Teacher Reflection 180: Day 15

Where do you expect to use Math outside of school?  Explain.

What type of math will it involve?

Write an example.

 

This is another important reflection for me, it gives me insight to what experiences the student has had in their previous mathematics classes.  It is a question that should stretch student’s thinking- if it doesn’t, the typical reason is that they have been taught to be answer-finders instead of critical thinkers.

 

Where do you expect to use Math outside of school?

This question will give you a lot of information on your students.  It will tell you if students see math as a tool to help them in their experiences outside of school, or if it is just another assignment they are expected to do while in school.  It also tells you the level of understanding students have of math, of how it could be used in the varying situations they will encounter.

Typical answers are: Construction, Cashier or Paying Bills.

While these are great examples, they are also limited.  When I first gave this question to students, I was happy that they were seeing mathematics for something other than exercises to keep them busy in class.  I was happy they saw some relevance outside of school, and it wasn’t until the 3rd year of receiving the same responses that I realized that students were not making connections to applications they will need outside of school- they were in fact just regurgitating discussions I had with them about why math is important.  I started to find examples students could encounter in real life.  I quickly found out however that it isn’t as easy as changing a problem from finding the perimeter of a rectangle to finding the fencing needed to enclose a pasture.

 

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Isn’t the second picture much more engaging than the first?  Won’t students only see the picture of the rectangle in textbooks, while they could see the second anywhere they traveled?  How can you go wrong in changing your focus?  Simply answered: You need to capture student interest and curiosity.  While  using an actual photo to pose the question might pick up a few more students’ attention, you actually aren’t inspiring more curiosity or thought than the picture on the left.

 

What if you posed a perimeter problem by showing the following video?

 

This would be a great 3 Acts problem (which I think I will create after this post) where you can have students figure out the perimeter of their gym using an alternate measuring system- students.

 

What type of math will it involve?

Students seem to think that the only mathematics you need is the four basic operations: addition, subtraction, multiplication and division.  They fail to see the application of any other type of mathematics and that is why they question their teachers so much.  They think that the mathematics they need for their jobs is the kind that can be done on a basic calculator, and shut themselves off when they identify operations outside the four (this includes these lovely grouping symbols).  Their stamina in pursuing an answer is also directly related to this.  Many of my students will happily go back and correct errors on basic operations problems, but refuse to engage their mind in critical thinking to solve or even correct something slightly more demanding.

I find that this response narrows down student’s experience with mathematics even more.  Many identify jobs or situations where mathematics is needed, but have little comprehension on what type of mathematics is involved in those fields.

 

Write an example.

With many students, I typically only need the first two questions to have a great handle on what knowledge base students have in math.  This question is basically the icing on the cake.  This one separates those high fliers I have in my room and I typically am hard on them with this response.  I challenge them to create a good example, and typically ask them if that problem is the only type they will face in their situation, leading them to go back and create more examples or revise their own into something more complex.

 

In my experience, this is a great reflection to get a solid handle on your student’s overall experience in math early in the year, and one I keep going back to in an attempt to gauge how well I am connecting mathematics to my students.

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Teacher Reflection 180: Day 13

Day 13:

The lesson or activity we did in class today reminded me of  (write what it reminded you of and explain the connection between the two)

 

I am going to be honest here, this is the single most powerful question I have found for myself professionally.  In a similar manner that I “recycle” ideas from other teachers and professionals, I use student responses to give me insight to connections to use for students.  Using student responses- I plan lessons, activities, projects.  It gives me a gateway into activating their prior knowledge on topics, and providing students this type of access seems to improve interest and engagement.

We can learn from anyone, listen to your students- they are a wealth of ideas.

Teacher Reflection 180: Day 12

What was good (or bad) about the lesson today?  Explain.

This question leaves a lot out there, and it was one that was hard for me to manage properly at first.  When you do student reflections in mathematics, I strongly suggest that you have a system to provide immediate feedback to students.  For me, most of my reflection questions are given in the form of exit tickets, and before students are allowed to leave my room they have to bring me their response, I read it and then provide students with feedback.  I will ask for clarification of their thoughts, provide a leading question if they are totally off the mark (which usually is in the form of “I don’t care about this and will write anything”), or provide positive feedback and an extension question to those students who have a great response.  The biggest thing here is that students know you read their reflections and will provide them with some sort of guidance based on their perspective of the lesson (a built-in RTI if you will).

That last sentence is one that took me a while to totally understand and even longer to develop good ways to provide feedback that would guide and encourage my student at their level versus my own.  Every year a student will complain that I do not help them.  I now actually hope and anxiously wait for that moment to happen.  When they do, I ask them to explain what they mean by that and to describe my actions in class that would support their stance.  What usually happens is that students will voice that I do not help them with what they think they need.  For too many students I have in class, that usually entails doing their work for them.  They are trying to get by with whatever they can, and they are not subtle with it.  Once they understand classroom expectations they accept them, I have had students defend those expectations to their parents.  The biggest thing I have found is to take time and do short individual conferences with students every other week, they appreciate it and it shows in their effort in class.

Read what students are saying and reflect on how you perceive the lesson.  Is there a better way to present the material?  Are there activities or stations you could implement to increase engagement and learning?  Do you accommodate all learner’s needs?  Are you going at a acceptable pace for students?  Are you giving students enough wait time?  Are you encouraging all students in your class?  Students will tell you what’s really happening in your classroom, tap into that resource and revise your plans in a way that will make learning better for you and your students.

Don’t feel bad about implementing an idea from your students, you aren’t any less of a teacher for taking a student’s idea and making a great lesson based on it.

Teacher Reflection 180: Day 11

Day 11:

Something I learned today was ________________________ (be specific! An answer of math is too general)

An example of this is ____________________

If I made a problem for a test using this concept it would be:

I tend to ask the first question a lot for reflection, for a few different reasons.  I am trying to develop student’s vocabulary, confidence and communication skills about mathematics.  I want my students to be able to openly discuss mathematics, without worrying about how they describe things, what vocabulary they use, or even worrying about peer’s reactions to their thoughts.  One way to start this is by scaffolding questioning so that students have a guided response (which feels safer to students), but I also want students to be able to transition from this scaffold as quickly as possible.  One trend in my students the past five years is that everything they have done in math has been overscaffolded.  Students who need no help with problems or those that needed just a little push in the right direction have gotten so much “fill in the blanks” instruction that they no longer have the confidence to strike out on their own with their work.  One of the big factors that leads to this is the fact that with AYP and NCLB, there has been a push to get the students who score low on tests or those that are “bubble kids” extra instruction.  Schools are trending away from providing extra opportunities for students who excel at mathematics- leaving it to the classroom teacher.  While this type of RTI is a good change, many teachers also overlook these students to focus on the same subset of students in an attempt to increase test score ratings for their classroom.  The fact the MN Department of Ed also put testing scores into teacher evaluations just compounds this problem.  We need to remember that no child left behind also means not allowing these students to falter or become stagnant in their own learning.

I ask that first question often to get student’s own thoughts: raw, unprompted, pure.  Seeing the growth a student takes over the course of a year in their ability to explain their mathematical thinking and strategies is great for both students and myself.  If students struggle with the openness of this question I will ask them more guided questions individually as they come to me to check in with their reflections.  It gives me a lot of insight on how students perceive information in class, what do they remember- what things actually make an impression.  I tend to find those small things, a weird picture or joke- or even an untimely interruption of class, usually are the ones that students remember.  Do I try to do that every lesson, no.  I am a firm believer of giving students structure in class but also that if you do the same thing too many times, it’s effectiveness wanes.  By providing a multiple approach to teaching (keeping an overall structure but rotating how material is presented, explored and practiced) I have found students to make connections and have more “sticky” moments that stay with them and connect concepts.

I ask the final question for many different reasons.  I have found that students think of the concept with a whole different perspective when they have to design a problem containing the mathematics versus just manipulating the numbers to find an answer.  Many students will design a problem and when I ask them to re-examine it, find that they did not address the concept they were intending.  It also provides me with a good test or quiz bank of questions.  I am assured that students will know how to solve the problem (because I typically have them share their problems as a warmup for the next day), and they take a different approach to solving problems designed by peers.

So what was something you learned in class today?

Teacher Reflection 180: Day 10

Something I learned today was _____ (be specific! An answer of math is too general)

 

_____ was similar to the lesson yesterday because _____ (write a couple of sentences explaining how they are)

 

Today’s reflection questions for students is all about how they perceive my lessons.  It is a check to make sure what I think I am doing in class is what I actually am doing.

 

1) What are students taking away from the lesson?

There are many factors that effect how students perceive lessons, but ultimately I am responsible for what students take away from my class.  Are they paying attention to  the critical outcomes of the lesson?  How well can they describe them?  Right now I am having students define the objective of the day, and that is going very well.  It also provides students a learning objective in their terms, one that is more accessible to them.  I have found that the first question is starting to smooth out for students, there are less corrections or clarifications that need to be made.

2) How well am I connecting content for students?

This is a huge concern for me every day.  How are students taking the information we discuss in class and internalize it?  Are they  a user or implementor?  This last question has been my biggest focus the past month.  My students have very large gaps in their mathematical knowledge.  They remember rules and try blindly applying them wherever they can.  I actually see two things largely contributing to this: testing and calculators.  We test our students so much, and for the sake of speed and efficiency, those test have a large multiple choice bank.  Students can either just guess at answers, or grab their favorite math crutch- the calculator.  Many of my students have very low frustration levels when it comes to math, and once they feel they do not know how to solve a problem but have a calculator they try a different form of guessing.  They take combinations of numbers and operations until the value on the calculator matches one on the test.  This then becomes the answer in their mind, and I have had many students get upset when they get those questions wrong- “It’s right!  The calculator gave me that answer!”  I have really started to focus heavily on having students communicate the process of solving problems instead of giving me answers.  Students will still try to use calculators and give me a solution, but they are starting to realize that I am having them focus on how they read problems, what information they need and what mathematical operations they need to perform.

3) Where do I need to go from here?

This is a critical question I ask myself every day, every hour and many times within those hours.  I have become less focused on following a deadline on standards and have adapted my lessons to make sure I meet the needs of my students.  Taking away the “deadline” pressure has allowed me to relax, promote good classroom discussions and focus on student understanding and learning versus what learning I believe I have supplied them.  Formative Assessment is a huge buzzword in education, and it’s not anything new to teachers- it’s just something that many may or may not focus on.  The word assessment brings formal testing to mind for many teachers, students and parents- but it is not.  Questions, discussions, practice and reflections all have an important role in providing you with critical information on what your students understand and what you need to do next.

Teacher Reflection 180: Day 8

When it comes to a job which is better: getting it done fast OR getting it done right?

Explain when getting it done fast is better:

Explain when getting it done right is better:

When it comes to Math which is better: getting it done fast OR getting it done right?

Explain when getting it done fast is better:

Explain when getting it done right is better:

Why do your students feel speed is better?  How has this opinion been supported by real life experiences?

This is a very important question to get a feel for.  Students hide behind the statement “When are we ever going to use this in our lives?” and there are a lot of jobs that support speed as a factor of performance.  Research the examples they provide to determine how speed effects evaluation.  I have found that unless you provide students with some visuals and facts about jobs outside of school that they will listen but not hear you.  Provide students with examples of jobs that promote quantity over quality, and even find a video clip or two that students could watch.  Have them discuss things they noticed after watching the clip and see if their outlook changes.

This type of research will give you a basis of how you can combat the need to rush through work in class.

Why do your students feel doing things right is better?  How has this opinion been supported by real life experiences?

Similar to speed, do some research to find jobs where quality is demanded over quantity.  Do the same things, find videos, show them.  Have students talk about what they saw and which of the two factors they now believe is more important.  Then hit them up with typical salaries for the jobs you found.  I have found quality/expertise jobs to offer higher pay.

 

Why do your students feel speed is better in math?  How has this opinion been supported by school experiences?

Math for many students is timed.. for everything!  We do math minutes, 5 minute warm-ups, timed tests- even the class is set on a strict time schedule.  Many of my students want to complete things within the time allowed and not worry about quality.  They think a math lesson has to be completed in one day.  They feel projects are on a 1-2 day time frame.  They often comment to me about the time they have wasted by doing a problem wrong, or they don’t want to try to work on a problem unless they know they are doing it right because of the same constraint.

There are times that I also support this outlook, I currently set a timer for class to remind me about class reflection at the end of the hour.  Once that buzzer goes, we drop what we are doing.  I have caught students glancing at the timer by the board to see how much time they have left to complete their current work.  How often do we set up timed stations or activities with the justification of keeping students engaged, moving, fresh?  Currently I am working to slow down my classroom (even working on the timer for reflection) to show students that this is not important.  Students initially think that I’m doing them a favor and allowing “goof off” time, until they start thinking about the work we do, get involved in the discussions, and start to make their “brain hurt.”  That last phrase has been spoken a lot this year, and I’m starting to take it as a badge of honor.  Even though they say their brain hurts, they are working their hardest to find answers, justify their work and analyze the work of others.

Why do your students feel doing it right is better in math?  How has this opinion been supported by school experiences?

Right now there are only a few students who feel that doing it right is better than doing it fast.  The bad side to this is those students feel that the answer is all that matters, not the journey.  This is another reason I have refrained from giving official grades on papers- instead I ask a question to provoke the student to clarify or analyze their approach to the problem.  Giving students small input to assignments and having them rework the problems has really helped many of my students, but it comes at a cost- time.  Learning isn’t something that happens instantaneous for our students, they need time to be messy, make mistakes, correct them, compare them.  That is the way I want to encourage my students to think about Math, so they can grow to their full potential.