BARROW HANLEY MEWHINNEY & STRAUSS INC
SC 13G, 1999-02-12
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<PAGE>
 
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                  SCHEDULE 13G

                   Under the Securities Exchange Act of 1934*


                             Tupperware Corporation
- --------------------------------------------------------------------------------
                                (Name of Issuer)


                                  Common Stock
- --------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                    899896104
                        --------------------------------
                                 (CUSIP Number)


                                December 31, 1998
- --------------------------------------------------------------------------------
             (Date of Event Which Requires Filing of this Statement)

Check appropriate box to designate the rule pursuant to which this Schedule is
filed:

         [x] Rule 13d-1(b)

         [_] Rule 13d-1(c)

         [_] Rule 13d-1(d)

*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter
disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).


                                Page 1 of 4 Pages
<PAGE>
 
- -----------------------------
CUSIP No. 899896104                    13G
- -----------------------------



- -------------------------------------------------------------------------------
    1.    NAME OF REPORTING PERSON
          S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

            Barrow, Hanley, Mewhinney & Strauss, Inc.
                       752403190
- -------------------------------------------------------------------------------
                                                      (a)        [_]
    2.    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (See Instructions)

                                                      (b)        [_]
- -------------------------------------------------------------------------------
    3.    SEC USE ONLY

- -------------------------------------------------------------------------------
    4.    CITIZENSHIP OR PLACE OF ORGANIZATION

                   A Nevada corporation
- -------------------------------------------------------------------------------
                               5.    SOLE VOTING POWER
         NUMBER OF                            3,363,300 shares
          SHARES               ------------------------------------------------
       BENEFICIALLY            6.    SHARED VOTING POWER        
         OWNED BY                             700,200 shares    
           EACH                ------------------------------------------------
         REPORTING             7.    SOLE DISPOSITIVE POWER   
          PERSON                              4,063,500 shares
           WITH                ------------------------------------------------
                               8.    SHARED DISPOSITIVE POWER     
                                              ----                
- -------------------------------------------------------------------------------
    9.  AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
                                       4,063,500 shares
- -------------------------------------------------------------------------------
   10.  CHECK IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES
                CERTAIN SHARES (See Instructions)
- -------------------------------------------------------------------------------
   11.  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)           [_]
                                        7.0%
- -------------------------------------------------------------------------------
   12. TYPE OF REPORTING PERSON (See Instructions)
                                       IA
- --------------------------------------------------------------------------------


                                Page 2 of 4 Pages
<PAGE>
 
SCHEDULE 13G
- ------------

Item 1(a)   Name of Issuer:
                    Tupperware Corporation

     1(b)   Address of Issuer's Principal Executive Offices:
                    P.O. Box 2353
                    Orlando, FL  32802

Item 2(a)   Name of Person Filing:
                       Barrow, Hanley, Mewhinney & Strauss, Inc.

     2(b)           Address of Principal Business Office or, if none, Residence:
                    One McKinney Plaza 3232 McKinney Avenue, 15th Floor Dallas,
                    TX 75204-2429

     2(c)   Citizenship:
                    A Nevada corporation

     2(d)   Title of Class of Securities:
                    Common Stock

     2(e)   CUSIP Number:
                    899896104

Item        3 If this statement is filed pursuant to Rules 13d-1(b), or
            13d-2(b): The reporting person is an Investment Adviser registered
            under Section 203 of the Investment Advisers Act of 1940.

Item 4      Ownership:

     4(a)   Amount beneficially owned:
                    4,063,500 shares

     4(b)   Percent of Class:
                    7.0%

     4(c)   Number of shares as to which such person has:

            (i)     Sole power to vote or to direct the vote:
                            3,363,300 shares



                               Page 3 of 4 Pages
<PAGE>
 
           (ii)     Shared power to vote or to direct the vote: 
                            700,200 shares

           (iii)    Sole power to dispose or to direct the disposition of: 
                            4,063,500 shares

           (iv)     Shared power to dispose or to direct the disposition of:
                            --

Item 5     Ownership of Five Percent or Less of a Class:
                    Not Applicable.

Item 6     Ownership of More than Five Percent on Behalf of Another Person:

                    The right to receive or the power to direct the receipt of
                    dividends from, or the proceeds from the sale of, the common
                    stock is held by certain clients of the reporting person,
                    none of which has such right or power with respect to five
                    percent or more of the common stock.

Item 7              Identification and Classification of the Subsidiary
                    which Acquired the Security Being Reported on by the Parent
                    Holding Company:

                    Not Applicable.

Item 8     Identification and Classification of Members of the Group:
                    Not Applicable.

Item 9     Notice of Dissolution of Group:
                    Not Applicable.

Item 10    Certification:

           By signing below the undersigned certifies that, to the best of its
           knowledge and belief, the securities referred to above were acquired
           in the ordinary course of business and were not acquired for the
           purpose of and do not have the effect of changing or influencing the
           control of the issuer of such securities and were not acquired in
           connection with or as a participant in any transaction having such
           purpose or effect.

After reasonable inquiry and to the best of its knowledge and belief, the
undersigned certifies that the information set forth in this statement is true,
complete and correct.

                                  BARROW, HANLEY, MEWHINNEY &
                                  STRAUSS, INC.


                                  By: /s/ Bryant M. Hanley, Jr.
                                      Name: Bryant M. Hanley, Jr.
                                      Title:   President

February 11, 1999



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