The ever demanding question of when calculators should be used and at which level (include the graphing calculator in these thoughts). This question, among several others is discussed in this chapter.

My personal thought is that by the time the students reach pre-algebra, we are focusing on much deeper concepts than calculations and arithmetic. I do not have a problem allowing the students to use calculators. However, we are teaching many of the concepts the graphing calculator does on its own. I think it is still important that students learn the basics, like graphing a line, a parabola, etc. by hand before graphing calculators are allowed. Then at least the student understands what the calculator is doing for him/her.

YES!!! This is a good statement Sandy and I agree that a type of balance between the two is necessary. One is never sure which method a student will understand the best and the 'checks and balances' between the two is good stuff!!!

In the barriers section, the writer brings up an interesting point that often students do not experience technologies and tools that may not promote mathematical reasoning or sense making. I can use YouTube to show them how to do something, this isn't much different then just watching me for a break... Smartboards can be a great tool. Depending how they are used, they may be no more relevant than a fancy chalkboard... So, technology and tools can be a tricky subject. I guess I go back to the idea of different modes of learning, how it's used, depth of knowledge created or needed to effectively use it and do kids understand the math behind what the tool just did for me or are they "trusting" what the tool tells them... Students to receive and use information differently than I did as an eighth grader. It is up to me to understand "how" to best approach and infuse the idea of tools and technology. Also, as I finish this, I am not sure of all of the tools/tech out there for use much less how to use it effectively, training can be an issue for teachers too...

OK So I thought we were on Assessment & remainder of the document so I just got done reading pages 92 through 110. So I am am behind or ahead however you want to look at it! Assessment: It was interesting to me the statement; " The assessment emphasis tends to be placed on the evaluation of the student achievement, academic programs and the performance of teachers" . My understanding of this part is that we shouldn't be using this, rather we should be using assessments for "... the rich accountability for using assessments processes to impact student learning and improve instruction......." We need to get back to this , by I am a little worried about our upcoming effective instruction policy! It say and I quote: Unproductive Beliefs - the purpose for administering standardized high-stakes mathematics assessment is to categorize students and evaluate teachers" - isn't this were we are heading??? Instead of ; Productive Beliefs - using assessments to improve instruction and assist mathematics teachers with evaluating strengths and weaknesses of their programs. Unproductive beliefs that a single high-quality assessment can be used to make important decisions about students and teachers" rather than Productive beliefs that " Assessments should help our students become better judges of their own work, support them in recognizing quality work when they produce it, and support them in using evidence to advance their own learning." I really hope that are SLO test help students and teachers show growth in their learning and give teacher and students the evidence they need that they are growing mathematically in the mathematics field. I think by using the ACT ave score and trying to increase it to say 25 would be considered a unproductive belief. the recommendations that ; " decisions about licensing teachers, evaluating teachers, or passing students should never be made on the basis of a single score on a high-stakes assessment" is a good recommendation! I feel we really need to " provide timely intervention support to all students based on assessment results that would require the allocation of additional instructional time to some students within the existing school day" really needs to happen. I know we have math matters and that I feel is a good start , how ever somehow I feel we need to make it more transparent so that we can bring in and take out students who need the additional remediation. Professionalism: I really agree that we need to share ideas, insights and practices as we collaborate. I think we are just OK at this. I think that are PLC time is really good and we just need to continue to grow and really start talking about our instructional practices(in the reading they say this may take up to 3yrs!) and what are really good instructional practices. I think we really should observe each other in a non-threatening situations discussing what we really like about the lesson observation and maybe an idea to grow. What would really be good is to observe each other trying new instruction strategies that we are not comfortable with and give feedback to each other in a non-threatening way! Maybe listing some things that we are trying to accomplish in our class and then having a peer come in and observe what we wanted them to look for to see if they think we are accomplishing it. I think this could be the next step that might help us improve student learning. I hope the new effective instruction policies implement do not hinder this notion??

I think the best tests we have in Pre-Cal are are non-calculator test or the 2 day test where day 1 is no calculator and day 2 is calculator. It really shows the Math they know.

Calculators. Such a slippery slope. What I got from this section was that we need to be teaching students how and when to use technology to help in the problem solving process. What always gets lost in the shuffle of using calculators is the ability of students' to decide if the answer the calculator is giving is reasonable. To do this there must be a fundamental understanding of what the calculator is doing. I like what John said about Pre-Calc doing 2 part tests. Part 1 show the fundamental understanding of the concept, part 2 use tech to solve a bigger problem.

As I watch my students use their smart devices 'appropriately' in class :) I know that it is important to teach a portion of math class with the support of these calculators! The number of times I am on google looking up a calculating device to help with a real life math problem is quite often...I don't want to get something wrong!!! My mind is always estimating what the right answer should be just to keep an eye on these programs (they only are doing what we ask them to do). Therefore I think that it is important to introduce students to these programs/apps as well. They need to be able to access and use these correctly or they are doomed!!! REMEMBER WHEN MCDONALDS ORDER TAKERS DID THE MATH FOR THE BILL ON PAPER??? The other portion of class it is ok to do non calculator math. Sometimes these are best done with warm up or cool down opportunities... and also with estimating opportunities... and when sensible numbers are involved and you ask your students to not 'insult their intelligences' by using a calculating device!

My personal thought is that by the time the students reach pre-algebra, we are focusing on much deeper concepts than calculations and arithmetic. I do not have a problem allowing the students to use calculators. However, we are teaching many of the concepts the graphing calculator does on its own. I think it is still important that students learn the basics, like graphing a line, a parabola, etc. by hand before graphing calculators are allowed. Then at least the student understands what the calculator is doing for him/her.

ReplyDeleteYES!!! This is a good statement Sandy and I agree that a type of balance between the two is necessary. One is never sure which method a student will understand the best and the 'checks and balances' between the two is good stuff!!!

DeleteIn the barriers section, the writer brings up an interesting point that often students do not experience technologies and tools that may not promote mathematical reasoning or sense making. I can use YouTube to show them how to do something, this isn't much different then just watching me for a break... Smartboards can be a great tool. Depending how they are used, they may be no more relevant than a fancy chalkboard... So, technology and tools can be a tricky subject. I guess I go back to the idea of different modes of learning, how it's used, depth of knowledge created or needed to effectively use it and do kids understand the math behind what the tool just did for me or are they "trusting" what the tool tells them... Students to receive and use information differently than I did as an eighth grader. It is up to me to understand "how" to best approach and infuse the idea of tools and technology. Also, as I finish this, I am not sure of all of the tools/tech out there for use much less how to use it effectively, training can be an issue for teachers too...

ReplyDeleteOK So I thought we were on Assessment & remainder of the document so I just got done reading pages 92 through 110. So I am am behind or ahead however you want to look at it! Assessment: It was interesting to me the statement; " The assessment emphasis tends to be placed on the evaluation of the student achievement, academic programs and the performance of teachers" . My understanding of this part is that we shouldn't be using this, rather we should be using assessments for "... the rich accountability for using assessments processes to impact student learning and improve instruction......." We need to get back to this , by I am a little worried about our upcoming effective instruction policy! It say and I quote: Unproductive Beliefs - the purpose for administering standardized high-stakes mathematics assessment is to categorize students and evaluate teachers" - isn't this were we are heading??? Instead of ; Productive Beliefs - using assessments to improve instruction and assist mathematics teachers with evaluating strengths and weaknesses of their programs. Unproductive beliefs that a single high-quality assessment can be used to make important decisions about students and teachers" rather than Productive beliefs that " Assessments should help our students become better judges of their own work, support them in recognizing quality work when they produce it, and support them in using evidence to advance their own learning." I really hope that are SLO test help students and teachers show growth in their learning and give teacher and students the evidence they need that they are growing mathematically in the mathematics field. I think by using the ACT ave score and trying to increase it to say 25 would be considered a unproductive belief. the recommendations that ; " decisions about licensing teachers, evaluating teachers, or passing students should never be made on the basis of a single score on a high-stakes assessment" is a good recommendation! I feel we really need to " provide timely intervention support to all students based on assessment results that would require the allocation of additional instructional time to some students within the existing school day" really needs to happen. I know we have math matters and that I feel is a good start , how ever somehow I feel we need to make it more transparent so that we can bring in and take out students who need the additional remediation. Professionalism: I really agree that we need to share ideas, insights and practices as we collaborate. I think we are just OK at this. I think that are PLC time is really good and we just need to continue to grow and really start talking about our instructional practices(in the reading they say this may take up to 3yrs!) and what are really good instructional practices. I think we really should observe each other in a non-threatening situations discussing what we really like about the lesson observation and maybe an idea to grow. What would really be good is to observe each other trying new instruction strategies that we are not comfortable with and give feedback to each other in a non-threatening way! Maybe listing some things that we are trying to accomplish in our class and then having a peer come in and observe what we wanted them to look for to see if they think we are accomplishing it. I think this could be the next step that might help us improve student learning. I hope the new effective instruction policies implement do not hinder this notion??

ReplyDeleteI think the best tests we have in Pre-Cal are are non-calculator test or the 2 day test where day 1 is no calculator and day 2 is calculator. It really shows the Math they know.

ReplyDeleteCalculators. Such a slippery slope. What I got from this section was that we need to be teaching students how and when to use technology to help in the problem solving process. What always gets lost in the shuffle of using calculators is the ability of students' to decide if the answer the calculator is giving is reasonable. To do this there must be a fundamental understanding of what the calculator is doing. I like what John said about Pre-Calc doing 2 part tests. Part 1 show the fundamental understanding of the concept, part 2 use tech to solve a bigger problem.

ReplyDeleteAs I watch my students use their smart devices 'appropriately' in class :) I know that it is important to teach a portion of math class with the support of these calculators! The number of times I am on google looking up a calculating device to help with a real life math problem is quite often...I don't want to get something wrong!!! My mind is always estimating what the right answer should be just to keep an eye on these programs (they only are doing what we ask them to do). Therefore I think that it is important to introduce students to these programs/apps as well. They need to be able to access and use these correctly or they are doomed!!!

ReplyDeleteREMEMBER WHEN MCDONALDS ORDER TAKERS DID THE MATH FOR THE BILL ON PAPER???

The other portion of class it is ok to do non calculator math. Sometimes these are best done with warm up or cool down opportunities... and also with estimating opportunities... and when sensible numbers are involved and you ask your students to not 'insult their intelligences' by using a calculating device!