A Reflection on Assessment

In a couple of days I will be presenting at Bit14 with Aviva Dunsiger. Our presentation is bridging the divide: Opening our four walls. However, I digress from my blog title. The reason why I am writing this is because I was also asked to co-facilitate a discussion with Brian Aspinall on assessment in a changing 21st century learning. This is going to happen on Thursday at 10:00 in the learning commons.  It is a free forming discussion but I thought I would get the ball rolling with some of my own thoughts and more importantly questions.

First of all with our assessment document in Ontario (Growing Success) there is a big emphasis on assessment for learning, as learning and of learning; with a large focus on assessment as learning and for learning. This is a big shift for many of us teachers who before this did a lot of assessment of learning. Not to say that this isn't important but that there has been a big shift in thinking about assessment.  This shift also aligns strangely enough with a wider acceptance on qualitative data versus quantitative data.  That observations and discussion are just as valid and important as the number that we can collect.  Which brings me to the reason for our learning commons discussion.

The discussion came about when Brian made a post about a brand new app call Photomath. Basically its an app that can do algebraic equations for you. The question that Brian raises is what are we assessing when an app can do the math for us? Should we be assessing basic skills like this?

My response to this was there needs to be a shift to not what is the answer but how do you know the answer is correct. It reminded me of the calculator debate when I was in school. I still remember this movie we had to watch in grade eight and the two children were adding up some money. One of the girls takes out a calculator and clearly gets the wrong answer but strongly argues that she is right. When asked why, she states because the calculator told me. It turns out that the calculator was running low on batteries and if you used basic common sense then you would have known the answer was wrong. The point wasn't so much that she got it wrong but that there was faith in the answer because the technology told her so. The problem is that students then and now need to have a good conceptual understanding of the work before jumping into abstract thinking. They need to understand the process in learning.

The world has changed a lot since we were in school, heck even since I was in school (which to be fair was not that long ago). If you honestly look back and think about those school days, the information that we were given potentially would have lasted us our life time. To be fair the information our parents were taught did last them their lifetime. However, that is not so with the kids we are teaching. Technology has changed the way we use, process and understand the world around us. We live in a world were tomorrow has endless possibilities. The scary part is that I am preparing kids for a future with obsolete information and knowledge.  Which is why philosophies on assessment have drastically changed.

A couple of years ago I was giving a test to my students. I looked up and saw that my students went right to talking with their math partners, trying to solve the questions. I was about to stop them and state that this is a test I need to know what you know when I realized that I already knew what they knew. Because of teaching in a constructivist approach, I knew where they were struggling, what strategies they would answer, and how they would communicate. In fact I knew why certain students were talking and asking questions and I knew what next steps would be useful for them. This test wouldn't tell me this, in fact it was wasting two hours of time that I could be conferencing with my students and helping them move forward.

Students collaboratively working on creating success criteria for an assignment

Now I said I knew a lot, why?  The reason is that in my teaching I am always conferencing with students, individually, and in groups. I have honest conversations with them and ask them questions to test their knowledge. Based on their responses and work samples I am able to see where fit on a continuum of learning. In fact I can confidently say that I understand my students more from this method then I do with a summative assessment like a test that I would have traditionally given. Not only that but my students move faster up that continuum because of our conferences and reflections that are done everyday versus just studying for one test to then forget about it the next day.

For me it is more important to teach my students to be curators or data, critical thinkers, problem solvers and have creative/adaptable thinking skills.  I say this because the information I am teaching them will soon be obsolete.  Now please don't get me wrong and say that students don't need to have basic skills or test taking abilities. Unfortunately in this school system and society they still need those test taking skills and yes students do need to learn basic skills (arithmetic, writing, reading, etc.) but the emphasis shouldn't be on memorizing to retain for an hour but to go deeper with that thinking and be able to understand why we are using it not just knowing and forgetting.  

This brings me to my questions and ones that I hope everyone help can answer:

1) What assessment tools do you prefer and use in the classroom?

2) What skills are needed, as a teacher, to make assessment as and for learning effective for growing student achievement?

3) What do you think about the shift in assessment? Is it warranted? needed?

4) If we are moving to a more assessment as and for learning, how to we do this?

5) What is the biggest resistance to this change? How do we over come it?

I am really excited for this conversation as I think we are on the brink of exciting change in education. Would love to hear your comments and ideas about this topic, no matter what they are.

Fraction kit and playing games

Fractions have always been a passion of mine. Started researching the concepts in my math part 1 AQ class and have been fascinated ever since.  I even ended up completing my Masters' of Education thesis in the subject.  Through my studies I came across fractions, Marilyn Burns' fraction kit and games.  I still haven't found something anywhere close that helps students understand fraction concepts like this kit.  

For those not familiar with it, let me tell you about it.  The kit in itself is very simple, it is five strips of paper. Each piece is to be cut to a corresponding fraction (halves, quarters, eighths, sixteenths, and a whole). 

Now you may ask yourselves how is this the best thing ever it's just a bunch of paper. It's the best thing ever because of the talk that it generates. Since finding this in my research I have done some modifications that really bring out the talk. 

First and foremost, I have them create the kits. It does you no good to create them for your students.  By them creating the strips, the students explore how fractions are division, fair sharing, why fractions are a part of a whole and many more fractional concepts.

Second, I created a context to go with the problem. As many of you know who read this blog, I truly believe in contexts. A good context makes kids think beyond arithmetic and focus on mathematical big ideas.  For this problem I tell my students a story of how I need to clean up my mom's back yard, she has a huge yard and in payment my mom buys me a large party sub. Now many students now don't know what a party sub is because they don't sell them anymore, so you may have to show them a picture: 

The students are so impressed and they can't believe that I would eat this much. Now I tell them that just before I was about to eat lunch one of my friends popped over. Now what?  This continues all the way to eights, the door bell ringing every time we figure out portion we need to cut.  For sixteenths I tell them this is what we are going to do as I really don't have sixteen friends; however by now we have really constructed a good understanding of the pattern that is happening.  Now why this context. I like this context because it is a linear model like the strips. Having the sub also means students have to think about measurement and division because technically you cannot fold a sub, as all the pieces fall out. The other part is students often will try cutting the their strips horizontally instead of vertically. Now this also brings up interesting discussions about equivalency versus congruency but this context stops that because if students cut a sub horizontally they don't really get all of the sub.

Third I don't have the students label their fractions.  When I have done this with my fours it was mainly because I didn't want them to associate a particular fraction with the strips whole. Basically, 1/2 strip is 1/2 of the kits whole not 1/2 somewhere else.  A big misconception with students thinking is that a what they learn is he only representation of a particular fraction. When you label the students don't understand that the size of the whole matters.  That 1/4 can be bigger than 1/2 depending on the size.  However, now that I am in primary I see a whole new benifit, it makes students understand what a fraction is. Why is 1/4, 1/4? While my students where playing cover-up, one of Mariyln burns fraction kit games, they asked me which fraction is 1/4? I turned it around and asked them. They then just picked a random strip up. I the. Asked them why that one? This discussion continued as students explored that the amount of pieces that we break our sub into is our denominator and the amount we use is our numerator.   If I had them label the fractions they never would have explored this concept and I would never have realized that they struggled with it.

The final change is the questions that I ask around this particular problem.  It's not just to make the stud ets create the kit but to think about the big ideas around fractions. Have a listen to my grade two class discussion on fractions:

Day 1 of our Fraction Talk

Day 2 of the Talk:

It is quite interesting the talk that can come from building these kits and the big ideas that come from it. I have played this game in junior and primary and personally I would do this for middle school as well.  In junior I start to add fifths, tenths, thirds, sixths, ninths, and twelves.  By adding these other fractions you also start to see other misconceptions of students halving strategies but for primary halving is still okay.  I hope you really try the kits and see the benefits of it in your classroom.

You can find all of my fraction research and resources on my site: Bit.ly/Soresources.  Feel free to use anything you want.

Problem based in learning in the context of math wars. Thoughts are myp.o.v.

I was recently given an article from Suril Shah (@thrilsuril), a colleague of mine in the peel Board, (http://news.nationalpost.com/2014/02/28/does-discovery-learning-prepare-alberta-students-for-the-21st-century-or-will-it-toss-out-a-top-tier-education-system/) and then later on another article from another colleague Aviva Dunsiger, a teacher in the Hamilton School board (http://www.theglobeandmail.com/globe-debate/canadas-math-woes-are-adding-up/article17226537/ ).  Both articles discuss (or rather reprimand) the notion of “Discovery Math” needless to say I had to respond.

As many of you know from my blog posts, math is a very important passion of mine.  I have in a way devoted my educational career to learning about math education and how it can help transform student learning.  This has gone on for me for the last 9 years of my teaching career and five years before volunteering at an amazing school in Peel.  Over the course of these 14 years the arguments in the above articles have always been happening; so I think it is funny that when Ms Wente mentions that this is a “new faddish fuzzy notion.”  Since mathematics was first introduced into the curriculum in the fifteenth century it has always been a debate over skill versus conceptual understanding.  This debate will always be there all I can give you is fact from experience and from the classroom (which I will say many who write articles in the Newspaper or make policy cannot).

Let me first start of with my own evolution.  Like many of you I was taught with very traditional methods.  My father drilled in me from a young age that fact recall was the most important thing.  I still remember practising for hours on hours flash cards and being randomly asked multiplication questions to see if I knew these facts.  I also remember that my Math class was all in a work book and my teacher sat at the front of the room and wrote many things on the board and then we did questions to practise and show what we learned.  This continued all the way through school and as I got into the high school and eventually University this is what I remember of my Math class.  Did it help?  No, I don’t think it did.  Don’t get me wrong, I did learn math.  In fact Math has never been a hard subject for me (except problem solving).  I was able to work through and memorize what was needed and then when the test came I was able to retell those facts and get an A.  My problems never came until University Calculus.  Here I because I didn’t have a good foundation in Calculus I struggled, in fact I failed. 

Sorry I digress here.  This method of teaching stuck with me, more so because this was all I knew.  During University I changed majors and decided to become a teacher.  I was able to volunteer at an Amazing school in Peel and soon learned Reform Mathematics (what discovery math was called at that time).  I was also fortunate enough to have an Amazing principal who let me question her and learn what reform mathematics was all about.  At first I said the same things that many of these article, and our parents say when they see problem based learning. You have probably heard these before (I know they are in the article):

1)      What is wrong with Rote, it worked for me?
2)      What about facts? There not learning them like I did?
3)      I memorized and got good grades?
4)      They can’t possible learn this on their own?
5)      What do you mean discovery? What is your job then?
6)      You’re the teacher so teach?
7)      This look chaotic, there is no order, how can they learn?
8)      What about the language, seems like more reading than math?

I can go on but they start to sound the same.  During this process I was able to see students truly excel and showcase their learning.  In fact, looking at scores (which is not the end all to be all), the school went from 42% to 93% in that first year in mathematics.  I was also able to reflect on my own learning and how I learn.  This started the ball rolling and has helped me to ask questions back.  Here are a few to think about:

1)      How do you truly learn as an adult learner? 
2)      Do you memorize things and then succeed? Or did you have to make mistakes, go back and relearn or have someone help you through it?
3)      When you are learning do you like to ask questions? Or just sit and receive information?
4)      (my favourite one) As a successful adult how did you become successful? What traits do you like in your employers?

Here are my thoughts to these questions:

I personal learn by doing, struggling, asking questions and then going back to relearn it.  True mastery comes from doing something over and over and over again.  Yes I can see how this backs learning facts, and I am not saying facts are not important, but my learning is in context to the concept not in isolation.  Memorization only works with some things but I still make mistakes no matter what I am doing and then I learn from them.  As for success to me I value students who are free thinkers, creative, adaptable and able to see past just simple direction.  This has been the case even when I was managing people in the private sector in my University jobs.  I don’t think the world can evolve from people who can only follow direction and not think beyond what is on the paper.

With this in mind I began my teaching career.  Here I too continued to question but now I also had to field questions from the general population about my style of teaching.  Here are my responses.

Q: Why is this better than traditional learning?

 A: I hope that I may have answered this above but most students, and adults do not learn through traditional learning.  There are a very few who do and we also have to consider that style but many don’t.  Learning is developmental.  It doesn’t happen in a linear fashion and PBL allows for this to happen.  Learning in PBL also doesn’t happen in isolation from the world, or other subjects.  It is always connected to a context, which helps all students to hold on to something and work with it.  Furthermore, all learners can access PBL, whether gifted or with a learning disability all students can do the problem.  Also, personally, it makes the day go by a lot faster, I enjoy it and so do my students.  Check out this video: http://curriculum.org/secretariat/justice/insights.html for student reflection on what context can do.

Q: You know my kids don’t know facts, why aren’t you teaching them?

A: First and foremost, I want this to be said, “FACTS ARE IMPORTANT!” they must be taught and learned; however, how are we learning them.  Let’s go back to my question back to you.  Can you recall something where pure fact learning has help you be successful?  If yes, no think was it just fact memorization or was it in a context?  Fact knowledge is important and needs to be done.  I prefer to do this through games and mini-lessons.  This allows me to talk about a strategy and have students discuss the pros and cons of the strategies.  The talk focuses the learning.  Check on my previous blog post on it.

Q: “Teachers and Students are learning together” Great so now we have the blind leading the blind!

A: This is the one that bothers me the most.  It bothers me because PBL actually takes more understanding, more planning and a lot more patience then traditionally teaching.  I have almost completed my thesis, in where I researched the impact of my questions on students learning of fractions.  It was interesting to see where I had moments of direct teaching that my students stopped talking.  In fact, they just sat there.  Which is exactly what traditional teaching does, students sit and listen then do.  PBL takes planning.  In another of my posts I talk about five practises that teachers should be following for PBL implementation (http://mrsoclassroom.blogspot.ca/2013/11/blog-post.html ).  Teachers actually need to learn the mathematics and it is through critically placed questions that the learning is brought out.  Students develop at a faster rate through this proper questioning style and can achieve a higher level of understanding.  I have grade twos right now who are learning about equivalent fractions, ratios, division and adding three digit numbers in their head.  It is truly amazing to see what they can do.  But this takes planning on my part.  It takes understanding of learning trajectories and  understanding what students are doing (so you can redirect or push beyond) and understanding the math to be effective in PBL.

Q: Test scores are falling?

A: this might be so but I would caution you on this.  First of all tests are a snap shot of learning at a particular moment in time.  They have a place in assessment.  In my personal opinion a very far place but a place nonetheless.  There are many factors to low test scores: 1) poverty, parents education, home life, social problems that day, being sick, stress, reading level, context, etc. The list is endless.  When we put all emphasis on test we are taking away so many other factors of learning.  I know more about a student from a problem that they solve then by what they can retell me on a test, just a matter of fact.

 I am going to stop here for now as I think I have written more than I ever have in a blog.  This topic is very dear to me and I have heard a lot of the questions in this “Math War.” It will not go away but please don’t take this as a discouragement to stop PBL or even start.  To me PBL is the best way for ALL students to learn.  It gives the teacher the most time for true assessment and understanding of their students needs and next steps.  It allows you to meet all levels of students and be able to get to all of them.  I have and will continue to only teach through PBL (problem based learning).  Love to hear your personal stories, questions or answers to this lovely debate. 

Accountable Talk in the Classroom: Practical Advice for the Classroom

I have recently finished one great book and one great article on Accountable Talk and Classroom Discussions. 

Stein, M. K., Engle, R., Smith, M. & Hughes, E,  Orchestrating productive mathematical discussion: Five practices for  helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10, 313-340. 

Chapin, Suzanne, O'Connor, Catherine, & Anderson, Nancy. Classroom Discussions: Using         math talk to help students learn. California: Scholastics. 2009.

Accountable talk is one of my passions as I have spent the last four year studying the impact it has on my classroom.  I highly reccomend these two readings for anyone interested in learning more about accountable talk.  However, I also know that in teaching we really don't have time to sit down and read.  For this reason I thought I would summarize them for you and include them in my blog (I appologize in advance as this will create a rather long post).  These ideas come from the two resources above and my own thesis work.  I hope they are practical advice for anyone in their teaching practice.

Implementing Classroom Discussions

Establishing and Maintaining a Respectful, Supportive Environment:

·         LAY DOWN THE LAW (in a collaborative manner):

o   that every student is listening to what others say

o   that every student can hear what others say

o   that every student may participate by speaking out at some point

o   all have an obligation to listen

·         neither student or teacher will participate in bad environment.  Everyone needs to feel comfortable.

·         Emphasize the positive and forestall the negative

·         Establish classroom norms around talk, partner work, and discussions (what does it look like, sound like and what should we be doing)

·         everyone has the right to participate and an obligation to listen

Focusing Talk on the Mathematics:

·         During the discussion time you need to focus the talk on math:

o   plan your questions carefully

o   Have good formative assessment happening at all times

o   Make a plan as to what big ideas you want to cover

o   Anticipate problems and possible solutions

Providing for Equitable Participation in the Classroom Talk:

·         Here are some strategies that will assist you in making it all equitable:

o   Think-pair-share

o   Wait time

o   Group Talk

o   Partner Talk

o   Debates

o   Random  Choice on who Talks

 

Types of Talk Moves:

Talk Moves That Help Students Clarify and Share Their Own Thoughts

·         Say More:

o   Here you literally ask the student to explain more.  "Can you tell me more?", "Tell us more about your thinking.  Can you expand on that?"; or "Can you give us an example?"

o   This sends the message that the teacher wants to understand the students' thinking.

·         Revoicing:

o   It is sometimes hard for students to clearly articulate what they are trying to say by revoicing or having a student do this it allows the original student to check and make sure what they said is true or to hear it in a new way

o   It is not just repeating but more of paraphrasing the students ideas

·         Model students thinking:

o   This is not so much a talk move as it is a way to help talk

o   As students talk record what they are saying without comment.  When they are done ask them , is this what you meant?

o   This allows students to reflect and think about what they said in comparison to what was written

·         Wait Time:

o   Wait time is so important.  I cannot stress this enough.  The longer you wait the better responses you will get.  It allows students to process what you or another student asked and be able to formulate their thinking

Talk Moves That Help Students Orient to Others' Thinking

·         Who can Repeat?

o   I would classify this under the first category but it also helps students with understanding what their peers are saying

Talk Moves that Help Students Deepen Their Reasoning

·         Press for reasoning

o   Here you are basically asking students to think about why they did this.  This can be done by asking:

§  Why do you think that?

§  What convinced you that was the answer?

§  Why did you think that strategy would work?

§  Where in the text is their support for that claim?

§  What is your evidence?

§  What makes you think that?

§  How did you get that answer?

§  Can you prove that to us?

o   Not only are these excellent talk moves but excellent questions that push students beyond their thinking and make excellent mathematical connections.

Talk Moves That Help Students Engage with Others' Thinking

·         These are excellent questions that help students build upon their own thinking and the thinking of the community

·         Do you agree or disagree...and why?

o   This really brings students into direct contact with the reasoning of their peers

o   You can do this by:

§  Thumbs up or thumbs down

§  Why do you agree or disagree?

·         Who can add on?

o   When you ask this question make sure that you wait for answers as this may need time to develop connections.

Five Practises suggested by Stein, M. K., Engle, R., Smith, M. & Hughes, E.

1: Anticipation (P.322)

The first thing is for the teacher to look and see how students might mathematically solve these types of problems.  In addition, teachers should also solve them for themselves.  Anticipating students’ work involves not only what students may do, but what they may not do.  Teachers must be prepared for incorrect responses as well.

2: Monitoring students' work (P. 326)

While the students are working, it is the responsibility of the teacher to pay close attention to the mathematical thinking that is happening in the classroom.  The goal of monitoring is to identify the mathematical potential of particular strategies and figure out what big ideas are happening in the classroom.  As the teacher is monitoring the students work, they are also selecting who is to present based on the observations that are unfolding in the classroom.

3: Selecting student work (P.327-328)

            Having monitored the students, it is now the role of the teacher to pick strategies that will benefit the class as a whole.  This process is not any different than what most teachers do; however, the emphasis is not on the sharing, but on what the mathematics is that is happening in the strategies that were chosen. 

4: Purposefully sequencing them in discussion (P. 329)

With  the students chosen, it is now up to the teacher to pick the sequence in which the students will present.  What big ideas are unfolding, and how can you sequence them for all to understand?  This sequencing can happen in a couple of ways: 1) most common strategy, 2) stage 1 of a big idea towards a more complex version or 3) contrasting ideas and strategies.

5: Helping students make mathematical sense (P.330-331)

As the students share their strategies, it is the role of the teacher to question and help  them draw connections between the mathematical processes and ideas that are reflected in those strategies.  Stein et. al. suggest that teachers can help students make judgments about the consequences of different approaches. They can also help students see how the strategies are the same even if they are represented differently.  Overall, it is the role of the teacher to bridge the gap between presentations so that students do not see them as separate strategies, but rather as working towards a common understanding or goal of the teacher.

 

Trouble Shooting Talk in the Classroom

My Students won’t Talk:

v  First ask yourself: our my students silent because they have not understood a particular question? --> sometimes they need to hear the question a few times and have time to think

§  if this is the case then give students time to think  (wait time is very important)

§  also revoice it or have another student revoice the question

v  Second they may be shy or unsure of their abilities:

§  If this is the case you may need to revisit strategies for talking

§  Think-pair-share is an excellent way to get kids comfortable to talk

§  it will also take time to get kids comfortable.  Wait time again is important as it holds students accountable.  Also making them feel comfortable and that mistakes are okay will assist with this difficulties

The same few students do all the talking:

v  Wait-Time:

§  I know that I say this a lot but it allows the other students to think and then participate while making the ones who always participate  (it will feel awkward at first but wait as long as you can)

v  Have students Revoice:

§  This is good strategy to bring validity to students answers and encourage others to talk

v  Conferencing with the ones who talk a lot:

§  You also don't want to ignore the ones who talk  all the time.  You can talk to them and let them know that you are not ignoring them but are just trying to allow others to participate.

v  Turn-Taking/ Random presenters/ group discussions:

§  These are all roughly the same strategy.  It allows you to have certain presenters share their thinking without offending or allowing others to take over the conversation

Should I call on students who do not raise their hands?

v  there is research to suggest that students will learn by listening but you will also hinder the class progress in discussion.  To help try creating a positive space that allows all students to feel comfortable and willing to participate.

v  "right to pass": 

§  allow students at the beginning of the year the right to pass.  You'll notice that they may do this at first but as you build the community they do this less and less

v  Call on reluctant to students after partner talk:

§  Often when you give them a chance to share first they are more willing to share or at least have a response from their partner

My students will talk, but they won’t listen

v  Set the classroom Norms:

§  remind each students that they have the right to be heard but that this also means an obligation to listen

v  Students Revoice:

§  When students need to revoice then they have to listen

Huh?” How do I respond to incomprehensible contributions?

v  The temptation is to simply say, "Oh, I see.  How interesting...." and quickly move on to another student.

v  Try Revoicing or repeating what they have said.  After you have done this ask them is this what you meant?

v  Record their strategy on the board and ask them is this what you meant?

Brilliant, but did anyone understand?

v  Repeat what they said, then have another student repeat what they have said (if really important have many students repeat)

v  Break the explanation up into small chunks and revoice or have the students

I have students at very different levels

v  Pair students in ability groups:

§   Similar abilities with similar abilities.  This allows students to contribute at their level and to also struggle at their level.  In addition, it allows you as the teacher to differentiate as needed.  When you scaffold you can do so by group not by individuals

v  Parallel Tasks:

§  Give students similar tasks but with varying degrees of difficulty (still around the same big idea)

What should I do when students are wrong?

v  First ask yourself is there anything wrong with having the wrong answer?  Sometimes wrong answers provide rich and meaningful discussions

v  Need to establish Norms around respectful discourse and discussion with wrong answers

v  Mistakes are always an opportunity for learning to happen

This discussion is not going anywhere or Students’ answers are so superficial!

v  This may be happening because you are asking to many students to share or revoice the ideas that are happening in the classroom or in the case of superficial classroom  norms have not been established or the types of questions have been simple and direct

v  Use the working on phase as an opportunity to direct your bigger discussion:

§  As you are walking around and looking at work, look for the progression your students are taking.  This will lead you to a group discussions.  What questions are the students asking themselves?  What problems are occurring?  What big ideas are they trying to work out, have worked out or are struggling with?

v  Look at the type of questions that you are asking:

§  As teachers we are comfortable asking questions but do our questions already have responses?  Are we leading the kids to OUR thinking or our we allowing the students talk to LEAD the thinking.  Yes you are very much in control of the discuss and have to lead but it is not YOUR thinking but THEIRS that should be articulated.

§  Higher order questions build-upon or go beyond the thinking that is being presented.  As a teacher we need to help with the connections in mathematics.  Compare student work?  Compare strategies, Pros and Cons, naming and identifying.  We need to go beyond just show and tell