The panel does provide insights into its understanding of the different approaches:
The discussion about math skills has persisted for many decades. One aspect of the debate is over how explicitly children must be taught skills based on formulas or algorithms (fixed, step-by-step procedures for solving math problems) versus a more inquiry-based approach in which students are exposed to real-world problems that help them develop fluency in number sense, reasoning, and problem-solving skills. In this latter approach, computational skills and correct answers are not the primary goals of instruction. Those who disagree with the inquiry-based philosophy maintain that students must first develop computational skills before they can understand concepts of mathematics. These skills should be memorized and practiced until they become automatic. In this view, estimating answers is insufficient and, in fact, is considered to be dependent on strong foundational skills. Learning abstract concepts of mathematics is perceived to depend on a solid base of knowledge of the tools of the subject. Of course, teaching in very few classrooms would be characterized by the extremes of these philosophies. In reality, there is a mixing of approaches to instruction in the classroom, perhaps with one predominating.
I found the passage that Instructivist quoted rather jarring and wrote the following comment to Tyrrel Flawn, the Exec. Dir of the National Math Panel. The comment is now part of the public comments:
I am concerned with the last two sentences of the second paragraph. The statement that extremes of either type of these philosophies are not used exclusively in classrooms and that actually both types are mixed implies that there is no problem. To suggest that the inquiry-based philosophy has had no effect because it has not been used in its pure form, or because it is mixed with direct instruction is a specious argument and conveniently sidesteps an extremely significant issue.
The problem is more complex than characterized by these last two sentences. First of all, there are degrees of discovery or inquiry-based learning. There is general agreement within the psychological community that knowledge is ultimately constructed by the learner in order to be absorbed. But such construction can occur with passive type learning (i.e., direct instruction) just as it can with hands-on activities (discovery learning). Thus all types of learning is discovery oriented, and one has to look at the gradations of discovery learning. Some types have minimal guidance, and other types rely on structured guidance such as that found in textbooks such as Singapore, Saxon, or Dolciani.
There are a host of math programs being used, however, that are informed by constructivist theory of the minimal guidance variety, such as Investigations in Number, Data and Space; Everyday Math, Connected Math, IMP, Core Plus, and Math Trailblazers. Some of these programs such as Investigations, Trailblazers and Everyday Math, do not have textbooks. Teachers who must teach from such programs are unwittingly conducted discovery-based classes by virtue of how the program is put together. Students are often not given enough prior information before being presented with a problem that they must solve in group work, leading to inefficient solutions.
Furthermore such programs typically do not teach to mastery since students will be exposed again next year to the same topic through “spiraling.” The "spiraling" concept is picked up by other texts and programs, which then engenders the use of discovery in classrooms, since mastery is no longer as pertinent as it once was. The last two sentences would seem to ignore the highjacking of math programs going on because of the increasing pervasiveness of the inquiry-based philosophy.
I would hope that consideration is given to better characterizing the discussion of inquiry-based learning versus direct instruction.
"Of course, teaching in very few classrooms would be characterized by the extremes of these philosophies. In reality, there is a mixing of approaches to instruction in the classroom, perhaps with one predominating."
I'm glad Barry picked up on this and set the panel straight. As long as fuzzy manuals (some constructivist math programs don't have textbooks) are prescribed in schools, things can't be fine and dandy as the panel believes.
No findings yet. We must wait another year.
ReplyDeleteThe panel does provide insights into its understanding of the different approaches:
The discussion about math skills has persisted for many decades. One aspect of the debate is
over how explicitly children must be taught skills based on formulas or algorithms (fixed,
step-by-step procedures for solving math problems) versus a more inquiry-based approach in
which students are exposed to real-world problems that help them develop fluency in number
sense, reasoning, and problem-solving skills. In this latter approach, computational skills and
correct answers are not the primary goals of instruction.
Those who disagree with the inquiry-based philosophy maintain that students must first
develop computational skills before they can understand concepts of mathematics. These
skills should be memorized and practiced until they become automatic. In this view,
estimating answers is insufficient and, in fact, is considered to be dependent on strong
foundational skills. Learning abstract concepts of mathematics is perceived to depend on a
solid base of knowledge of the tools of the subject. Of course, teaching in very few
classrooms would be characterized by the extremes of these philosophies. In reality, there is
a mixing of approaches to instruction in the classroom, perhaps with one predominating.
I found the passage that Instructivist quoted rather jarring and wrote the following comment to Tyrrel Flawn, the Exec. Dir of the National Math Panel. The comment is now part of the public comments:
ReplyDeleteI am concerned with the last two sentences of the second paragraph. The statement that extremes of either type of these philosophies are not used exclusively in classrooms and that actually both types are mixed implies that there is no problem. To suggest that the inquiry-based philosophy has had no effect because it has not been used in its pure form, or because it is mixed with direct instruction is a specious argument and conveniently sidesteps an extremely significant issue.
The problem is more complex than characterized by these last two sentences. First of all, there are degrees of discovery or inquiry-based learning. There is general agreement within the psychological community that knowledge is ultimately constructed by the learner in order to be absorbed. But such construction can occur with passive type learning (i.e., direct instruction) just as it can with hands-on activities (discovery learning). Thus all types of learning is discovery oriented, and one has to look at the gradations of discovery learning. Some types have minimal guidance, and other types rely on structured guidance such as that found in textbooks such as Singapore, Saxon, or Dolciani.
There are a host of math programs being used, however, that are informed by constructivist theory of the minimal guidance variety, such as Investigations in Number, Data and Space; Everyday Math, Connected Math, IMP, Core Plus, and Math Trailblazers. Some of these programs such as Investigations, Trailblazers and Everyday Math, do not have textbooks. Teachers who must teach from such programs are unwittingly conducted discovery-based classes by virtue of how the program is put together. Students are often not given enough prior information before being presented with a problem that they must solve in group work, leading to inefficient solutions.
Furthermore such programs typically do not teach to mastery since students will be exposed again next year to the same topic through “spiraling.” The "spiraling" concept is picked up by other texts and programs, which then engenders the use of discovery in classrooms, since mastery is no longer as pertinent as it once was. The last two sentences would seem to ignore the highjacking of math programs going on because of the increasing pervasiveness of the inquiry-based philosophy.
I would hope that consideration is given to better characterizing the discussion of inquiry-based learning versus direct instruction.
"Of course, teaching in very few
ReplyDeleteclassrooms would be characterized by the extremes of these philosophies. In reality, there is
a mixing of approaches to instruction in the classroom, perhaps with one predominating."
I'm glad Barry picked up on this and set the panel straight. As long as fuzzy manuals (some constructivist math programs don't have textbooks) are prescribed in schools, things can't be fine and dandy as the panel believes.
I found the passage that Instructivist quoted rather jarring
ReplyDeleteI felt the same way.