Please follow this link to my inquiry blog
inventingunderstanding.blogspot.com
Happy Holidays
Melanie
Sunday, December 13, 2009
Sunday, December 6, 2009
Chapter 11 – Looking to the Future
When I first began this chapter I was certain that I would find that teaching methods and grouping practices at Amber Hill had changed to resemble those at Phoenix Park.....imagine my surprise to learn that the opposite had occurred....and all because of pressure from some “big wig” inspector who believed in and encouraged transmission models of teaching and the pressure put on the school by new middle-class parents.
Boaler uses her study to show “what is possible” when teachers try to deliver instruction in a way that stretches thinking and supports all students, but in this final chapter she shows what is possible when people are not willing to accept that there is a better way to teach mathematics other than a procedural approach, an approach which according to Boaler “has served few students well in the past - offering limited opportunities for understanding, identification, and affiliation with mathematics.”
Is this the same “back to basics” approach we hear of so often? An approach which Cheek and Castle question whether it was actually ever abandoned? I had an interesting conversation with a friend a while back, he works as a math itinerant with a school district and frequently hears teachers talk of adopting a “back to basics” approach in their mathematics classrooms, to correct and remediate deficiencies students bring with them from other grades.....it should stand to reason then if such an approach is successful that we will stop hearing of students who “don’t know their basic facts”, however, if everyone is using such an approach, then why then are the problems still there? Is it because math is not about knowing, but about understanding....I think so. Disconnected pieces of knowledge and rules will not serve students well in the long run, it might get the test, but it will not get them through life.....it will not allow them to transfer their knowledge to new situations, nor will it allow them to feel confident in their problem solving abilities.......why then is such an approach favoured by many? Is it because, like ability grouping, it is an easier approach for the teacher?
As I finish up this course I am wishing more and more that I had a classroom of my own, a classroom in which I could allow students to explore, inquire, create and understand...... I am certain I would need guidance along the way, but I can clearly see than such an open approach would allow students to experience greater success, much like those at Amber Hill......and it would allow them to really get back to basics.....to get back to creativity.....thank you Jo Boaler and Sir Ken Robinson for opening my eyes......
Boaler uses her study to show “what is possible” when teachers try to deliver instruction in a way that stretches thinking and supports all students, but in this final chapter she shows what is possible when people are not willing to accept that there is a better way to teach mathematics other than a procedural approach, an approach which according to Boaler “has served few students well in the past - offering limited opportunities for understanding, identification, and affiliation with mathematics.”
Is this the same “back to basics” approach we hear of so often? An approach which Cheek and Castle question whether it was actually ever abandoned? I had an interesting conversation with a friend a while back, he works as a math itinerant with a school district and frequently hears teachers talk of adopting a “back to basics” approach in their mathematics classrooms, to correct and remediate deficiencies students bring with them from other grades.....it should stand to reason then if such an approach is successful that we will stop hearing of students who “don’t know their basic facts”, however, if everyone is using such an approach, then why then are the problems still there? Is it because math is not about knowing, but about understanding....I think so. Disconnected pieces of knowledge and rules will not serve students well in the long run, it might get the test, but it will not get them through life.....it will not allow them to transfer their knowledge to new situations, nor will it allow them to feel confident in their problem solving abilities.......why then is such an approach favoured by many? Is it because, like ability grouping, it is an easier approach for the teacher?
As I finish up this course I am wishing more and more that I had a classroom of my own, a classroom in which I could allow students to explore, inquire, create and understand...... I am certain I would need guidance along the way, but I can clearly see than such an open approach would allow students to experience greater success, much like those at Amber Hill......and it would allow them to really get back to basics.....to get back to creativity.....thank you Jo Boaler and Sir Ken Robinson for opening my eyes......
Chapter 10 – Ability Grouping, Equity, and Survival of the Quickest
If I were to provide advice to Boaler as to how she could improve this book for further editions I would suggest that she rename Chapter 10 – “DIS-ability” Grouping.
The disconnect between student and teacher needs, student and teacher beliefs and student and teacher ideas regarding ability grouping became very clear as I read this chapter and prepared to lead the discussion.
I was shocked first and foremost by the fact that the set decisions (and set implications) are often hidden from students, and that they may actually spend a great deal of time working in a class unaware of the set that they are in. The rationale for this is that students often become demoralized and unmotivated when set decisions are made known.....and with just cause I believe.....wouldn’t you be upset to know that no matter how hard you work, that even if you know 100% of the material you can still only receive a low grade on a standardized test, I know I would. I think I would be even more upset if this knowledge was withheld from me for a long period of time, if I thought I was doing well, only to find out that I was doing so well because I was actually working at a much lower level than I had thought. So who does this decision to withhold set decisions from students really benefit? The teachers of course, they don’t have to deal with students acting out or not completing work because “what’s the point if you can only get a low grade?”
This disconnect between students desire to do well and their opportunities to do well remained on my mind as I read the rest of the chapter. Students felt cheated by a system that teachers put in place because they feel it is not realistic to assume that all students can achieve A-levels......but why should the decision to decide who can try for A-levels rest with teachers? Why should the decision be made so early? Shouldn’t all students (like those at Phoenix Park) be given the same opportunities to learn and succeed, and then if the set-up of the exam requires that students be placed into sets can’t the decision be made much closer to the exam (much like at Phoenix Park).......oh, wait.....to teach in such a way requires much more work on the part of the teacher.....which brings me to my next point....
The nature of the lessons in ability grouped classes allows teachers the ability to work at a fixed pace, to deliver lessons using a one size fits all approach.....with little regard for understanding or students ability to keep up to the pace of the work; some students will become bored, some will become frustrated, but that’s the way the games is played.....
Speaking of games, the set up of the ability grouped classes encourages competition among students, which is alright for some, for the students who are competitive by nature, who do well in a competitive environment. But what about the students who experience anxiety and constant pressure because they feel as they are constantly being judged against their peers....what about those top set girls? The competition may have caused them more harm than good, and again, the competition was for the benefit of the teachers, not the students.
The grouping of students also appears to have been done for the benefit of the teachers, with some students reporting that they had been placed in a lower set than would have been expected due to their behaviour. This is discomforting to think that we would restrict a students potential based on their behaviour as opposed to examining factors, such as boredom or frustration that might be influencing their behaviour.
It’s interesting to note that ability grouping was designed to maximize student potential and achievement, but the data presented by Boaler is in sharp contrast to this. The students at Phoenix Park performed much better than Amber Hill student on the GCSE’s even though initial assessments suggested that achievement levels ought to have been similar? And if Amber Hill students were taught using a method that was designed to increase potential shouldn’t they have done much better than Phoenix Park’s students.......they were expected to....
But the measures put in place to bring about those high expectations did not meet the needs (or expectations) of students. The methods would put in place largely to assist teachers in maintaining structure in lessons, in planning one lesson to deliver to all students; they were not designed to stretch and support thought and understanding as did the lessons at Phoenix Park, they were not designed to maximize student enjoyment and success. The design of lessons at Amber Hill and the decision to ability group results in DISabled thought, DISabled achievement levels and DISaffected learners.......
The disconnect between student and teacher needs, student and teacher beliefs and student and teacher ideas regarding ability grouping became very clear as I read this chapter and prepared to lead the discussion.
I was shocked first and foremost by the fact that the set decisions (and set implications) are often hidden from students, and that they may actually spend a great deal of time working in a class unaware of the set that they are in. The rationale for this is that students often become demoralized and unmotivated when set decisions are made known.....and with just cause I believe.....wouldn’t you be upset to know that no matter how hard you work, that even if you know 100% of the material you can still only receive a low grade on a standardized test, I know I would. I think I would be even more upset if this knowledge was withheld from me for a long period of time, if I thought I was doing well, only to find out that I was doing so well because I was actually working at a much lower level than I had thought. So who does this decision to withhold set decisions from students really benefit? The teachers of course, they don’t have to deal with students acting out or not completing work because “what’s the point if you can only get a low grade?”
This disconnect between students desire to do well and their opportunities to do well remained on my mind as I read the rest of the chapter. Students felt cheated by a system that teachers put in place because they feel it is not realistic to assume that all students can achieve A-levels......but why should the decision to decide who can try for A-levels rest with teachers? Why should the decision be made so early? Shouldn’t all students (like those at Phoenix Park) be given the same opportunities to learn and succeed, and then if the set-up of the exam requires that students be placed into sets can’t the decision be made much closer to the exam (much like at Phoenix Park).......oh, wait.....to teach in such a way requires much more work on the part of the teacher.....which brings me to my next point....
The nature of the lessons in ability grouped classes allows teachers the ability to work at a fixed pace, to deliver lessons using a one size fits all approach.....with little regard for understanding or students ability to keep up to the pace of the work; some students will become bored, some will become frustrated, but that’s the way the games is played.....
Speaking of games, the set up of the ability grouped classes encourages competition among students, which is alright for some, for the students who are competitive by nature, who do well in a competitive environment. But what about the students who experience anxiety and constant pressure because they feel as they are constantly being judged against their peers....what about those top set girls? The competition may have caused them more harm than good, and again, the competition was for the benefit of the teachers, not the students.
The grouping of students also appears to have been done for the benefit of the teachers, with some students reporting that they had been placed in a lower set than would have been expected due to their behaviour. This is discomforting to think that we would restrict a students potential based on their behaviour as opposed to examining factors, such as boredom or frustration that might be influencing their behaviour.
It’s interesting to note that ability grouping was designed to maximize student potential and achievement, but the data presented by Boaler is in sharp contrast to this. The students at Phoenix Park performed much better than Amber Hill student on the GCSE’s even though initial assessments suggested that achievement levels ought to have been similar? And if Amber Hill students were taught using a method that was designed to increase potential shouldn’t they have done much better than Phoenix Park’s students.......they were expected to....
But the measures put in place to bring about those high expectations did not meet the needs (or expectations) of students. The methods would put in place largely to assist teachers in maintaining structure in lessons, in planning one lesson to deliver to all students; they were not designed to stretch and support thought and understanding as did the lessons at Phoenix Park, they were not designed to maximize student enjoyment and success. The design of lessons at Amber Hill and the decision to ability group results in DISabled thought, DISabled achievement levels and DISaffected learners.......
Chapter 9 - Girls, Boys and Learning Styles
Girls just wanna understand........no wait.......girls just wanna have fun........but can they enjoy mathematics and "have fun" if they don't understand?
As I read this chapter (and many others) my own mathematical experiences started to make a little more sense and I gained a new level of confidence that had been lacking for many years. Boaler asserts that “women tend to value connected knowing, characterized by intuition, creativity and experience, whereas men tend to value separate knowing, characterized by logic, rigor and rationality.” This is especially interesting because when I took advanced mathematics in high school the class was almost entirely females, yet the teaching style seems to have catered more towards the learning style of males, lessons were presented much like those at Amber Hill, in a series of disconnected ideas, sequential steps to practice and “know”, things that you didn’t “need” to understand, you just had to “remember”.......but I couldn’t remember, I couldn’t “know” something without understanding it, so rather than stay in a program which I knew I was unlikely to experience success in I switched to the academic math program. This class consisted of far more males than females, yet the teaching style was directed more towards that of females. There was more time allowed to make connections and build understanding, math was no longer simply a game with rules that had to be followed. The pressure and competition of the advanced class had been removed, and there was time to ask questions that related to understanding, time to try our own way of doing things or to figure out just why “the rules worked”.
I sympathize with the girls at Amber Hill, aware of the fact that instruction was not meeting their needs, but unable to do anything about it. Students at Amber Hill were assigned to sets and were not able to make the choice to move between them, I had that choice, but in doing so I had to make some sacrifices, for example, I knew that by switching to the academic class that the math classes I could take in university would be restricted would be restricted; however this was just fine with me at that point, as I had no desire to take math classes beyond high school, looking back now I wish I had taken more math classes in University and that I had remained in the advanced program, but alas hindsight is 20/20.....
A question that remains with me after reading is why should the girls at Amber Hill have been expected to compromise their desire for understanding and replace it with a desire for speed akin to that of the boys? Why should they change who they as learners to meet the teacher’s needs? Is there an approach that would allow both genders to be successful........enter Phoenix Park, the open ended inquiry projects allowed boys and girls to experience success with mathematics, why then is such an approach not emphasized and utilized everywhere? Is it because it is an approach that requires more of the student, but far more of the teacher that the direct instruction method?.......this leads to the next chapter and ability grouping.....
I wish I had been present for the discussion on this chapter, it would have been interesting to hear what others had to say on this topic, to hear their experiences and ideas related to gender and learning styles. Hopefully the blog posts will allow me to gain a sense of the discussion.
As I read this chapter (and many others) my own mathematical experiences started to make a little more sense and I gained a new level of confidence that had been lacking for many years. Boaler asserts that “women tend to value connected knowing, characterized by intuition, creativity and experience, whereas men tend to value separate knowing, characterized by logic, rigor and rationality.” This is especially interesting because when I took advanced mathematics in high school the class was almost entirely females, yet the teaching style seems to have catered more towards the learning style of males, lessons were presented much like those at Amber Hill, in a series of disconnected ideas, sequential steps to practice and “know”, things that you didn’t “need” to understand, you just had to “remember”.......but I couldn’t remember, I couldn’t “know” something without understanding it, so rather than stay in a program which I knew I was unlikely to experience success in I switched to the academic math program. This class consisted of far more males than females, yet the teaching style was directed more towards that of females. There was more time allowed to make connections and build understanding, math was no longer simply a game with rules that had to be followed. The pressure and competition of the advanced class had been removed, and there was time to ask questions that related to understanding, time to try our own way of doing things or to figure out just why “the rules worked”.
I sympathize with the girls at Amber Hill, aware of the fact that instruction was not meeting their needs, but unable to do anything about it. Students at Amber Hill were assigned to sets and were not able to make the choice to move between them, I had that choice, but in doing so I had to make some sacrifices, for example, I knew that by switching to the academic class that the math classes I could take in university would be restricted would be restricted; however this was just fine with me at that point, as I had no desire to take math classes beyond high school, looking back now I wish I had taken more math classes in University and that I had remained in the advanced program, but alas hindsight is 20/20.....
A question that remains with me after reading is why should the girls at Amber Hill have been expected to compromise their desire for understanding and replace it with a desire for speed akin to that of the boys? Why should they change who they as learners to meet the teacher’s needs? Is there an approach that would allow both genders to be successful........enter Phoenix Park, the open ended inquiry projects allowed boys and girls to experience success with mathematics, why then is such an approach not emphasized and utilized everywhere? Is it because it is an approach that requires more of the student, but far more of the teacher that the direct instruction method?.......this leads to the next chapter and ability grouping.....
I wish I had been present for the discussion on this chapter, it would have been interesting to hear what others had to say on this topic, to hear their experiences and ideas related to gender and learning styles. Hopefully the blog posts will allow me to gain a sense of the discussion.
Saturday, November 21, 2009
Chapter 8 - Developing identities
Mathematical empowerment. What a loaded phrase from chapter 8. What does it mean to be “mathematically empowered”? Boaler suggests that the students at Phoenix Park were mathematically empowered because they were flexible in their approach to mathematics, because they were prepared to take what they had learned and adapt it to new situations. The flexibility in their thinking and approach to mathematics was reliant on two key features, one being that students believed the math they were learning was adaptable, that it had many uses and could be applied in numerous situations and secondly it relied on students ability to adapt and change the math methods, to think mathematically. These students do not see any separation between the mathematics they are learning at school and the mathematics they are using in real life, they feel that they have knowledge and skills that are of use to them, as opposed to being in a possession of fragmented and disconnected ideas about mathematics, much like the Amber Hill students.
Who we are as teachers will determine who our students become as learners and users of mathematics. If we provide them with challenges and aim to have them construct meaning for themselves then our students are likely to develop this sense of “empowerment” that Boaler describes in the Phoenix Park students. On the contrary, if we provide our students with set procedures and methods, rules that they must follow without having a true understanding of the mathematics behind “the rules” then we are likely to produce students of a similar calibre of those at Amber Hill. Students who are led to believe that they will do well in mathematics if they “follow the rules” but who find that in the real world they are not prepared to think about and make sense of problems of a mathematical nature, students who have a false sense of security that has been provided by cuing systems, rules and practice.
I know that I would like to prepare my students to face “the real world” of mathematics; I would like them to approach problems with the certainty that they are capable of arriving at a solution through their own thinking (without having to rely on long forgotten rules). I would like my students to believe in themselves as learners and users of mathematics but I would also like them to believe in the mathematics. In constructing their own knowledge, taking time to investigate and make sense, taking time to understand, time to see why “the rules” work without just practicing rules. I believe students can become more skilled in their use of school mathematics, whether it is for school use of real world use. How can I achieve this? How can I ensure that my students are not just becoming passive users of mathematics, that they are not simply “playing the game” or “following the rules” much like the students at Amber Hill? I think that even at a young age students can assume some of the responsibility for the construction of knowledge, knowledge that is built through hands on investigations rather than worksheets or text book questions that follow a chalk and talk session directed by the teacher. Can we really expect young students to grasp some of mathematical concepts at a symbolic level when they have not had enough time to experiment with it at a concrete level? We see from Boaler’s work that it didn’t work at Amber Hill, so it is likely to fail our own students as well.
Like the teachers at Amber Hill and Phoenix Park I too have my student’s best interest at heart when I plan my mathematics lessons. The challenge now is to combine best interest with best practice, to use instructional methods that allow students to construct knowledge and apply knowledge, in the classroom and in the real world.
Who we are as teachers will determine who our students become as learners and users of mathematics. If we provide them with challenges and aim to have them construct meaning for themselves then our students are likely to develop this sense of “empowerment” that Boaler describes in the Phoenix Park students. On the contrary, if we provide our students with set procedures and methods, rules that they must follow without having a true understanding of the mathematics behind “the rules” then we are likely to produce students of a similar calibre of those at Amber Hill. Students who are led to believe that they will do well in mathematics if they “follow the rules” but who find that in the real world they are not prepared to think about and make sense of problems of a mathematical nature, students who have a false sense of security that has been provided by cuing systems, rules and practice.
I know that I would like to prepare my students to face “the real world” of mathematics; I would like them to approach problems with the certainty that they are capable of arriving at a solution through their own thinking (without having to rely on long forgotten rules). I would like my students to believe in themselves as learners and users of mathematics but I would also like them to believe in the mathematics. In constructing their own knowledge, taking time to investigate and make sense, taking time to understand, time to see why “the rules” work without just practicing rules. I believe students can become more skilled in their use of school mathematics, whether it is for school use of real world use. How can I achieve this? How can I ensure that my students are not just becoming passive users of mathematics, that they are not simply “playing the game” or “following the rules” much like the students at Amber Hill? I think that even at a young age students can assume some of the responsibility for the construction of knowledge, knowledge that is built through hands on investigations rather than worksheets or text book questions that follow a chalk and talk session directed by the teacher. Can we really expect young students to grasp some of mathematical concepts at a symbolic level when they have not had enough time to experiment with it at a concrete level? We see from Boaler’s work that it didn’t work at Amber Hill, so it is likely to fail our own students as well.
Like the teachers at Amber Hill and Phoenix Park I too have my student’s best interest at heart when I plan my mathematics lessons. The challenge now is to combine best interest with best practice, to use instructional methods that allow students to construct knowledge and apply knowledge, in the classroom and in the real world.
Sunday, November 15, 2009
Chapter 7 - Exploring the Differences......
What stuck with me the most from this chapter was the false sense of success the Amber Hill students must have experienced in mathematics, particularly those in the higher sets. Students worked through the classroom assignments and textbook work with little difficulty, if they followed the steps and memorized the rules then surely they could do well in maths. However, when the time came for the GCSE’s and the questions were posed in an unfamiliar way, when cuing systems were removed and the math had to be applied as opposed to memorized the Amber Hill students found they were ill-prepared for the test. They realized that when their memory failed them they had little else to turn to; they had no real understanding of the math.
On the flip side of this coin we have the Phoenix Park students, while they may not have been prepared for the test entirely in that there were some topics that they had not encountered or been taught through their project work, these students still fared better in the GCSE’s because they could think about the math. These students could make the connections between mathematics and its real world applications. They did not rely on the cuing systems which Amber Hill students struggled without. They were more willing to try questions when the answer or method wasn’t instantly apparent.
Towards which end of this spectrum are our own students lying? Are they prepared for new and challenging tasks? Are they willing to take risks in mathematics to increase their understanding or are they reliant on us as teachers to provide them with the answers to “difficult questions”?
How often do we hear our colleagues talking about classes that just don’t “get it”, classes that don’t “know their basic facts”? Why is it that year after year we hear these same questions, even though we know that we have taught these skills and ideas? Amber Hill’s teachers were especially concerned with their students’ success, so much so that they provided all sorts of “helpful hints” to get them through the math, all sorts of rules that they “just had to remember” and we can see in the end how these students fared. Let’s set things up differently for our students, let’s encourage them to think, to make sense on their own and to truly understand the mathematics we are “teaching”.
On the flip side of this coin we have the Phoenix Park students, while they may not have been prepared for the test entirely in that there were some topics that they had not encountered or been taught through their project work, these students still fared better in the GCSE’s because they could think about the math. These students could make the connections between mathematics and its real world applications. They did not rely on the cuing systems which Amber Hill students struggled without. They were more willing to try questions when the answer or method wasn’t instantly apparent.
Towards which end of this spectrum are our own students lying? Are they prepared for new and challenging tasks? Are they willing to take risks in mathematics to increase their understanding or are they reliant on us as teachers to provide them with the answers to “difficult questions”?
How often do we hear our colleagues talking about classes that just don’t “get it”, classes that don’t “know their basic facts”? Why is it that year after year we hear these same questions, even though we know that we have taught these skills and ideas? Amber Hill’s teachers were especially concerned with their students’ success, so much so that they provided all sorts of “helpful hints” to get them through the math, all sorts of rules that they “just had to remember” and we can see in the end how these students fared. Let’s set things up differently for our students, let’s encourage them to think, to make sense on their own and to truly understand the mathematics we are “teaching”.
Saturday, November 7, 2009
Who's really in charge here......
Discussions in class lead me to question who is really in charge of the learning in our classrooms? If we are supposed to meet our students at their level and take them through the curriculum over the course of the school year, why then are school districts imposing rigid schedules and outlines for us to follow in our classrooms? What if our students are not ready, what if they need more time? How can we truly do justice to a math program and our students math education if we are so caught up with "staying on track" of a schedule imposed from above, the schedule should come from the grassroots level, from the students themselves. It only stands to reason that if we move on to newer and more complicated areas of mathematics before our students are ready, before they have a good understanding of "the basics" that they will continue to struggle, that they will never "catch up", that they will never enjoy mathematics or come to see it's usefulness.
I have to say I never experienced this strict regime when teaching in Alberta, nobody imposed a schedule on me, and I was actually encouraged to spend additional time on areas where students were struggling, knowing that in the end it would allow my students to grow in mathematics as a good foundation had been put in place. Nobody ever told me what HAD to be assessed at each reporting period, I also exercised choice over the resources and assessment methods used within my classroom, if the other grade level teacher chose to give pencil and paper tests and I chose to assess in a different manner that was ok, we did what worked for us, and for our students. Here we have teachers who not only must assess in the same manner, but on the same day.......whatever happened to differentiation? Since when does one size fits all work for students? for teachers?
If we are to provide our students with a truly rich mathematical experience then we must tailor that experience to meet their needs and to meet our needs as teachers. We need to make the choices that are best for our students, choices about when and how to assess, how quickly to move through the curriculum, choices about the types of activities and resources we use, choices that allow our students to make sense of mathematics and build their own understandings of concepts; as opposed to rushing through a series of text book lessons, expecting students to make sense of abstract symbols and concepts without the hands on, concrete experiences that although they may take more time and effort to complete can provide our students with a much deeper understanding than a teacher provided demonstration and pages of pencil and paper practice.
It's time to give the control back to those who need it, the students. Let them dictate the speed of our lessons, the activities we use and the assessment tasks. Let's give them the opportunities they deserve, the opportunities that many of us were not afforded during our own math education.
Melanie
I have to say I never experienced this strict regime when teaching in Alberta, nobody imposed a schedule on me, and I was actually encouraged to spend additional time on areas where students were struggling, knowing that in the end it would allow my students to grow in mathematics as a good foundation had been put in place. Nobody ever told me what HAD to be assessed at each reporting period, I also exercised choice over the resources and assessment methods used within my classroom, if the other grade level teacher chose to give pencil and paper tests and I chose to assess in a different manner that was ok, we did what worked for us, and for our students. Here we have teachers who not only must assess in the same manner, but on the same day.......whatever happened to differentiation? Since when does one size fits all work for students? for teachers?
If we are to provide our students with a truly rich mathematical experience then we must tailor that experience to meet their needs and to meet our needs as teachers. We need to make the choices that are best for our students, choices about when and how to assess, how quickly to move through the curriculum, choices about the types of activities and resources we use, choices that allow our students to make sense of mathematics and build their own understandings of concepts; as opposed to rushing through a series of text book lessons, expecting students to make sense of abstract symbols and concepts without the hands on, concrete experiences that although they may take more time and effort to complete can provide our students with a much deeper understanding than a teacher provided demonstration and pages of pencil and paper practice.
It's time to give the control back to those who need it, the students. Let them dictate the speed of our lessons, the activities we use and the assessment tasks. Let's give them the opportunities they deserve, the opportunities that many of us were not afforded during our own math education.
Melanie
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