Spiralling

A new concept to me (but something I have thought about before) is the idea of Spiralling Curriculum.

It makes so much sense, but I can also understand the hesitation of teachers to use it. We have a system that has been in place forever. We have checklists to check, report cards to write, and things to do; how can we fit this Spiralling into what we have to do?

Spiralling curriculum is the idea of keeping what we learn throughout the year going all year. Not just dividing different topics and strands into units, doing it once, testing on it, and then not revisiting it again during the year.

We're doing our students a disservice by saying after Term 1 that they don't know how to do something as a 4th Grader that soon in the year. We have all year for our students to become successful, so why do we give such stringent timelines for our students to learn in? Especially when it may take some students multiple introductions to a topic to become familiar and for the "aha" moment to come to them?

Below, watch Spiraling the Curriculum to Get Sticky Learning, a TEDxKitchenerED talk by Kristin Phillips:

I think the thing that sticks with me the most, is the idea that we don't really retain information that we are not using. That exam I crammed for in University, I couldn't tell you now any of the information I needed to know that day for that exam. The stuff I have went over repeatedly over and over again over months, years, decades - I can tell you about that stuff.

So why do we expect our students to remember certain units, strategies and skills a year after they learned about before?

Need more information on Spiralling? Check out this brochure:
http://everydaymath.uchicago.edu/about/why-it-works/spiral/

Three-Part Math Lessons

There's been a lot of talk about Three Part Math Lessons and the benefits of a three part lesson in comparison to the type of lesson I would have been subjected to when I was in elementary school.

So, how do I find the two types of lessons compare:

Traditional Math Lesson	Three-Part Lesson
Teacher brings forth the lesson for the day, going over the concept or idea (as much time as it takes to teach lesson, take questions)	Lesson starts out with whole class (usually) and brings forth the concept in order to ensure students have the practical understanding of what will be happening (“Getting Started” – approx. 10-15 minutes)
Students are then usually given sheet work to do, or work from the math textbook.	Students are given 30-40 minutes to work through a mathematical task – may be shared, guided or an independent activity/with groups, partners or alone.
Work may go unchecked or unmarked. Teacher may not be aware of struggles or misunderstandings of what was being worked on until a quiz or test is done for assessment	Teachers have a chance to circulate and observe and provide guidance and extra support as needed
Students may be bored, disinterested or unable to grasp on simple paper based learning	Students have an opportunity to explore, discuss and learn through their peers and hands-on activities
Pass or fail. Understand or not kind of mentality	Chances to actively understand, and work at solving the problem through perseverance
Usually no follow-up until assessment of some type is performed	“Reflecting and Connecting” of about 10-15 minutes is brought at the end of the class as a chance to discuss and unwrap some of the ideas and learning that occurred during the “Working on it” time. Chance for the teacher to ask questions and assess the students’/class’ understanding of the material
Not many chances to share ideas and solutions with peers, or find out if the class is understanding properly	Chance to articulate ideas, make connections and make talking about math normal.

The point of the Three Part Lesson is not to drill facts and singular ways to use math into our students' minds, but to instead allow our students a chance to come up with ways to use strategies and skills to solve problems. It's a chance to discuss with a partner or a group ways that they could solve the problem given to them by the teacher. Each group may come up with completely different ways to solve through a problem, and all come to the same answer.

Some groups may come up with incorrect answers, but as a safe community in the class (it's important to build a "safe community" by practicing what good communication looks and sounds like) there's a chance to take risks and learn through making mistakes. 


Having students do more themselves to aid in their learning gives them more control, independence and the ability to persevere through problem solving.

My own math classes in elementary school were right or wrong answers, and right or wrong ways of doing things. By allowing students a chance to problem solve with teacher guidance, we are giving our students the idea that math can be used in many different ways to solve lots of different real life problems. By coming together as a community at the end, we are able to see different ways of thinking and see how we can use different strategies in different ways that one may have not thought about before.

Have you used a 3 Part Lesson in Math before?

What kind of problems do your students like to solve?

Long Range Plans lead to Unit Plans lead to the Lesson

You can't have a lesson without knowing what Unit you're doing, and you can't know what Unit you're on without a Long Range Plan.

So, where do you start?

First, you need to know what the students already know. Unfortunately, you'll need to know where you're going before the students even step foot in your room, so taking note of the previous year's curriculum expectations can go a long way.
This does of course mean, that when you meet your students, you might need to do a little tweaking to your plans to ensure that you are not trying to dump a new idea on them without any prior learning or skills needed to be successful.

Remember to keep ahead on the "Big Ideas" and not get stuck on individual expectations. Through the Big Ideas, you will have a chance to hit on those expectations, and maybe even more expectations in other subjects (remember Cross Curricular lessons can make learning more fun and engaging!).

It's important to make sure that certain "Big Ideas" that require a skill from another strand don't come before they have had a chance to master that skill. We want our students to come away from that Big Idea eager to learn more, not feel more confused and frustrated.

The more you link the Big Ideas, the better the understanding for your students!

When planning the Unit itself, and the lessons within it, remember to ensure that besides what the lesson is about, what expectations you are hoping to check off, and what resources you will be using, to have a plan in place for the types of assessment that will be taking place over the course of the unit. According to the Growing Success document, “essential steps in assessment for learning and as learning, teachers need to: plan assessment concurrently and integrate it seamlessly with instruction; share learning goals and success criteria with students at the outset of learning to ensure that students and teachers have a common and shared understanding of these goals and criteria as learning progresses; gather information about student learning before, during, and at or near the end of a period of instruction, using a variety of assessment strategies and tools; use assessment to inform instruction, guide next steps, and help students monitor their progress towards achieving their learning goals; analyse and interpret evidence of learning; give and receive specific and timely descriptive feedback about student learning; help students to develop skills of peer and self-assessment” (Growing Success 28-29). If a clear picture of what assessment will entail is not outlined before, how will you know the students are learning or if the class is heading in the right direction? 

Next, when it's time to do your lessons, don't forget to use the 3 Part Math Lesson format and to give yourself plenty of time for Math. It is imperative to give plenty of time for each lesson (at least an hour is suggested) in order to give your students a chance to break down and work on through the problems that we give them.

Look for my next Blog entry on the 3 Part Math Lesson for more!

How do you plan out your year?

How do you plan our your units?

What suggestions would you have for a brand new teacher planning out for the first time?

Cross-Curricular Planning

I know when I was in Teacher's College, I didn't have a lot of chances to plan outside of the box. If we were in Math, we were planning a Math lesson. If we were in Science, it was Science... and so on. But when you think about it, a lot of our lessons can easily be tied together so that not only are we checking off boxes and cementing knowledge from other areas of the curriculum, but we're showing that subjects like math don't only exist in math class -- it's out there for us to experience anywhere and anytime!

I haven’t specifically had the opportunity to do cross-curricular activities involving math in my own teaching yet, as I was limited in what I could do in teacher’s college during my practicums, and now am usually fairly limited at what I am left to teach as an occasional teacher.  I have had the fun of bringing geometric shapes into art with students, and that was a fun activity, but I could see some sort of cross-curricular activity where students need to use math in order to get the numbers for a persuasive writing/media assignment dealing with a topic from science, social studies or social justice.

Let's face it though, tying subjects together – especially bringing math into other subjects – makes math seem more like a real world skill that students need. Math becomes more than something that math teachers and mathematicians only use, and something everyone uses in their everyday lives.

It also makes math more fun and hands-on, especially if some sort of creative activity is tied to it. Geometry can just feel like a bunch of shapes that no one needs to know the names of, but if you go and do something neat and artistic with those shapes, they become more real and concrete.

Grade 2s working on their Geometric Abstraction

While looking for cross curricular lesson plans, I accidentally came across an article about a teacher who was able to incorporate math along with physical fitness and writing! I thought it was a neat that the kids got so excited about running, which made them excited about writing about it, and at the same time were better understanding fractions (1/4, 1/2, 1/3 miles compared to a full mile). 
There's a teacher who took her own interest, made it her students' interest, and got them excited about not only fitness! She got them excited about writing and math too! 

An interesting lesson I found online was one for Grade 4 dealing specifically with financial literacy, but pulling in language, math, social science and science:

At the end of these lessons, students will know, understand and/or be able to identify the pros and cons of mining versus recycling.
a) Students explain that mining and purifying minerals is an expensive process
b) Students demonstrate mining provides good paying jobs to Canadians
c) Students identify the two of the most important minerals used in building our society are iron and aluminum

Students are using a lot of prior learning in various subjects in order to determine the financial implications.

Let's not forget a personal favourite of mine, using musical notes to help us understand fractions. Or is it fractions helping us understand musical notes?

https://www.pinterest.ca/pin/99360735508065217/

Do you plan cross-curricular lessons?
What have been your most sucessful cross-curricular lessons?

Constructivist Planning

When you think of planning, do you think of planning in a way where your students are able to fully grasp what they are learning?

I think it is important to place a priority on understanding when we are planning because with this understanding comes the ability to use math in real world applications, and not just in math class. 

Finding Math (symmetry) during free-play in Grade 1

The Constructivist Approach to planning and instruction connect with the priorities of understanding in that we are giving our students the concrete foundations and the “big ideas” and they are given the ability to apply these ideas to real life math: “Students need to construct their own understanding of each mathematical concept, so that the primary role of teaching is not to lecture, explain, or otherwise attempt to 'transfer' mathematical knowledge, but to create situations for students that will foster their making the necessary mental constructions” (Constructivism in the Classroom). To me, that means that instead of the transfer of knowledge from teacher to student, we are merely guiding them to seeing the bigger picture so that they can have their “aha moment” and realize how to use these concepts in everyday situations through connections made through discovery.

azquotes.com

We can make understanding happen by allowing our students to discover ways to solve through big ideas in math using manipulatives, by having group activities (learning through other strategies fellow classmates might use), and giving real life “problems” to solve. I highly enjoy the mathematical questions that are asked at one school I frequent every Friday – they are always made to go along with an educator at the school, the students themselves, or something else happening in the school community. The students enjoy trying to figure out the answers to the questions, and I find it interesting trying to figure out how to bring the questions to that grade’s skill level. The last one I did had me and a class of 20 grade ones counting by 20s using the squares on the carpet to figure out how many students their teacher had taught in her 32 years before retirement!  It was real-life, and it wasn’t just a matter of the answer is around 640, it was that their teacher had taught over 600 students and they were just 20 of the over 600 she had met. They fully connected with that, and we had fun getting up and moving around rather than counting out over 600 manipulatives!

Grade Twos having fun playing around with symmetry

Do you agree with the Constructivist approach to planning, teaching and learning?

What kinds of real-world activities do your students get the most excited about? Do you think they've learned the Big Ideas better thanks to that real-life connection?

Resources Consulted: 

Constructivism in the Classroom. (n.d.). Retrieved July 3, 2018, from http://mathforum.org/mathed/constructivism.html

Small, M. (2013). Making Math Meaningful to Canadian Students, K-8 (2nd ed.). Toronto, ON: Nelson Education. Retrieved July 6, 2018, from http://www.nelson.com/pl4u/wp-content/uploads/2014/09/making_math_meaningful_chapter_1.pdf?e1d0f5

Steen, L. A. (november 2007). How Mathematics Counts. Making Math Count, 65(3), 8-14. Retrieved July 6, 2018, from http://www.ascd.org/publications/educational-leadership/nov07/vol65/num03/How-Mathematics-Counts.aspx

Big Ideas

I think sometimes as teachers, we all get a little too involved in making sure that we cover every single little detail of the curriculum - and there are definitely some details we have to take in! I recently got an updated Social Studies Curriculum booklet and was shocked to see that since my time at Althouse, it had more than doubled in size! There's a lot to cover, and every time the curriculum changes, there seems to be more that we need to teach to ensure our students have gotten the best.

Sometimes these small little things almost seem to cover the fact that overall, we have Big Ideas we want our students to come away with. So when planning our lessons, we need to ensure that we are using Big Ideas.

The three reasons why understanding and using big ideas is important for planning in mathematics I found through reading that really spoke to me were:

• That students will be able to eventually connect these “big ideas” or concepts to their prior and future learning (mentioned in both readings), which will help with keeping that mathematical idea alive having so many ways to connect the big idea;

• That students will have the opportunity to take away their own ways of strategizing and using the “big ideas” instead of being handed smaller bits and pieces and being told what to use and when;

• Allowing the student to see “the big picture” and thus allowing them to “make connections that allow them to use mathematics more effectively and powerfully. The big ideas are also critical leaps for students who are developing mathematical concepts and abilities” (Number Sense and Numeration, Grades 4 to 6, page 12). From this I took that our students will have a greater control over their learning of the concepts, which in turn will give them the power to use their math knowledge in more ways than just in math class.

I have been in a lot of different classrooms over the last few months as an Occasional Teacher, and you can definitely tell who has been trying very hard to use the “big idea” framework with their math, and it’s neat seeing the students come up with their own ways of solving math “problems” (one school I go to has Friday Morning Trivia every week, and it’s always a blast whether I am in grade one or grade five seeing their brains try and figure out the best solution!), but I also see how crazy and all over the place it can be. I can try and scaffold and guide them more in the right direction, but some students are so set in their awesome and creative minds, that it can be difficult!

There’s also the perception in society that we are not teaching “real math” anymore, which I think is hard to discredit when someone could walk into a math class and see students strategizing around a “big idea” rather than quietly sitting at their desks doing rote math activities. But, in that vein, I think of how in my elementary math days you could ask your teacher why we do something a certain way, and just get an answer of, “because, you just do” rather than having the “big idea” of why or how. This did not give a lot of students the connection to the bigger picture that is needed in order to retain the learning and find ways to use it outside of school (or further in school by studying math past the time you “had” to).

How will you be bringing "Big Ideas" into your classroom planning? 

What "Big Ideas" do you find your students catching onto better than others?

Resources Consulted:
Ministry of Education. (2003). A Guide to Effective Instruction in Mathematics: Kindergarten to Grade 3 (pp. vii-ix). Queen's Printer for Ontario. Retrieved July 6, 2018, from http://www.edugains.ca/resourcesLNS/GuidestoEffectiveInstruction/GEI_Math_K-3/K_3_NumberSenseNumeration.pdf

Ministry of Education. (2006). Number Sense and Numeration, Grades 4 to 6: Big Ideas (Vol. 1, pp. 11-13). Queen's Printer for Ontario. Retrieved July 6, 2018, from http://www.edugains.ca/resourcesLNS/GuidestoEffectiveInstruction/GEI_Math_K-6_NumberSenseNumeration_Gr4-6/NSN_vol_1_Big_Ideas.pdf