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.

Why teach through inquiry? A real testimonial

Now I know that I have posted on this subject before but with the day I had I just had to write about it again.  Inquiry: WOW!  Man I love it.

I know that recently there has been a lot of discussion about inquiry in the classroom and if it is really making students learn.  There has also been a huge push to go "back to basics" all I have to say is wish you were in my class (even school) today.  Today's math problem was quite simple: 

"Mrs. Standring, our proud principal, needs help.  Our school has been open for two years now and we got more kids this year, because of that the fire Marshal has asked her to make a new fire plan.  I was telling her that we were studying measurement and she thought you could help.  How far is our door to the nearest fire door?"

The kids went nuts. It took them a while to get over the fact that they were helping Mrs.Standring.  Well they just started with the questions: what tools can we use? How are we starting? Which door is closer?

Most of them saw that a meter stick would be the best measurement tool, we had been talking about measurements for some time and been measuring in non-standard too and knew that it was inconsistent. So they all grabbed meter sticks and off they went.

We got a bunch of numbers and came to the carpet to discuss. They were all in confusion, why do we have different numbers. We used a standard measurement? We then asked the students to demonstrate how they measured.  Some saw that when you lift the ruler up, you sometimes, overlap the space or leave a gap.  I then asked them how can we prevent that?  This brought up the discussion of leaving marks, or placing fingers.  They went back at it.

Students then came up with an answer but when I asked them to tell our principal they didn't know what to say.  This of course then led us into a discussion about explanation texts, which we then made some success criteria and off they went to write.  When the bell rang half way through the students were very upset that they didn't have enough time to finish there work.

Not only did this problem happen in my classroom but my teaching partner did it too.  Her kids thought string was the best and then bring it back to measure against a meter stick.

Now you may read this and say so what? So what! The best part of this is that all this discussion was student driven. All collaboration, student driven, all learning student driven.  Yes as a teacher I am incharge.  I have planned this problem, I have thought of the big ideas and questions but it is the passion, and learning of my students that drive this problem.  Also, when looking back (though I will say to make it worth while this should be done first) my students met over 37 expectations from the curriculum and all of the learning skills that are in the report card.  In addition, the talk was amazing and the learning even more. Not only this but when it comes to assessment I have it all, with no tests.  I know my students skills, next steps and a mark of work.

Inquiry for me is the only way to teach.  Yes, students do need facts and knowledge but that fact and knowledge is gained through the inquiry process.  Also, if a student doesn't have that to start with as a teacher it is my job to scaffold the question so that they do learn; however, it should still be done in a way that the student is discovering the learning.

Now in the end, there is no wrong way to teach, all learning is valid and good. But through inquiry students do grasb and understand concepts faster and with a deeper understanding. It's been amazing to see our students development as our school adopts this approach. There is less review needed from year to year and the students are talking more and communicating their thoughts.  For me there are a couple of key reasons to teach through inquiry:

1) Students learn and enjoy the lessons more then traditional teaching styles

2) It covers more curriculum and deeper knowledge

3) Students retain information

4) Learning is integrated in real life, why separate at school

5) It validates the students and makes them buy into their learning. If they are invested you have less behaviours

6) students easily tune a teachers voice out but not their peers

7) It's fun for me too! Shh don't tell my students

What are some potential problems: (though to me they are not problems)

1) Problems take time: learning is not easily divided into 30, 40 minute time blocks

2) Can be and should be noisy but productive

3) Takes more planning: yes it takes more planning. You cannot wing inquiry. Even though it may appear as if it is winged or that the teacher is doing nothing it is an art form and requires a lot more planning (will tough on that in a minute)

4) Parents: you will get parents complaining and questioning your practice.  This is new for many and with new comes questions and fears. Stand up and proudly defend your practice because when they hear and see their kids they will love you.

5) you may not have all of the answers

What do I need to do to teach through inquiry?

1) know your content and curriculum: when you know your students learning it is easier to formulate questions and scaffold students learning.

2) plan: I wrote a previous blog post about planning but essentially you need to plan.  Inquiry does not happen by the seat of your pants.  You need to anticipate students questions, problems, and ideas.  You need to know what the big ideas are and where you want the lesson to go.  You need to understand learning trajectories and see where your class is and should go next and you need to do the problem first.

3) inquiry should be contextual and related to the kids life.  The best inquiries are ones in which the students really wonder or can invest in.

4) have fun and don't be afraid to make a mistake.

Overall, I feel inquiry has been one of the best things I could have done. It really benefits the students and it makes my assessment easier.  I would love to hear your thoughts on inquiry? Have you tried it? Struggles? Pointers? Thanks for reading.

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