008/chapters/Learning-Through-Reflection.aspx) -I consider both of these important aspects in developing student agency – helping students to be the drivers of their own education, rather than passive receivers of information. Examples:a) As students are problem solving stop them periodically to check-in. Ask them to reflect on what they are doing and have done so far: “what’s working?” “what’s not working?” “Do you understand why you are doing?” “Do you need to think about it differently?” “Could you think about it differently or solve it in a different way?” “What could help you in this moment (picture, discussion with others, tools, etc.)?”b) Students can keep a learning journal or keep their own notes to document their current understanding of math concepts and as they are doing this they can be asking themselves “if I read this in a month, will I know what I’m talking about?” They can use pictures, analogies, examples, or anything else that will help them to communicate their understanding.c) Use contexts often – this helps with the ‘why are we learning this’. When students solve problems rooted in contexts they see it as useful and meaningful.d) Ask “WHY?” all the time. Annoyingly often. We want our students to get into the habit of proving and justifying their ideas. You might also give sentence stems (on a poster) for students to use (especially helpful for ELL and FRIM learners):“My estimate is because ______”“I think the answer is ______ because ______”“I used (this method) to solve the problem because ______” In my experience it does take some time to get students into this habit and at first, they don’t like the “becauses”, which I understand – it’s challenging to explain our thinking at times but it’s also really importante) Do daily reflections at the end of every lesson. I recommend leaving 4-7 minutes for this. I usually do this orally for a few reasons: it’s faster, easier for most students and I like the students to hear each other’s reflections. I usually ask students to rate their level of understanding of the concept with their fingers (1-4) as well as a verbal reflection in answer to a question specific to HOW we learned such as “how did using the base 10 blocks affect your understanding of place value?” or more general questions like “what was the most challenging aspect of today’s lesson?” “What mistake helped your learning today (their own or someone else’s)?” etc. I also feel the need to reiterate the fundamental message from my first blog in this series: relational learning is key! If we truly want to use the FPPL then we must start by building respectful relationships with our students and also we MUST look for each student’s strengths and gifts, rather than viewing them through a deficit lens. I first heard the expression “bias of lowered expectations” used at a FNESC conference a few years ago and it hit me like a bus because I knew I was guilty of it. When we are looking at our students through our own set of values we may not even see their gifts because they are not what we might consider academic or ‘school related’ gifts. I wonder what would happen if we found their strengths and incorporated them into our teaching. Relational learning means that we learn from each other. There is a reciprocity of learning and teaching. This is also a way to share power with your students. Search for ways that you can learn from your students – I really think you might be surprised at what you learn and also how this relationship dynamic changes how students show up for learning. Lastly, I want to encourage you to really listen to your students’ mathematical thinking. It may seem wrong or illogical at first but be curious about their ideas, rather than being on the hunt for the ‘right answer’. If we can meet our students where they are at, in terms of their understanding, we can better support them in moving forward. I’ve often had to ask students to repeat their thoughts 2 or 3 times as I try to make sense of it and understand it and this act shows them that their ideas are worthy of talking about and thinking about.
Race and Math Education – Educating Now
In this post I will share some thoughts about how we can reach towards equitable education for all of our students as well as work towards reconciliation. Difficult Conversations... I believe we need to educate ourselves on the true history of Canada and the systemic racism that is still embedded within our education system and other government systems. I know this is uncomfortable for many non-Indigenous people but without really understanding the impacts of colonialism – past and present – I’m not sure we’ll ever have an educational system that will be equitable. I’m in the rabbit hole with this concept and am not an expert at all but think it’s important to share these ideas because it’s all too easy for non-Indigenous folks to ignore what’s going on because it doesn’t affect us directly and because we can. However, BIPOC (Black, Indigenous, People of Colour) cannot ‘opt out’ because they face racism as a part of their lived experiences. Furthermore, if we don’t have a decent understanding of how our own worldviews differ from our students’ and how our lived experiences differ from theirs, then we are likely to have big blind spots in our teaching practices Until quite recently, I had been completely ignorant and naive about racism in our society. It wasn’t until I read “White Fragility” that I even understood that racism is a system, not an act, and that most people misunderstand what racism and white supremacy mean. Since reading that book (which I highly recommend), I’ve been following a lot of teachers on Twitter, who are actively addressing the systemic racism that lies within the education system. If you read the last few blog posts I’ve written then you’re now already aware that there are different worldviews and that those have a big impact on learners. Imagine you were educated in a system that promoted a totally different set of values to those of your culture? What would it feel like to be in a classroom, helping your friend understand a quiz so he can be successful and be called out for cheating, even though you’ve been taught from your family and community that the most important aspect of education is to help one another? How would it feel to be taught math using only symbols and abstractions when you’ve learned through experiential learning at home for your whole life and the symbols just don’t mean much to you? I’ve come to realize that we’ve been gearing our education system around Western worldview values. This feels to me like we’re continuing to colonize a group of people who have already been colonized almost to death (and many have been colonized to death). I’m well aware that we are living in a time right now that is so noisy with political strife and racial wars that it makes it difficult to figure out what feels right or wrong. As I read parts of the Indian Act, the Truth and Reconciliation report, ‘An Inconvenient Indian’, ‘Unsettling the Settler Within’ and listening to podcasts like “All My Relations”, I have come to understand that I really had no idea what was really going on within our political system and education system in terms of the treatment of Indigenous peoples. It’s been eye opening and sobering to say the least and I have so much more to learn. I feel it’s my responsibility as someone who some people listen to (that’s you!) to speak about these issues. Understanding the history of our country will better equip us with the tools we need to educate all of our students in ways that acknowledge and respect their cultures. This is what I believe ‘Truth and Reconciliation’ is. There are so many big issues like these that I’m grappling with and will continue to explore. If you’re anything like me, this may feel very overwhelming for you and you may be wondering “what can I do?” or “where do I start?”. I don’t have definitive answers for you as I’m just beginning my own learning but here are some suggestions: Read the books I listed above Share what other books, articles and podcasts we could read/listen to that will help educate us. I know we’re busy but summer break is coming up…maybe add a book or two into the rotation of your other ‘summer reads’. Follow people on Twitter who are from different cultures, races and places than you. Here are a few that I follow that have offered me some significant insights: @NativeApprops, @apihtawikosisan , @LBmathemagician , @DingleTeach , @ShanaVWhite , @ValeriaBrownEdu , @Mathgarden , @YehCathery ,@Pam_Palmater , @NicoleBridge1 , @beRealcoach Engage in these difficult conversations with others. I think we should be talking about this during staff meetings. I think we should be talking about racism with our students too but we need to be mindful and well enough educated to do so properly. Seek out professional development opportunities that are geared towards equity Read books written by Canadian Indigenous writers (I’ve really enjoyed the novels, memoirs and history books I’ve been reading and I feel like they give me a glimpse into a lived experience that is vastly different from my own, thus expanding my perspective, or the lens through which I see the world). Some that I’ve read recently are: ‘Monkey Beach’, ‘Johnny Appleseed’, ‘The Marrow Thieves’, ‘Indian Horse’ (I’ve loved all Richard Wagamese’s books). Here are some other suggestions: https://www.cbc.ca/books/108-indigenous-writers-to-read-as-recommended-by-you-1.4197475 Attend Indigenous community events (when public are welcome) – even when it feels scary being a minority as maybe experiencing this will be the best education we could ask for. We can’t magically learn all we need to in any short amount of time so I look at this as a life-long, continuous journey. I intersperse these books with my other reading and will continue to do so. I’ve got a stack of books that I’m diving into next that were recommended to me by colleagues: ‘A Fair Country’, ‘Indigenous Writes’, ‘Potlatch as Pedagogy’, and ‘Tilly and the Crazy Eights’ Thank you for taking the time to read about these important issues. Please comment and share to continue this much needed conversation! Note: I’ve given you some links to some of these books but many are also available through the public library, which is where I accessed some.
Culturally Responsive/Sustaining/Revitalizing Pedagogies Resources: – Educating Now
Books: Websites/articles: https://scenicregional.org/wp-content/uploads/2017/08/Mirrors-Windows-and-Sliding-Glass-Doors.pdf (Rudine Sims Bishop’s article)http://www.ascd.org/publications/educational-leadership/sept95/vol53/num01/A-Framework-for-Culturally-Responsive-Teaching.aspxhttps://www.tolerance.org/classroom-resourceshttp://www.teachingworks.org/images/files/TeachingWorks_Paris.pdf Webinars: https://www.youtube.com/watch?v=O2kzbH7ZWGghttps://www.tolerance.org/professional-development/webinarshttps://www.nelson.com/learningonline/pl.html (scroll down for culturally responsive math webinars with examples of lessons)https://www.angelanardozi.com/webinars https://www.youtube.com/watch?v=5m6c4aUYZow&t=43s Lesson plans: https://sites.google.com/site/ethnomathematics/lesson-planshttps://www.todos-math.org/index.php?option=com_dailyplanetblog&view=entry&year=2019&month=05&day=22&id=11:ethnomathematics-mathematics-de-todoshttps://coe.hawaii.edu/ethnomath/curricula/
Sequences For BC Math Curriculum – Educating Now
I get asked a lot for scope and sequence and so here are some ideas for each grade K-8. Please keep in mind the following when viewing the sequences for each grade level: [caption id="attachment_1260" align="alignnone" width="1200"] Math Scope and Sequence[/caption] Sequence: There are lots of right ways to organize the content and each sequence is one way you may choose to use. Combining topics that are applications of others or that naturally align will benefit students by giving them ways to implement their learning and by seeing the connections between concepts. The more connections students can make, the better! It also benefits you because it can reduce the amount of time you might spend on concepts if you taught them all as stand-alone concepts. Get creative – if you have ideas about how concepts can be connected, try it out! The content is NOT the most important aspect of the curriculum – the curricular competencies are the vehicle through which you will teach so they are to be used in order to teach the content. You will use multiple competencies in order to teach each content standard. Each sequence will start with review or the most basic content first so that we help our students get a strong foundation before attempting to build on it. However, I strongly advise using diagnostics (paper and pencil and/or interview) in order to know if you need to revisit previous years’ content areas. We need to meet our students where they are at and so charging ahead with the current grade level’s content may not be appropriate. Scope: See the elaborations in the curriculum for ideas for scope – they will guide you in a variety of activities to dig deeper into the content. Also use the Big Ideas as a guide. The goal is to teach students the content by using the competencies to get to the Big Ideas. If your students understand the big ideas, it’s time to move forward. If you aren’t sure what a content standard means or an elaboration means please comment on this post or email me so we can offer support! Sometimes the language used is really tough to understand (especially if you are not math trained). How long you spend on a given concept will depend entirely on the students in your class. Some years a fraction unit would take 2-3 weeks, while other times it took 6 weeks. The goal is for all students to achieve mastery at the most minimal level, with as many as you can achieving mastery at all levels. Students who understand the concept well conceptually and procedurally can be challenged with some problems related to the concept (nrich.maths.org has some great problems that are easy to give to students and also https://www.cemc.uwaterloo.ca/resources/potw.php has great problems for these students) These are the sequences I created for each grade level. Please share and give feedback! I’d love to hear what worked: Kindergarten Scope & Sequence Grade 1 Scope & Sequence Grade 2 Scope & Sequence Grade 3 Scope & Sequence Grade 4 Scope & Sequence Grade 5 Scope & Sequence Grade 6 Scope & Sequence Grade 7 Scope & Sequence Grade 8 Scope & Sequence