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Seeking a School with Strong Math/Science
Questions about Math in Elementary School
We are considering moving our child from our local public elementary school to a private school. My daughter loves science and nature and I want to be sure we look at schools that will support and encourage her interests in that area. We also would like a school where she may find students with similar interests. Do you have a science lover at a local private school? Are there schools with particularly strong science programs? A school that goes until 8th grade would be ideal so that we don't have to do multiple transitions. Thanks in advance for the advice! Parent of a budding scientist
I believe that the Tehiyah Day School solution to science programming is a marvelous exemplar of making the best of school: Its vision for science is an interdisciplinary, project-based inquiry approach, in which children ground both subject matter content and research methodology in their natural inquisitiveness. I identify at least four activity dimensions that apparently have been conducive to the positive experience Neomi has had with science at Tehiyah Day School: (1) Respect and deep concern for all living creatures and the environment; (2) Holistic, integrated approach to curriculum, where logic, mathematics, history, language and cultural studies, and art (!) all cohere around a focal unit theme, such as earth (second grade) or life cycles (third grade); (3) Experience-based approach, including gardening at school, numerous field trips to ranches, tidal pools, and local natural resources requiring community attention; (4) Customization and empowerment by giving each student agency in preparing summative posters and delivering classroom presentations (e.g., mapping ecological habitats in our back yard, photographing spiders, botanical classification of stems and roots); yet also (5) Collaboration, of the good type, in which individuals think hard together to enrich and challenge each other to find new wholes larger than the sums of the brainstorming parts. Perhaps the best test for Neomi's engagement is that the science she does at school comes home with her. She quizzes us at dinner (and we fail miserably, to her glee and our subsequent enlightenment): What is a xylem? a phloem? How does water go up a stem? What's the sun got to do with nutrients? Why do carrots have tiny hairs along the side? And is a spider an insect? Dor
We have a kindergartener who is gifted in math and science but a bit socially awkward and not much interested in drama or performing for others. We have toured Park Day and are particularly drawn to its focus on social skills and strong social justice curriculum. Do you think a math geek would be comfortable and accepted by other students at Park Day? patty
Here are two things that I think are relevant to your question. One is that kids at Park are taught from kindergarten on to honor and respect each other for who they are, and the result is kids who feel free to like what they like, whatever it is, and be who they are, whoever that is. My son and his (large group of) friends proudly call themslelves ''nerds'' because they like math and science and technology and music and books. But it's a name they chose for themselves, not one that anyone would have called them otherwise.
The second thing is that the math they've learned isn't just a series of equations. Kids at Park are challenged to find multiple ways to solve problem, and the math curriculum includes lots of discussion and writing about math in addition to the equations. DS
My son is still 4th grade and it might sound too early to talk about middle schools. I am starting research on private schools and particularly interested in schools in El Cerrito, Berkeley or North Oakland areas which have strong academic curriculum, especially in math for him. He has been very strong academically since K. Now he is in 4/5th combo class and thriving in terms of his academic performance and behavior. In the past few years, he was called to the principal's office for several times in result of his naughty behaviors. This year, his teacher is giving enough challenges, therefore he is very occupied and no time for misbehaving, which makes us really happy. As many of you, parents know that middle school time can be very difficult. I appreciate any school recommendations or advices regarding middle school choice. Anonymous
As a parent of a bright 12 year old 7th grader (a girl) with many interests, who enjoys math and science, and needs constant academic challenge, I would suggest you take a strong look at Windrush School in El Cerrito for your son. Windrush is a K-8 school with a separate middle school that goes from 6th to 8th grade. My daughter is my second child to attend Windrush middle school. My son (now a freshman at a private university on the east coast) was much like your son -- if not intellectually challenges could becom mischievous. Fortunately, the teachers and the curriculum at Windrush kept him engaged academically and helped him channel his energies in positive ways.
As far as math goes, Windrush has a great program. The two math teachers are engaging and have deep math knowledge. They make math fun my daughter reports (I hear there's food involved sometimes to keep math real). There's a math club for kids who are really into it. Across the curriculum there is an emphasis on project-based learning, problem-solving, and critical thinking. All teachers use some form of differentiation in their classroom to support and inspire all students to higher levels of learning.
As private schools go, Windrush is growing in its diversity. (We are an African American family). That diversity -- racial, social, economic -- adds to the richness of the community teachers, students, and parents create. Our family has really enjoyed being part of that community.
I would encourage you to take a tour or attend one of the upcoming middle school information sessions. You can check the website for upcoming dates and more information about the school at www.windrush.org Feel free to email me if you'd like more details of our experiences at Windrush.
Good luck in finding the right place for your son, Zaretta
Is anyone who has a child who is gifted in math pleased with how their school is teaching their child math? What is your school? What are they doing that you like? How old is your child? Has anyone found any non-school programs that they like teaching math to gifted kids? THANKS! Math Mom
It meets every Tuesday evening at the UC/Berkeley Math department, and each 2 hour sessions is run by professional mathematicians - professors, researchers, and grad students. Kids meet others who love math and learn novel mathematics ... and get challenged by novel math problems. Last week was the math of a Rubik's cube; coming up are sessions on geometry and Pascal's triangle.
The best part of the math circle is that nobody will understand everything from a Tuesday night, but everyone comes away excited!
The Berkeley Math Circle is one of the finest in the country; few other communities have a program in the same league. Cliff
In my opinion, there's no other school that can teach math as thoroughly as Berkeley Montessori School (where our kids have been enrolled for the past 6 years). While other schools teach children how to get the right answers (with schools boasting superior math curriculum teaching FASTER ways, often shortcuts, to the right answers), BMS teaches math in a way that gives students a really deep understanding -- the students truly internalize the math concepts (what's behind the concepts, how to expand on them, etc.). The challenging math curriculum and the superior teaching tools and method are the main reasons why we came to BMS (although, now that we're here, we realize that the amazing social curriculum is also a boon).
Another avenue for you.....somewhere in Palo Alto, Johns Hopkins University holds a math summer camp for gifted children. I've never researched it because it's far away and our kids are getting such a rich curriculum at our school. I can find out, though, since our Middle School math teacher has taught there for the past few summers -- please let me know and I can ask her for you.
Good luck, Agnes
Hello, Our son is in a high-ranking public elementary school and his 3rd grade teacher just reconfirmed for us that he is several grades ahead in math and has a great interest in science. (He is GATE identified, but that doesn't mean much - if anything in our school).
We are beginning to wonder what type of middle school we should consider. At this point, we are open to public and private, but not necessarily to homeschooling (I admire homeschoolers....I just don't think it is a lifestyle for us). What school in the east bay would you recommend for a child who loves to learn, particularily math and science? thank you in advance
I would like recommendations for East Bay middle schools that have excellent math and science depts., and offer advanced classes in these areas for gifted children.
We're having a big, deep issue in our household around the study of math and the acquisition of math skills. Our daughter is a high school junior and, due to a series of events beyond her control (moving after fourth grade to small, three room school house, accelerating through one grade mid-year - half of eighth grade then half of ninth - then returning to Bay Area and starting ninth grade over with peers due to move) her math education has been choppy and disrupted to say the least. Also, as it turns out, her way of perceiving math is very conceptual, and she has not been taught in a way that speaks to her learning style. Now she is ''behind'' and her self-esteem is really suffering. She is now in the hands of a great tutor and is working hard to make up for lost time as she prepares for her SATs. I similarly had a tough time in math all the way through, and joke about with her. Her math tutor even expanded on the joke by saying his daughter has a ''math allergy.'' We have said these things to her to make her feel more at ease, less alone and ''stupid.'' On the teen digest recently, I posted a question about how to help her with her deep negativity toward math. Posters resoonded with many thoughtful comments, including that this is my fault for making jokes about it and that I contributed toward her antipathy. When I asked my daughter about this, she basically said, thank god you are not a math genius mom - that would make me feel even more alone. So here's the question: at the end of the day, how much does math matter? I sail through life pretty successfully and I don't even balance my checkbook. Granted, my daughter has a job to do: she needs to do her best on the SAT and she needs to get into a great college and perhaps the world is a different place than when I went to UCLA a hundred or so years ago, and math mastery may be more integral to success. For what it's worth, she excels in the humanities. She is asking this tough question, how important is math, and I am trying to come up with a thoughtful response. Literate, not so numerate
In addition to its use in various applications, mathematics trains the mind in thinking analytically. I would encourage your daughter (and you) not to let go of this strategy for understanding how the world works so quickly. At the very least she should take some kind of Statistics class (without calculus, if necessary), and may be required to do so in college. Mom of a girl math geek
Anyone who is reasonably intelligent can be good at math. It might not come easily, but these are skills that can be learned like any other. And the fact that you AREN'T good at it is all the more reason not to give up on it. The last thing you want to teach your daughter is that she should only do things that come easily to her.
In fact, I think that's the strongest argument of all for math in your case. Even if she never needs math per se, learning how to master something that is difficult for her is a skill that is absolutely critical to her success in life.
PLEASE help your daughter. If she is good in humanities, she can be good in math. It sounds like she is asking for permission to close this door of opportunity for herself. Please keep it open for her.
You say she has a good conceptual understanding of math. I think math is important in a few areas: 1) Finances. You don't have to be all that great at math to do well with your finances. Dave Ramsey's book ''the Total Money Makeover'' will teach you all you ever needed to know about how to manage money without being good or even decent at math. 2) Career. If your daughter has any desire to enter a field of technology or science-related, math is going to be essential. She's going to have to have a basic understanding of it in some sense. For me, I was a communication major in college, then ended up doing technical writing, which turns out you need to have a good basic understanding of math in order to figure out what you are writing about.
Now, having said that, how you learn and prove you know math in high school in college is much different from the real world. In business and jobs, there are a lot of different kind of learners and if she understands math with a different kind of learning style than the one in school, she will have opportunities to explore that, as needed, for her job. For me, engineers go through very basic diagrams and analogies to teach me concepts I've either long forgotten, never learned, or never understood. And they patiently try and try, while I ask questions, until I understand just enough to get by. So, if she is good at humanities, decent at math, can ask a lot of questions, and is aware of her learning style, she probably will have no trouble succeeding in life. But, she's maybe going to have to learn how to adapt to others and explain how she needs to be taught (including possibly in college) in order to get there. Not a mathlete, but getting by just fine
I read your post then picked up the paper and saw this article about benefits of particular engineering / business majors. These workers can earn up to 50% more than those with humanities degrees: http://www.sfgate.com/cgi-bin/article.cgi?f=/c/a/2011/05/24/MNDF1JK147.DTL
So this reminded me of a book ''What I Wish I Knew When I Was 20'' by Seelig. I have not read it but I have heard Seelig speak and I was impressed - and it might be a good level / perspective for a teenager.
I'll also offer this extended observation. Part 1 - I've worked pretty heavily in the engineering / analysis / business fields for almost 15 years. I've seen a fair share of ok smart, only-somewhat-engaged engineers, accountants, analysts who I suspect make a lot more than awesome smart, fun, on-top-of-it administrative assistants. Breaks my heart, really.
Part 2 - It's important to look at the full trajectory. There are those who work as an engineer / analyst / etc for a couple years, then move into business or management. I think it opens a lot of doors, and it is not about a whole lifetime of doing ''x''. It always changes, particularly in today's world. (sales, product management, software management, etc.)
Another piece I heard on radio talked a study result: those who graduate during a recession with certain humanities degrees *never* catch up to peers who graduate during a boom time. Their lives are on a completely different trajectory. (For scientists or engineers, it might take 10 years or something like that to catch up, wage-wise)
People can be successful with or without the math, right? tons of success stories. I think life is more risky for those who don't engage on the math/analytical side though. I heard or read a piece once that talked about how the US is the only country that makes fun of those who are good at math and almost encourages people to 'give up' on the math. I think the jokes on those who believe it. Good for you to get the tutor. Hope it works out well! a believer in the opportunities of math
It's not the particular math subject itself that's important (algebra, trig, calculus or whatever else), it's the way that studying math teaches you to think. When you study math seriously and with dedication you begin to develop the skill of thinking analytically. Learning how to examine an issue from this perspective is an enormous asset in any field. My husband is a bioengineering PhD who has never taken a business class in his life, but he is currently being recruited by a major consulting firm because they are looking for people that can think analytically and problem solve. They recruit from the maths and sciences for this reason.
Math is really important, don't let your daughter miss out on this opportunity. I also agree that making jokes about it is only going to make things worse. Joking about it sends the message that it's not important. Just my opinion.
How important is literature? Music? Art? Most of us make it through an average day without producing any of these, and without truly needing to consume them, either. Presumably you wouldn't accept a tutor who used the phrase ''literature allergy'' or a parent who brags about sailing through life without reading. But you accept ignorance of the fields that make the modern world go round (and unlock how and why the actual world, you know, goes around)?
You simply cannot get more than a cursory appreciation for any sciences without a thorough grounding in mathematics. There are few serious challenges facing mankind whose cause or solution isn't intimately tied to scientific issues. These days, not being able to understand these things deeply pretty much robs you of being a fully informed and responsible citizen. People who do you grievous harm every day are counting (no pun intended) on your remaining scientifically and mathematically ignorant.
Mathematics (real mathematics, not mechanical 1+1 arithmetic -- having a similar distinction as literature versus basic literacy) is beautiful, enriching, one of the most uniquely human endeavours and one of the few that completely transcends historical and cultural boundaries.
If you're not numerate, you're not fully literate, either. Literate and numerate
One thing that I always noticed though, and you alluded to in your post...math is power. The most lucrative, most solid careers are overwhelmingly math-based. Now, money isn't everything, and there are certainly a few careers where one can be successful (whether personally or conventionally) that don't involve math. But there aren't many. I realized at some point that I was so ''bad'' at anything quantitative because I was afraid of it. I consciously let explanations of math concepts float over my head, refusing to open my brain to the possibility that I could actually be competent in the subject.
Then, I realized that if I wanted the career I'd planned (management consulting), then I'd have to master the thing I was most afraid of. Now I'm considering getting another master's degree - this time in finance.
Your daughter needs to take a good hard look at what she wants to do as far as a career (yes, she's young, but it's not too early to start thinking of these things). For the vast majority of people just saying ''the humanities'' isn't going to cut it (although there is tremendous evidence that a liberal arts education is second to none in helping critical thinking skills). Maybe what she needs is to see the potential application of math before making a decision that it's not for her. If her dream has zero math involved, then that's good too - she'll know she doesn't have to worry about it! Embraced My Inner Math Geek
If one's goal in going to college is to be prepared for a specific job, one can go to vocational school! The purpose of an Ivy League education is to receive first rate, well rounded exposure to understanding the world we live in, and to develop an analytical and intellectually expansive mind. One learns to communicate and articulate one's thoughts, and certainly there is no "guarantee" of a job, but one's chances are vastly improved with a high quality education. A "prestigious" school does not just boast exceptional professors, but the quality of a greater percentage of students is exceptional as well. Ivy League students are highly vetted and the experience of meeting one's fellow students, making contacts that can last a lifetime, and learning from one's peers is that much more rewarding. Lastly, I will say, many top companies and institutions do hire from the Ivy League (they have college recruiting programs specifically for this), and often not in the exact field the student has majored in because they know that a well conditioned, well-trained mind is flexible, adaptable, analytical, can learn quickly and is an asset to the organization.
In conclusion I would say, math is very important---and tutoring for the SAT's might be very helpful. And where you go to school is important too. Just look at the percentage of graduates from Ivy League schools who have gone on to make significant contributions to the world. And this is not to say one can not get a good education or become a successful member of society going to a less prestigious school, but it would be very foolish indeed to discount the value of an Ivy League education! Fan of the Exercise of Undertanding
We have an issue that we could really use some help with; it concerns our daughter, who is currently a high school junior. She is a smart cookie, loves the humanities, excels in social sciences, is working on her third language. She has always always had a hard time in math, and due to some moves on our part, and changes in schools at crucial junctures, she's had some big disruptions in her study of math; these disruptions have created setbacks which have compounded her level of frustration and her profound sense of inadaquacy. She's never had a math class she especially liked, and in her freshman year in a local public school, she actually had a geometry teacher who barely spoke English, and that year did our daughter a great disservice, from which she has barely recovered. She is now working with an SAT tutor, but she is far behind her peers and so discouraged. We had hoped to do some cognitive testing, but it was too expensive and we weren't able to do the whole public school testing route to find out if she had some real learning differences in the subject. We joke that she has a math allergy (runs in the family on my side). But here with are, with the SAT's looming, and college applications on the immediate horizon, and the stakes are high, and she is so negative about her performance and so discouraged in this subject area, I just have no idea what to do for her. How important is this? What can I do to boost her self-esteem? I've been in touch of course with her teacher but he's not a lot of help and she feels he doesn't like her - I think he's just not sure how to reach her and doesn't put out a lot of effort to do so. She does really well on the Language Arts parts of the standardized tests she taken but dismally on the math. Now we're thinking about looking at colleges that don't give a lot of weight to SAT scores. But how limiting is that?? So we're in a bad, sad, upset place and the stakes are looking pretty high here. What to do, how can I help? Where to go from here? need to make some lemonade out of lemons here
And that, Ms. Ride stated, is a major reason why girls drop out of math in middle school when they did just fine in grade school.
Now, if your daughter was a concert pianist would you say ''I don't know where she gets that music talent - nobody in my family likes it''? Or would you curb such an absurd impulse because you know it would make you and her look like idiots?
Well, you've created a perfect case of math antipathy - dissing the skill while demanding she conquer it. And like any sensible kid, she's taken your excuses and used them to avoid facing the hard work required to master this field. Simply put, you created the problem because you illustrated perfectly that there was no need for math skills in your family. You made your bed of nails and now you don't like it.
OK - you screwed up. And now those nails are biting, because the SAT requires a decent math score to get into any reasonable university and she's got 5-6 years of math avoidance. Now you have to break the habit fast - and you're still acting badly: ''We joke that she has a math allergy (runs in the family on my side).''
Jokes don't encourage people to try harder. Stop it.
Math builds upon itself, so missing core elements creates great difficulty. The only course of action is simple: dedication to review over a period of a few years with a tutor. Only time and dedication will reveal what math essentials she's not getting, and only time and dedication will allow her to gain confidence in math.
Confidence is not ''given'' by mom. And she can't evade math proficiency in a global economy no matter *what* her future major. At Stanford Law School I reviewed work on statistical models using Bayesian filtering of discrimination incidents. In history the cutting-edge work deals with data crunching to reveal trends. Literature, political science, economics, urban planning - all quantitative.
Math skills matter. Keep with the tutor and give it the time it deserves - even if she delays going to college for a year or so. Better she goes to college confident of her abilities instead of habituated to excuses for hard work. Good Luck
That comment was spot on. No one, I mean no one would make jokes about being illiterate, but seemingly it is okay to be innumerate. Well, no it is not okay in today's world(and this is a life/job issue not an SAT issue.)
Basically, your daughter has to work hard to correct the problem. You would not be as relaxed about this if she could not read! Nor would you have let this fester for years. Now, this is not to say that you don't care. Obviously you care enough to post a question.
This is not to say that she should be subjected to drill and kill nor that it will be easy, but she and you need to work at fixing the problem, and yes it is a problem.
One thing I highly, highly recommend is using the Khanacademy.org's website. It's free; it's unbelievably good. Sign up on the practice tab and your daughter can start on it as far back as she needs to go, i.e. she can start at basic arithmetic and go through calculus. You can monitor her progress and achievement is reinforced. It is simply the best free tutoring on the web.
And by the way I used to be an English teacher, but I know how important math is! nr
I would be happier if he did better at math, but it just isn't meant to be, and it would make all of us miserable if we expected him to excel at it. What's important is that he (like your daughter) has academic passions that he can pursue in college. Carrie
Our student would like to drop a pre-cal course because of bad grades and what it might do to their GPA. That means graduating with 3 math courses in HS. We're already omitting UC schools from consideration, but what does it do for their chances of being admitted to a CSU? Assume a GPA of under 3 and an SAT under 1000. frustrated parent
As for college prospects, he didn't apply to UC or CSU, but he's already been accepted to two excellent small liberal arts colleges and got a nice scholarship at one of them. He still has several more to hear from. (A friend of his has a less-than-3.0 GPA and got into Humboldt, so it is possible.) I am very happy that we released him from his math misery. It's Hard To Be Good at Everything
My high school junior son has been a struggling B-/C+ student in math throughout middle and high school, and is campaigning not to take pre-calc in his senior year. I understand this desire, but I don't want to harm his chances for getting into a good college if he skips a final year of math. One possibility that has been raised is taking statistics, which seems more appealing. He's passionate about history, so he can see how statistics would be applicable to his intended field of study, unlike pre-calc. His small high school does not offer statistics, however. I have only been able to find AP Statistics online, and am worried that it might be too difficult. Does anyone have any advice or experience with online courses, statistics in particular?
The key determiners to getting into the college of his choice are good SAT (and SAT2 in some cases), GPA / coursework, and activities. If he did well (600+) on the math portion of the SAT and very well (650+) on the reading / essay portion, has taken and done well in courses like AP English with a good overall GPA, and he's done some extracurricular activities (debate?, speech?, community service? leadership?), he should talk to an adviser he trusts to guide him to apply to colleges which will suit his interests and will see him as an asset. He'll do fine, so stop worrying.
If he should decide later that his major requires statistics and he also needs precalc, most colleges nowadays offer precalc as well (even Berkeley does), or he can take it at a community college. My son had to satisfy the UC language req and decided to do it at DeAnza College over summer instead of UCLA because it was more economic and allowed him to focus on his major at UCLA. There are many options at this stage, but the best advice I ever heard from a councilor was ''Trust your kid - they're moving into adulthood and need to make their own decisions''. Good luck. Lynne
However, here's something to consider. I have run into many students who were social science and statistics majors but who had only taken a course in non-calculus-based statistics. They thought that they could get away with it because statistics and calculus are two different subjects. However, you need calculus to do statistics.
Your son might be putting the cart before the horse here. IMHO, he should be taking pre-calculus or at least know that he will have to take it very soon. Otherwise, his effort may be wasted. There are No Shortcuts
My daughter is a sophomore in high school and was accelerated in middle school such that she is now taking precalculus this year. She is very bright but will be going a liberal arts direction in college (she is an excellent writer and has considered creative writing). Math is not a strong point for her and while she is quite competent, she struggles a bit to keep up. I have heard varying reports from high school counselors that to get into the top UC schools, students must take calculus. I would like to know if this is true even if the student isn't likely to go into math/science as a major? She's having such a hard time this year and I hate to put so much pressure on her to perform decently so it doesn't hurt her GPA. Should she take calculus next year? Are there any other options? Jennifer
I wanted my daughter to take AP stats in 12th grade but she decided not to at the last minute. She's taking all classes that she wants and is doing really well. Point in case.
When your daughter's a senior, I can highly recommend her taking the ''writing short stories'' class. If she likes creative writing this is IT! Actually, this is probably the ONLY class my daughter took in 4 years where she did any creative writing. anon
Hello all. I am wondering if my HS junior can possibly get into a 4 year college (probably a state college due to finances) without taking all the maths required (geometry and algebra 2). She has a difficult time with math, even with tutoring. She has A's and B's in all her other classes. Does she have to go thru the community college route, I assume take the 2 maths there, and then transfer? Also, is DVC the best 2 year college around, as I've been hearing or are the other junior colleges just as good (and closer to home). Thanks. mom of junior high schooler
My son will be a freshman this fall. He current takes Algebra 1 now. I would like him who complete Geometry this summer and take Algebra 2 in the 9th grade. I need some advices. Middleschool Parent
Hello - my 5th grader is one of a cohort of kids (10 or more) who'll all head to Longfellow in the fall, which I'm quite satisfied about in general. I'm happy that Longfellow has wonderful math teachers. But I understand that a significant percentage of their students enter in 6th grade being 'below proficient' in math. Consequently, much effort goes towards helping those kids gain proficiency in 6th grade. Meanwhile, this cohort of kids including my child have come from a teaching experience where their teacher worked diligently to challenge them in math, and now most of them are well beyond proficient. Does anyone have any ideas about how to keep this cohort challenged when it comes to math? (They're all doing Spanish immersion so they're all in the same class.) I'm quite willing to hear about afterschool/evening options for math challenges. Hire a tutor to work with any of these kids in afterschool sessions off-campus? Other ideas? I don't particularly want to force the school to make special accommodations because 1) I do believe their focus should be on bringing kids up to proficiency, and 2)these requests to the school only result in school staff thinking you're 'entitled'. Any ideas out there? math curious
Here's the general web site: http://www.msri.org/web/msri/static-pages/-/node/5
The Oakland/Eastbay math circle meets at Laney college and is pretty easy to take a group of students to on an informal basis. When I attended most of the teachers leading the activities were Cal Mathematicians/Grad students leading activities on topics related to their research. The wonderful thing about this style of teaching is it starts off with easy access points and then goes into an understanding of deeper mathematics.
Berkeley Math Circle -- which is more of an Eastern-European style circle and pretty competitive. http://mathcircle.berkeley.edu/
My understanding is that if you want to set up a math club/circle the people at MSRI/Math Circles will help you. What you would need is a sponsoring teacher and a group of parents to organize/supervise in the afternoons. This might be a second step after attending another circle for a year or so to understand how they are organized.
Another possibilitity is The Julia Robinson Math fair at Stanford is coming up in May. The festivals occur at different locations several times a year (Cal is in January.) These are half day math festivals where students can try many different problems and experience math in an exciting environment. http://www.msri.org/web/msri/static-pages/-/node/210
If the children you want to encourage to think more about math are girls there is an ''Expanding your Horizons'' conference at Mills College where students/grad students from Mills and Cal present math and science workshops for middle-school and high school students.
Math Paths is a sleep-away math camp aimed at providing support and education for future mathematicians. It starts at 6th grade. It's aimed at students who love solving problems and are interested in mathematics competitions.
Hi: I am looking for a (pre algebra) math workbook for my daughter who will be entering 8th grade in the fall. Have you found any math workbooks to be particularly helpful? Any you particularly like (or dislike?) Do you know a local place where one can buy them? Thanks LR
There is also the Dummies book: http://www.amazon.com/Basic-Math-Pre-Algebra-Workbook-Dummies/dp/0470288175/ref=sr_1_2?s=books&ie=UTF8&qid=1312077472&sr=1-2 that you should be able to find locally.
We are using a Dummies workbook for review of Geometry before school starts in a few weeks. -Math Review ever summer!
My daughter is starting middle school this fall. She's always been an excellent student, with particular strengths in language and art. However, her math skills are good - not extraordinary as are some of her other skills, but more than adequate. However, a couple of weeks ago she said to me ''I'm not that good at math.'' I know this isn't true, and that she is comparing her math skills to her reading and writing, but I'm concerned that at 11 years old she's at an age where self-doubt in girls about math abilities is reinforced, even with teachers who make an effort not to do this. I'm searching for resources that will help shore up her confidence about math. She doesn't need a tutor, just to know that she CAN do this and her skills and abilities are fine. I looked at the books by Danica McKellar, but they are designed to make math fun for girls who are into celebrities, hair and makeup, etc. - things in which my daughter has no interest. Does anyone know of other ways to build confidence in this area? We live in San Francisco but are usually in Berkeley on the weekends. Don't need another mathphobe
One other thought; almost all of my top math students say they are not good at math (in spite of their A's). I ask them why they think that when it is so obviously not true and they always say, ''Because it's so hard.'' That's because math IS hard. It is not some candy- ass subject like English or history where the biggest challenge is to try to stay awake as you read about the dusty battles of Napolean. In math you must USE your brain and actually THINK. And this is a hard thing to do. You can almost feel your brain in pain as you try to work through a problem. So tell her, just because math seem hard, doesn't mean at all that she is not good at math, it just means that even for smart people, math is hard.
PS I was not very confident in math when I was young and now I see that part of it was because I didn't have any guidance as to how to LOOK at it. I'm a great PROBLEM-SOLVER, love puzzles and playing pool, and that's what's it partly about, but no one one really broke it down that way. I also had an awful foundation...'nuf said...
Good luck! anon
Perhaps she would like to have a more instant recall of basic math facts (i.e., times tables). Ask her if she wants help with that, then you two can work together on quizing each other this summer. Knowing the times tables inside and out can make the rest of math much less stressful, at her grade level.
Consider what tyope of math she did this last year in school. Many folks are better at spacial stuff than they are at equations (or the other way around). If this is the case, you can encourage her and remind her that everyone has strengths, and each of us has to work hard on something.
The last bit: if an honors math track is offered where she goes to middle school, ask her if she is interested, and if she isn't, don't push her into it. It is likely best, in my opinion, that she excell in the regluar class than bomb in an excellerated class. Her near- term success, may set the stage for future growth i skills, and at least, won't squash her self-image more. Mom
Marilyn Burns: ''Math for Smarty Pants,'' and a number of other recreational math books.
Theoni Pappas: Books for kids (and adults) about math topics and history.
You could ask Diesel to order the books for you, or go up to Lawrence Hall of Science and see if they are in their bookstore (the best bookstore in the east bay for math/science books for kids and teachers.)
You could also check out some of the math games (SET is my favorite; or Mastermind); and ''Family Math'' a book that LHS puts out with games for families to play. math teacher
My daughter has just started the 7th grade, and already she is complaining about her math class. (Pre-Algebra) My husband and I have tried many different tutors in the past 3 years, and they have helped to a degree. However now, Christina wont even try or attempt to work on math. She is now telling me that ''she isn't smart enough'' to do math, and that she ''wont need it anyway.'' I have tried reassuring her to no avail. My husband and I really don't know what to do about this. Any advice out there?
I would highly recommend finding a skilled teacher/learning specialist/ed therapist who is also well versed in Making Math Real. This is an incredible approach to teaching math and can be used in instruction to support any textbook or math program. Learning Specialists or Ed. Therapists who use MMR will do direct instruction, help students form a picture and link this picture to the math procedures.
makingmathreal.org will give you more info. about their program, but they won't recommend people. Lots say they have been ''trained'' - which might mean they have taken a class or two. But it's more the teaching not the program... you need to find a highly skilled teacher who also uses MMR. Best is to hook up with someone who has also been an instructor (or second best an intern) in their summer camp program. Learning specialists and teachers who have been trained in special education also have been trained to work with lots of different learning styles and can focus in on your child's specific processes of learning. MMR instructor
We're looking for a good math enrichment website that is free or by subscription that our 6th grader could use for math enrichment (not remedial - he's in advanced math now). We don't want to enroll him in a formal program, but want a website (preferably interactive) we can use when he is home from school or bored. Preferably pre-algebra, intro algebra, or applying math that he would be learning in the 6th grade. Nancy
I've also heard good things about the Berkeley Math Circle, and the Oakland Math Circle, but haven't tried them yet with my sixth grader. Carol
I'm seeking math options for a middle schooler. He is currently a 7th grader getting an A+ in 8th grade algebra at his private middle school. Next year he will stay at the same school for 8th grade, but his teacher has stated that his math class will consist entirely of independent study, with at most 1 class period/week with her. Aside from the fact that I don't want to pay tuition for my son to teach himself math, my son is not happy about the idea of independent study. It was offered this year and he declined. I also think he will rarely get his 1 class period/week with the teacher. I'm pursuing Honors Geometry at Berkeley High as a possibility and was wondering if there were any other options for him? Any ideas? Thank you
My 7th grader is bored and frustrated with his 7th grade math class. The teacher allows him to work independently with another child because they have tested out of the regular curriculum. But he says this just means that they get to work ahead in the book by themselves. He came home saying, ''Mom, I don't like to teach myself math.'' Any ideas or recommendations of classes or tutors? I should deal with the school, but I think that is unlikely to get me any results in time to save his love for math. I have looked through the list of tutors on the web-site, but I'm not sure that a traditional tutor is what he needs. Thanks for any suggestions.
My daughter is doing very well in 6th grade math and would like to move on to algebra rather than taking 7th grade math next year. Have other parents had this experience? How did it work out?
1) At first, she had to do a lot of catching up, because every one else had pre-Algebra and she hadn't - learning new terminology and such. That settled down after a while.
2) At the end of the year, she earned a B, which did not qualify her to take Geometry at Berkeley High. (She needed an A.) In order to qualify, she had to take a scheduled test at Berkeley High, which she did well on, so she got to take Geometry.
The problem is, that if she had not passed the test, we were told she would have to take Algebra all over again in eighth grade, because Math is required and King doesn't have anything more advanced to offer. That would have been embarrassing and disappointing for my daughter, and I fear it would have turned her off to math. I question whether it's a good idea to take Algebra in 7th grade if you run the risk of doing well and still having to take the entire year over again. Beverly
My daughter ''hates'' math. She is not bad at it, but regularly complains that it is boring and too easy. I know this is not uncommon for girls but I am so disheartened to see this happening at such a young age, especially as a female computer scientist myself.
I have talked to the principal several times about the issue, and even had her moved into another class to see if that helped. The new teacher seems to have made it only slightly more bearable for her. I should add that she LOVES this teacher, who she also has for science class, so I do not believe there is a personality conflict going on.
She is really an artist at heart with very strong verbal, visual, and creative skills. It has occurred to me that the real problem is that the Saxon math curriculum just doesn't engage her. I believe the curriculum is great in general - my son is excelling in the program - but no one program works for every child, and this is the only curriculum offered at their school.
What can I do to show her that math is fun, that she can feel confident about being good at it, and that it is not a class to dread? Have any of you been where I am and managed to raise a daughter with a positive attitude towards math? Help please
My son is in the 2nd grade and loves advanced board games, math, engineering, legos, reading, etc. Overall, he's much more advanced academically than socially. I'd love to hear ideas of things to do with him where he can feel challenged with the above interests. He's been asking about math tournaments or board game venues, etc. He does chess, and I'd like to see what else is out there. Also, if anyone has a similar son around 7.5 years old who would like to touch bases then please do. mary
The first is a game with a bunch of cars and trucks on a grid and you have to use logic to get them out. There are easy to expert set ups; my 4-year old can do through about #15, my husband (PhD in math) got stumped after spending about 30 minutes on one of the expert levels.
Set is an amazing card game. You have 81 cards which has 1, 2, or 3 figures; the figures can be 1 of 3 shapes; the shapes can have one of 3 fillings; the shapes can be 1 of 3 colors. Lay out 12 cards and work to find sets of 3 where everything is either all the same or all different (so all 3 cards have red ovals with stripes, and one card has 1, one card has 2 and one card has 3 is a set but if there were 2 cards with 2 and 1 card with 3 that would not be a set).
The last can be ordered from www.jollygames.com. Slightly cheesey website but I've ordered from him and gotten the games fast. You lay out a grid of numbers and operators and then try to find the ''goal number'' using the numbers and operators you laid out.
There are math circles for elementary aged kids. My kid did the Berkeley circle last year which wasn't great for him (too much talking by the adults) though it may be different this year and it might be different for a kid who is older than mine was. There are other math circles in the Bay Area, the best one is probably at Nueva School but they only have 4 a year and they just had their last one. I know there are also math circles in Marin and SF.
There are math festivals (the Julia Robinson Math Festival was just held at Berkeley at the end of January and there is another at the beginning of May at Stanford), though they are typically for older kids. I know the Julia Robinson festival shoots for grades 6-12 though some younger kids do go. My guess is 2nd grade is a little too young but it is something to keep on your radar for when he is older.
I've heard good things (but never participated in or been to) the Maker Faire where people make random stuff and bring it in to show it off. It is at the end of May (http://makerfaire.com/bayarea/2011/). Maybe bring him this year and he could build something for next year?
I know there are a couple of rocket-building groups around, try Marin and Walnut Creek maybe. (Sorry, know very little about them.) Anon
My second-grader is jealous of the third-graders that he sees with math books, and has asked me if he can have one of his own. He's no genius, but is characterized as ''having strong math skills,'' and entertains himself by making up his own (simple) math problems and solving them. Do people have ideas of something mathbook-like that would be fun for him? Maybe something to stretch him a little but still feel like play? And a good place to buy something like this? Many thanks! Anon
A great place to explore math is Lawrence Hall of Science. They have tons of math and logic games out all the time. My son can go there and play those giant-sized games for hours. A great holiday gift would be a membership to LHS!
I recently read their book _Spark Your Child's Success In Math And Science_ which seemed more general than specific to me. But they have many resources listed in the back, including their Family Math products and the parent resource site http://www.lhsparent.org. I like to look at the selections in their store as well as the Exploratorium's store.
I am math and science challenged, despite my father being an astrophysicist. I'm hoping my 3 boys will exceed my capabilities! Math-aspiring
My soon-to-be third grader has never memorized her addition/subtraction tables. Multiplication was introduced last year and she hasn't memorized those tables, either. She counts on her fingers, usually getting correct answers. When I asked her teacher for advice, I was told my daughter is doing fine (so far she's been getting top grades in math) and will memorize math facts sometime on her own since she's bright and memorizes easily. My daughter says memorizing math tables is boring. I donbMarch 1998t think waiting for sometime is going to work.
Can anyone recommend ways to help a child memorize addition/subtraction/ multiplication (and eventually division) tables? I've heard of a device called the Flashmaster (www.flashmaster.com). Has anybody had experience with this? Is it worth buying? I know there's a Korean or Chinese method for using your fingers to quickly calculate but I can't remember how it works. Could that be a better way to help her out since she already uses her fingers? Does anyone know what this way of finger calculating is called and how it works?
I think you are right to encourage your daughter to memorize her math facts. And, your daughter is also ''right'' that it can be boring. Unfortunately, memorizing things is part of the ''real world.'' She will need to develop the discipline to do it. Memorizing math facts also makes it easier for students to learn more complex math such as measurement and problem-solving.
The Asian finger-counting is called chismbop or chisanbop. It is fun and I could show your family how to do it. It won't replace the need to memorize math facts; but, it is a fun way for kids to check their own work.
I'd recommend decorating some walls with big multiplication charts, organizing a game of ''math baseball,'' playing with concentration style card games with flash cards, etc. There are also free web-based games and customized worksheets on the web
Depending on what interests and motivates your daughter, you could also set up a contest or reward. There's no need to buy fancy toys or tools if you have the time to create activities on your own. If you are pressed for time (like most of us), I recommend LeapFrog's product line. Hope this helps. Debbie
he took a remedial course in the summer after 6th grade and memorized his multiplication...but in the end, i found out it was his addition/subtraction that still holds him back (will be a freshman in high school this year).
Just sharing my experience because the consequences of not memorizing them are huge! all his math is delayed because you use addition/subtraction in most every math problem and it takes him so much longer and he makes so many simple errors.
For her age, i do think counting on fingers is normal so it doesn't sound like you have much to worry about. But take it in steps, if they are learning multiplication in 3rd grade, make sure she's already memorized addition/subtraction. then for 4th grade, work on multiplication tables...the more they learn in math, the more they will need the basic skills and the longer it will take them to learn if they didn't memorize them already.
Given that, if i had a time machine, i'd put her/him in a program like Kumon, which is very simple, organized way to memorize basic math skills, but also does it using timers to get them to do it pretty quickly and get your kid on it regularly. just like chores, even if they don't want to do it (like they'd rather have ice cream than broccoli), it's something they have to do, and is relatively painless if your child is doing fine in school anyway. even something like 15 minutes every day, have them write down one set of addition (have her add all numbers 0-9 for #1...) and keep it going and make it rewarding.
good luck! whatever you do, don't leave it up to the school. i know some teachers often say not to worry because there are kids doing worse than yours, but that is not the standard you should hold your own kid to! math counts
Most of memorizing math facts for kids without learning differences is related to overpractice - practicing often enough so that memorization is automatic. Games make it easier to have that practice. There is a game "Equate" which is like scrabble but with equations instead of words.
There are a number of tips on memorizing facts on the Math Forum (at Drexel) website. Look at the Elementary Archive. http://mathforum.org/library/drmath/sets/elem_addition.html
My kid loves math and is doing above her grade level. She is in the second grade. How should I support this love, and supplement what she's doing?
I've already talked with the teacher and in-class possibilities seem limited. We play games from the Family Math book, and I know about ATDP. Has anyone done the Lawrence Hall of Science classes? Do math tutors (for encouragement, not remedial) help? I don't want to overcommit her afterschool/weekend time because I think kids should have time to ''be kids'' - but - it's not happening in her school. A common dilemma, it seems.
Thanks for your thoughts (general and specific). Any advice helpful (except for moving out of state, lol!) anon
We have been looking at K classes for our daughter for next year, and we are curious about the "patterning" projects we've seen displayed on the walls of several K and 1st-grade classrooms. The "patterns" involve colored strips of construction paper that are woven together, producing checkerboard formations, or sometimes children appear to be transferring a letter "pattern" (like ABACABA) to a corresponding color pattern (e.g., red,blue,red,yellow,red,blue,red). I have asked a few teachers what "pattern work" is for, and all we have been told is that it enables the learning of math concepts. Could anyone provide more explanation of "pattern work" and its use in math learning? We are really curious; neither of us learned math in this way. It seems like an awfully abstract leap for Kindergarteners. Anonymous
When they're transferring a pattern from one medium (colors) to another (letters), they're making the link between concrete and symbolic thought. Then perhaps the teacher will guide them to translate from the symbolic letters to another patterning medium -- perhaps shapes. So they start to see how symbolic representations can be useful.
One of my favorite "patterns" is that of Fibonnacci (sp?) numbers -- 1,1,2,3,5,8,13,21,34,55,89, etc. Can you figure out the "rule" for the pattern? The cool thing is that fibonnacci numbers are ubiquitous in nature -- the number of petals on a flower is always a fibonnacci number. Follow the spiral of a pine cone, and count the notches -- it's a fibonnacci number.
When I taught kindergarten, patterns were my favorite part of the math curriculum. -- Sandy
I need advice about resources for mathematically gifted children. My son, age 8, lives and breathes math. At age 4, he could count to 120 by by 6's, convert feet to inches, and determined that my husband, then age 40-1/4, was "37 and 13 quarters." Last week, he calculated that "10 to the google seconds is 10 to the 86th millennia" (or something like that). My husband tells me that is roughly right; I confess it is a bit beyond me. My son is bored silly in school, and I am wondering: (1) what can I legitimately expect (demand?) of the public school district in the way of enrichment; and (2) what resources are there outside the school system for a kid like this? Thanks for any input.
Look at the following web site: http://www.gtworld.org/index.html. They have a mailing list which may be able to give you more details.
The state of California's Education Code is at the web site below. See Chapter 8. http://www.leginfo.ca.gov/.html/edc_table_of_contents.html Good luck.
At what age do kids learn their times tables these days? Or maybe I should ask, at what age should they know them? I know some kids in 5th and 6th grade who have been taught to count on their fingers, and that's where they're still at. I'm shocked, but maybe for no good reason? Carol
I think the educational system here tries to avoid memorization (maybe a little too much in my opinion). I think at some point, the kids just have to use memorization/repetition to memorize things. We try to do alot of math with our son at home. We do try to help him to do some repetition in writing the multiplication tables and continue to review with him. At the same time, we try to let him use it on a daily basis whenever we can such as grocery shopping at the local store, or even when he buys candy with his own money. Diane
I am looking for fun science and math activities and games I can do with my four year old. The advice for helping kids learn language is pretty well advertised (read to them, talk to them, expose them to letters) but I have had a harder time finding suggestions on what to do for math and science. We have always counted together, and I sometimes ask her word questions to get her thinking about addition, and we sometimes play 'store' to play around with addition. But I feel like there has to be more. To be very clear, I am not looking for flash cards or trying to push my daughter or make her childhood overly academic or anything like that. I'm looking for fun things we can do together that will expose her to math and science, and let her explore at her own pace. I'm sure BPN'ers have lots of ideas and I look forward to hearing them! Thanks! Sarah
You said you are doing counting. Modify it a little. Ask them to count from 5 to 9 and skip 8. It presents a challenge! Then go to higher ranges. Then ask them to count down.
In the car we also play games where I give a word, the kids say what letter it begins with. Or I say a letter, and they have to come up with the word. Then give words and ask them what the last letter is (be careful! you have to choose these words carefully for young ones)
Flash cards are not fun, I agree, but there is nothing wrong with giving some flash card like problems but orally. Again, we do this often in the car. You can also try problems that are ''too hard for them'', but talk them through it and help them break it down. 9+5 is really 10+5 then you subtract one. And 10+ 5 is easier.
Ask them how many strawberries they ate. Tell them they had 5 strawberries the first time and 3 the next, so how many strawberries in all?
I'm not sure I'd worry about science lessons per say, but visiting lots of places can lead to explanations that would fall in that category (e.g. golden gate bridge, and read the signs and talk about how much cable is used). There are lots of little things, like your cheerio floats in the bowl, do you think a coin will? Why is there water on the outside of a cold glass? Just help them observe things and find explanations for them. - teaching opportunities everywhere
Other ideas: Counting at the store -- i.e. can you help me put 5 apples in the bag. Sorting/organizing objects -- buttons, cards, coins Counting coins -- Games: Lotto Connect Four Blocks legos Classifying leaves (get a book to help yourself with the vocabulary) Observing bugs, insects, birdsHave Fun! carol
The latter has a listing of many fun games on the first page. You might also investigate the literature on Making Math Real which advocates fun ''real life'' activities for learning math. It was invented by a Berkeley professor. For science, there are these great little cards of science projects that you can find at any good book store. parent of math challenged kid
cook (measuring helps math and the cooking is science) texture experiments (blind fold them and let them put their hands in cooked spaghetti, pudding, dried beans, etc...messy, but fun). make a baking soda volcano collect leaves and bugs grow a plant from seeds study dinosaurs do sun prints teach sorting and patterns: buy some tiny teddy bears from lakeshore learning...they are rainbow colored...have them sort by color, do patterns, count them. put pepper in a bowl of water, drop in a drop of dish detergent. beans in a jar. count them. study them.anon
In addition, I would just recommend getting some toys to help her explore nature such as a net, a bug box or other magnifier. Maybe start a small garden with her. My younger students have always enjoyed the Magic School Bus series (books and videos). They are factual and fun to enjoy together. Good luck. Science Teacher
I would like some opinions from this smart, supportive community on what may sound like an unimportant subject. It's this: should I try to re-learn math?
I'm in my 50s, a successful professional with a masters degree in history, educated and competent in most areas. Yet I can barely manage what would be considered 2nd grade math.
It's not a problem of memorization. For some reason, it's always been impossible to compute figures in my head. Numbers dissolve and switch position and vanish when I try to work the problem. I've often thought this is what dyslexics go through, except these are numbers, not letters.
The most I can multiply is by five and even then only single- digit numbers. Nor can I add numbers in my head beyond two single-digits. On paper, I can manage a little bit; if I have to add a column of four figures I can usually add two numbers at once, then the two results together.
I've lost quite a bit of money over the years when I've had to calculate on the spot, by overpaying or not claiming money to which I'm entitled. For instance, I've had people stop me from leaving a 5 dollar bill on a 7 dollar check because that's what I calculated to be a 20 percent tip.
I'm used to this I guess, and calculators and computers now can help do the work for me, though I get so flustered and embarrassed when I have to think on the spot, as in a line when peope are waiting.
So my question is: should I try to learn math again? And at my age, how? Is it even possible? This feels like a learning disability, but while I've heard of dyslexia being treated, I've never heard of such a program for math. Is there even a point to pursuing this? Learning to read opens up so many wonderful doors of imagination and experience and joy; would I find this in math, or is the subject just as cold and unyielding as I've always felt it to be?
Maybe I should just accept that I'm always going to be as incompetent in this area as ever, and move on.
Sadder but no wiser
While there, I had a retired classmate in your situation. She was re-taking math because it was something she wanted to accomplish in her life. She was slow at understanding the concepts. She utilized the math lab and we studied together and helped each other out in remembering concepts.
I think you should know that math can be fun and maybe you could come to enjoy it (especially if you pursue it in a way that brings you feelings of accomplishment). Talk to the math department at your local JC, and ask who is their most supportive/best math teacher, for someone who needs encouragement and is afraid of ineptitude (which is what it comes down to - your fear that you just can't cut it).
Start with a basic math class, and take it over and over if necessary! Only need to progress to higher levels if that feels good to you. This is about building your own math skill in a meaningful way for yourself - give yourself the time and space to do this. When you do take it, however, you must work your math everyday. The concepts are cumulative and require dedication/consistency.
Also, pick up the book ''The Brain that Changes Itself'' by Norman Doidge and you will see that people with all sorts of similar issues can change their brain to accommodate living in this world. Good luck! Brain Fit
There is also an article you could google too called ''Lockhart's Lament.'' It's a great description of how mind-numbing traditional math instruction can be. Even though I enjoyed math, I really think it is poorly taught in our educational system and I think it strangles all of the joy out of it so that many people freeze at the idea of it.
Anyway, I do think it's worth pursuing and that there may be other ways to look at math that might work better for you. There is also a Teaching Company DVD called the Joy of Thinking that might be worth exploring. These are sometimes available at the library too.
Anyway, I hope you enjoy your explorations. Good luck, and feel free to email me (firstname.lastname@example.org) if you would like to. Take care, Laurel
I try to pick up new skills periodically (I'm learning to program a microcontroller right now - just for kicks).
Here's my method: Post on craigslist (I use ''gigs'' section) as well as at the UC Berkeley career services center for a tutor in the subject you want. Offer to pay $15-25/hour for the tutoring services (if you can afford it). You'll get a lot of responses for math tutoring. Interview some people based on their initial response (just like hiring for a job). Try two or three in an initial lesson and see who you like.
My advice with a tutor is be clear with them upfront how much you can spend each month so they don't expect more time from you than you want. Learning some math should be no harder than learning to play a little piano or guitar.. Enjoy it - math is fascinating. Judiah
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